single phase convective heat transfer with nanofluids: an...
TRANSCRIPT
S ingle Phase Convect ive Heat Transfer wi th Nanof lu ids : An
Exper imental Approach
Doctoral Thesis
By
Ehsan Bitaraf Haghighi
Division of Applied Thermodynamics and Refrigeration Department of Energy Technology
Royal Institute of Technology
Stockholm, Sweden 2015
Trita REFR Report 15/01 ISSN 1102-0245 ISRN KTH/REFR/15/01-SE ISBN 978-91-7595-414-1 © Ehsan Bitaraf Haghighi 2015
ii
iii
Abstract
Nanofluids (NFs) are engineered colloids of nanoparticles (NPs) dispersed homogenously within base fluids (BFs). Due to the presence of NPs, the thermophysical and transport properties of BFs are subject to change. Existing technologies for cooling electronics seem to be insufficient and NFs, as reported in several studies, might offer a better alternative to liquid cooling. The main purpose of this study, by choosing a critical approach to existing knowledge in the literature, is to investigate experimentally the potential for replacing BFs with NFs in single–phase flow. Several NFs (mainly water based metal oxide NFs) were synthesised, and different experiments (including thermal conductivity, viscosity, heat transfer coefficient, and shelf stability) were performed.
The thermal conductivity and the viscosity of several NFs were measured at both near room and elevated temperatures; the results are reported and compared with some correlations. It is shown that the Maxwell model for thermal conductivity and the modified Krieger–Dougherty model for viscosity can be used to predict these properties of NFs within ±10% error, even at elevated temperatures.
A screening setup, including a test section with d = 0.5 mm and L = 30 cm, was designed for measuring the heat transfer performance of NFs in laminar flow. In addition a closed–loop setup with a 3.7 mm inner diameter and 1.5 m length test section was also designed to measure the heat transfer coefficients in both laminar and turbulent flow with higher accuracy. Based on the results, classical correlations for predicting Nusselt number and friction factor in a straight tube are still valid for NFs within ± (10 – 20)% error provided that the correct thermophysical properties are used for NFs.
Different methods of comparing cooling performance of NFs to BFs are then investigated. Comparison at equal Reynolds number, the most popular method in the literature, is demonstrated both experimentally and analytically to be misleading. However, if the most correct criterion (at equal pumping power) is chosen, a small advantage for some NFs over their BFs should be expected only under laminar flow. The investigation concludes with the proposition of a unique method and apparatus to estimate the shelf stability of NFs.
Keywords: nanofluid, convective heat transfer, thermal conductivity, viscosity, heat transfer coefficient, performance, pumping power, Reynolds number, shelf stability.
iv
v
Sammanfattning
Nanofluider (NF) kallas suspensioner av nanopartiklar (NP) i en vätska (base fluid, BF). Tillsatsen av nanopartiklar leder till förändring av vätskans termodynamiska- och transport-egenskaper vilket eventuellt kan utnyttjas för att anpassa egenskaperna efter speciella behov.
Befintliga teknologier för kylning av elektronik tenderar att vara otillräckliga och nanofluider kan, som föreslagits i olika studier, ge en möjlighet att åstadkomma effektivare vätskekylning än dagens kylmedier. Huvudsyftet med denna studie har varit att kritiskt granska tidigare publicerad information om nanofluider samt att genom nya tester av många olika nanofluider undersöka potentialen för att ersätta vanligt förekommande kylvätskor med nanofluider i tillämpningar utan fasändring. Ett stort antal nanofluider, huvudsakligen vattenbaserade metall-oxid nanofluider, karakteriserades genom bestämning av värmeledningstal, viskositet, värmeövergångstal vid rörströmning och möjlig lagringstid. De experimentella resultaten analyseras i detalj och jämförs med korrelationer från litteraturen.
vi
vii
Acknowledgements
“A hundred times every day I remind myself that my inner and outer life depend on the labours of other men.”
Albert Einstein (German–born theoretical physicist, 1879 – 1955)
First and foremost I would like to express my deepest appreciation to my supervisor Professor Björn Palm, who was not only a tremendous mentor for me, but also an ethical teacher and a supportive person during difficult times. Without his genuine and constant supervision and help this dissertation would never have been possible.
I would also like to thank my co–supervisor Dr. Rahmatollah Khodabandeh for his priceless comments and suggestions on my articles, and his valuable recommendations on my career path as a research scientist.
In addition, I offer my thanks to Professor Mamoun Muhammed, Dr. Muhammet Toprak and graduated PhD students Nader Nikkam and Mohsin Saleemi at the Functional Materials Division of KTH. They were our main project partners, and together we co–authored several papers.
My deepest thanks to all of my colleagues in the European project NanoHex; I will never forget a lot of good times we shared with each other. In particular, to David Mullen, senior R&D Engineer at Thermacore (UK), for his incredible job in coordinating the project; to Shak Gohir and Charanjeet Singh, respectively, Practice Director and Innovation Manager at Centre for Process Innovation (UK); to Professor Andrzej Pacek, University of Birmingham (UK); to Dr. Adi Utomo, Project Engineer at BHR Virtual PiE (UK); to Dr. Srinivas Vanapalli, University of Twente (the Netherlands); to Dr. Frank Meyer, Managing Director at CeraNovis GmbH (Germany); and to Heiko Poth, R&D Engineer at ItN Nanovation AG (Germany).
At the KTH Department of Energy Technology, thanks to Peter Hill, Lab Manager; Benny Sjöberg and Karl Åke Lundin, laboratory personnel; Anneli Ylitalo–Qvarfordt, Administrative Operations Manager; Hanna Bergström and Petra Rytterholm, PhD Educational Administrators; Sara Morén, Administrator–Secretary; and Alena Joutsen, Administrator–Economy. They provided me with a lot of support and information whenever I needed it.
viii
Many thanks to all my colleagues at the Division of Applied Thermodynamics and Refrigeration for sustaining a friendly and pleasant work environment. In particular, special thanks to Hatef Madani, Morteza Ghanbarpour, Zahid Anwar and Mazyar Karampour for their continuous hints, help and support.
Special Thanks to Amir Vadiei, graduated PhD student at the Division of Heat and Power Technology of KTH for the memories and the good times we shared.
It was a great pleasure to work with master students Shohreh Moshtarikhah, Mariam Jarahnejad, Itziar Lumbreras, Mersedeh Ghadamgahi, Simon Ströder, Mohammadreza Behi, Seyed Ali Mirmohammadi and Joan Iborra Rubio, in addition to internship students Thibault Brändle and Wassim Saifane. We built up a mutual learning environment and exchanged a lot of knowledge and ideas.
Very special thanks to my family! My mother, Mehran, and my father, Najafali have sacrificed a lot for me; words cannot express how deeply grateful I am for them. To Payman, thanks for being the perfect younger brother, and especially for your sympathy and support in my difficulties and for being a genuine person always, all the time.
A special thank you to my wife, Shirin, for her continued and authentic love, support, encouragement and patience when I was only thinking about my career. I am so grateful and fortunate to have found a great person like you to honestly dedicate time and effort for each other.
Last but not least, the financial support of the EU project NanoHex with reference number 228882 for this study, is highly appreciated.
Ehsan Bitaraf Haghighi
Stockholm, February 2015
ix
Table of Contents
1 Introduction ................................................................................ 11 1.1 Project foundation and backdrop .................................... 11 1.2 Aim of the study ................................................................. 12 1.3 Methodology ....................................................................... 13 1.4 Publications ......................................................................... 14
1.4.1 Primary articles ......................................................... 14 1.4.1 Other relevant publications ........................................ 16
2 Nanofluids in the Literature ....................................................... 19 2.1 Nanofluids and their significance..................................... 19 2.2 Thermophysical properties of nanofluids ....................... 21 2.3 Method of comparing the cooling performance of
nanofluids ............................................................................ 24
3 Theoretical and Empirical Formulas .......................................... 26 3.1 Pressure drop and pumping power ................................. 26 3.2 Convective heat transfer .................................................... 27
3.2.1 Laminar flow ............................................................ 28 3.2.2 Turbulent flow........................................................... 29
3.3 Suggested model ................................................................. 29 3.4 Stokes’ Law .......................................................................... 31
4 Experimental Procedures ........................................................... 33 4.1 Thermal conductivity ......................................................... 33 4.2 Viscosity ............................................................................... 33 4.3 Convective heat transfer .................................................... 35
4.3.1 Screening setup .......................................................... 35 4.3.2 Convective test setup, closed–loop ............................... 36
4.4 Sedimentation rate .............................................................. 38 4.5 Material characterisation .................................................... 39 4.6 Summary of materials and experiments .......................... 40
5 Uncertainty Analysis ................................................................... 41 5.1 Thermal conductivity ......................................................... 41 5.2 Viscosity ............................................................................... 42 5.3 Density and specific heat ................................................... 44 5.4 Temperatures ...................................................................... 44 5.5 Nusselt number and friction factor ................................. 45 5.6 Error propagation ............................................................... 46
6 Summary of Results and Discussion .......................................... 48 6.1 Papers 1, 2 and 3: Thermophysical and transport
properties of three NFs ..................................................... 48
x
6.2 Paper 4: Cooling performance of NFs in a small–diameter tube ....................................................................... 58
6.3 Paper 5: Heat transfer in laminar flow: comparison of results from two universities ............................................. 61
6.4 Paper 6: Heat transfer in turbulent flow: comparison of results from two universities ............................................. 63
6.5 Paper 7: A method predicting the cooling efficiency of NFs combining the effect of physical and transport properties ............................................................................. 70 6.5.1 Thermal conductivity ................................................. 71 6.5.2 Viscosity ................................................................... 74 6.5.3 The effect on the critical wall temperature of replacing BF
with NF ................................................................... 77 6.6 Paper 8: Shelf stability of NFs and its effect on thermal
conductivity ......................................................................... 79 6.7 Other Results ...................................................................... 83
6.7.1 SiC–α in EG–water 50:50 wt% .............................. 83 6.7.2 The effect of particle size ............................................ 84 6.7.3 The effect of surfactant ............................................... 87
7 Conclusion and Future Work ...................................................... 90
8 Nomenclature ............................................................................. 93
9 Appendix A ................................................................................. 97
10 Appendix B ................................................................................. 99
11 References ................................................................................. 105
11
1 Introduction
1 . 1 P r o j e c t f o u n d a t i o n a n d b a c k d r o p
Existing conventional air cooling technologies have reached their limits. Liquid cooling, even with possible enhancement techniques such as extended surfaces and mini–/micro–channels, may prove insufficient for high thermal flux electronics devices in near future. More efficient and inventive cooling technologies are now required to support technological development in many industries such as transportation, data centres, telecommunication and power generation. State–of–the–art engineered solid–liquid composite materials, called nanofluids (NFs), may be used for removing heat in high heat flux applications.
In order to improve heat management in existing industries, particularly data centres and power electronics, the collaborative European project NanoHex (Enhanced Nanofluid Heat Exchange) [1] was granted €8.3 million by the Seventh Framework Programme (FP7). The project was started in September 2009, and ended in April 2013. The NanoHex project was comprised of a consortium of twelve leading European companies and research centres. The main goal for the NanoHex project was to develop a formulation and a production pilot–line for a promising NF as a coolant, based on the partners’ existing laboratory results and facilities. Detailed information about the NanoHex project and partners can be found through this link: http://www.nanohex.org.
The overall strategy of the NanoHex work plan includes twelve work packages, and the role of the KTH Energy Department is shown in a simplified pert diagram in Figure 1. As shown, the KTH Energy Department was mainly involved in suggesting an appropriate formulation for NFs based on heat transfer experiments; work also focused on predicting the heat transfer behaviour of NFs.
12
Figu r e 1 : S imp l i f i e d p e r t d i ag r am f o r NanoHex wo rk pa cka g e s (WP) and r o l e o f t h e KTH Ene r g y Depa r tmen t .
1 . 2 A i m o f t h e s t u d y
The main purpose of this thesis is to investigate if the addition of NPs can enhance the heat transfer performance of commonly used fluids (e.g. water, ethylene glycol and engine oil). Heat transfer in NFs has been investigated for almost twenty years, but the results are still very confusing. One of the aims of this study is to have a critical approach to previous investigations reported in the literature, particularly in terms of comparing the convective heat transfer of NFs to that of their BFs.
In order to compare the cooling performance of NFs to BFs, the thermophysical and transport properties of NFs must be investigated experimentally and analytically. Furthermore, it is crucial to be confident that the accuracy of measurement data is acceptable.
It is also important to suggest rather rapid experimental and analytical screening methods for evaluating the cooling performance of NFs. Furthermore, it is essential to find a simple, inexpensive and standardized method to estimate the shelf stability of NFs. This is a key issue in practical applications.
13
1 . 3 M e t h o d o l o g y
The work towards these goals started in the preparation of appropriate experimental setups to measure the thermophysical and transport properties of NFs quickly and accurately. To measure the thermal conductivity and viscosity of fluids, two experimental setups were bought and a lot of time was dedicated to their calibration and the improvement of their accuracy. To measure the heat transfer coefficient of NFs, two setups were built up: a screening setup and a closed–loop. The screening setup, although achieving less accuracy, could evaluate heat transfer coefficient of NFs in much less time than the closed–loop. In addition, a simple method and apparatus to estimate shelf stability of NFs were proposed.
The NFs were synthesised by the different partners of the NanoHex project. The thermal conductivity and viscosity of NFs were measured and compared with some existing models. These data, in addition to the weighted average formulas for the density and specific heat, were used to analyse the measured data from the screening test. Later, especially for potential NFs, the heat transfer coefficient was measured in the closed–loop as well. At the end of the project, the shelf stability of NFs was investigated. Experimental results in both convective test setups were compared with classical correlations in order to examine their validity. During the tests, at some points for re-evaluating NFs, synthesis parameters such as particle sizes or surface modifiers were changed. Figure 2 shows a summary of this experimental procedure for NFs. To ensure the accuracy of measurements, an important goal of this study, parts of the experiments were cross-checked with the same samples (taken from the same batch) in similar test setups at other laboratories belonging to the NanoHex project partners (University of Birmingham (UK), Division of Functional Materials (FNM) at KTH (Sweden), and University of Twente (the Netherlands)).
Finally, an analytical method - a screening procedure - was tested to evaluate the advantage of replacing BFs with NFs based on the hottest wall temperature in heat sinks. This formula can be used as an alternative to time-consuming experiments to measure heat transfer coefficients.
14
Figu r e 2 : S ummar y o f ex pe r im en t s an d p r o c e du r e .
1 . 4 P u b l i c a t i o n s
The present thesis is mainly based on seven previously published articles, and one under publication, as listed below. These papers (seven journals and one conference proceeding) are referenced as Papers 1 – 8 in subsequent chapters of this thesis.
1 . 4 . 1 P r i m a r y a r t i c l e s
1. E. B. Haghighi, Z. Anwar, I. Lumbreras, S. A. Mirmohammadi, M. Behi, R. Khodabandeh, B. Palm, Screening Single Phase Laminar Convective Heat Transfer of Nanofluids in a Micro–tube, Journal of Physics: Conference Series, 2012, 395: 012036.
2. E. B. Haghighi, M. Saleemi, N. Nikkam, M. Ghadamgahi, R. Khodabandeh, B. Palm, M. S. Toprak, M. Muhammed, Measurement of temperature–dependent viscosity of nanofluids
15
and its effect on pumping power in cooling systems, Proceeding of the 5th International Conference Applied Energy (ICAE), Pretoria, South Africa, 2013.
3. E. B. Haghighi, M. Saleemi, N. Nikkam, R. Khodabandeh, M. S. Toprak, M. Muhammed, B. Palm, Accurate basis of comparison for convective heat transfer in nanofluids, International Communications in Heat and Mass Transfer, 52: 1 – 7, 2014.
4. E. B. Haghighi, M. Saleemi, N. Nikkam, Z. Anwar, I. Lumbreras, M. Behi, S. A. Mirmohammadi, H. Poth, R. Khodabandeh, M. S. Toprak, M. Muhammed, B. Palm, Cooling Performance of Nanofluids in a Small Diameter Tube, Journal of Experimental Thermal and Fluid Science, 2013, 49: 114 – 122.
5. A. T. Utomo, E. B. Haghighi, A. I. T. Zavareh, M. Ghanbarpourgeravi, H. Poth, R. Khodabandeh, B. Palm, A. W. Pacek, The effect of nanoparticles on laminar heat transfer in a horizontal tube, International Journal of Heat and Mass Transfer, 69: 77 – 91, 2014.
6. E. B. Haghighi, A. T. Utomo, M. Ghanbarpour, A. I. T. Zavareh, H. Poth, R. Khodabandeh, A. W. Pacek, B. Palm, Experimental Study on Convective Heat Transfer of Nanofluids in Turbulent Flow: Methods of Comparing Their Performance, Experimental Thermal and Fluid Science, 57: 378 – 387, 2014.
7. E. B. Haghighi, A. T. Utomo, M. Ghanbarpour, A. I. T. Zavareh, E. Nowak, R. Khodabandeh, A. W. Pacek, B. Palm, Combined Effect of Physical Properties and Convective Heat Transfer Coefficient of Nanofluids on Their Cooling Efficiency, Experimental Thermal and Fluid Science, 2014, (submitted, under review).
8. E. B. Haghighi, N. Nikkam, M. Saleemi, M. Behi, S. A. Mirmohammadi, H. Poth, R. Khodabandeh, M. S. Toprak, M. Muhammed, B. Palm, Shelf Stability of Nanofluids and Its Effect on Thermal Conductivity and Viscosity, Journal of Measurement Science and Technology, 24: 105301 (11 pages), 2013.
The present thesis, however, does not cover the publications listed below. Even so, the reader may find these papers instructive in answering further questions about the topics discussed:
16
1 . 4 . 1 O t h e r r e l e v a n t p u b l i c a t i o n s
1 . 4 . 1 . 1 B o o k c h a p t e r
1. E. B. Haghighi, A. T. Utomo, A. W. Pacek, B. Palm, Experimental Study of Convective Heat Transfer in Nanofluids, Heat Transfer in Nanofluids, CRC Press, Taylor and Francis Group (under publication).
1 . 4 . 1 . 2 J o u r n a l p a p e r s
1. M. Jarahnejad, E. B. Haghighi, M. Saleemi, N. Nikkam, R. Khodabandeh, B. Palm, M. S. Toprak, M. Muhammed, Experimental investigation on viscosity of water based Al2O3 and TiO2 nanofluids, Journal of Rheologica Acta, 2014, (submitted, under review).
2. M. Ghanbarpour, E. B. Haghighi, R. Khodabandeh, Thermal and rheological properties of water based Al2O3 nanofluid as a heat transfer fluid, Journal of Experimental Thermal and Fluid Science, 53: 227 – 235, 2014.
3. N. Nikkam, M. Ghanbarpour, M. Saleemi, E. B. Haghighi, R. Khodabandeh, M. Muhammed, B. Palm, M. S. Toprak, Fabrication of copper nanofluids via microwave–assisted route and their thermophysical characterizations, Journal of Applied Thermal Engineering, 65: 158 – 165, 2014.
4. N. Nikkam, M. Saleemi, E. B. Haghighi, M. Ghanbarpour, R. Khodabandeh, M. Muhammed, B. Palm, M. S. Toprak, M. Muhammed, Fabrication, characterization and thermo–physical property evaluation of water/ethylene glycol based SiC nanofluids for heat transfer applications, Journal of Nano–Micro Letters, 6: 178 – 189, 2014.
5. N. Nikkam, E. B. Haghighi, M. Saleemi, M. Behi, R. Khodabandeh, M. Muhammed, B. Palm, M. S. Toprak, M. Muhammed, Experimental study on preparation and base liquid effect on thermo–physical characteristics of α–SiC nanofluids, International Communications in Heat and Mass Transfer, 2014 (Accepted, under publication).
6. N. Nikkam, M. Saleemi, M. S. Toprak, S. Li, M. Muhammed, E. B. Haghighi, R. Khodabandeh, B. Palm, Novel nanofluids based on mesoporous silica for enhanced heat transfer, Journal of Nanoparticle Research, 13: 6201 – 6206, 2011.
17
1 . 4 . 1 . 3 P a t e n t
1. M. Saleemi, N. Nikkam, M. Behi, E. B. Haghighi, M. S. Toprak, R. Khodabandeh, M. Muhammed, Method and apparatus for a simple determination of the stability of suspensions, (submitted, Swedish patent application number: 1100961–0).
1 . 4 . 1 . 4 C o n f e r e n c e p a p e r s
1. N. Nikkam, M. Saleemi, E. B. Haghighi, M. Ghanbarpour, M. S. Toprak, R. Khodabandeh, M. Muhammed, B. Palm, Design and fabrication of efficient nanofluids based on SiC nanoparticles for heat exchange applications, European Materials Research Society (E–MRS) Conference, Strasbourg, France, 2013.
2. N. Nikkam, M. Saleemi, E. B. Haghighi, M. Ghanbarpour, M. S. Toprak, R. Khodabandeh, M. Muhammed, B. Palm, Nano–engineered SiC heat transfer fluids for effective cooling, Materials Research Society (MRS) Conference, San Francisco, USA, 2013.
3. N. Nikkam, M. Saleemi, E. B. Haghighi, M. S. Toprak, M. Muhammed, R. Khodabandeh, B. Palm, Rheological properties of copper nanofluids synthesised by using microwave–assisted method, 4th International conference on nanostructures (ICNS4), Kish Island, Iran, 2012.
4. N. Nikkam, M. Saleemi, M. S. Toprak, M. Muhammed, E. B. Haghighi, R. Khodabandeh, B. Palm, Microwave–assisted synthesis of copper nanofluids for heat transfer applications, 7th Nanoscience and Nanotechnology Conference, Istanbul, Turkey, 2011.
5. M. Saleemi, N. Nikkam, M. S. Toprak, S. Li , M. Muhammed, E. B. Haghighi, R. Khodabandeh, B. Palm, One step synthesis of ceria (CeO2) nanofluids with enhanced thermal transport properties, 7th Nanoscience and Nanotechnology Conference, Istanbul, Turkey, 2011.
6. N. Nikkam, M. Saleemi, S. Li, M. S. Toprak, M. Muhammed, E. B. Haghighi, R. Khodabandeh, B. Palm, Novel nanofluids based on mesoporous silica for enhanced heat transfer, International Conference on Nanostructured Materials, Rome, Italy, 2010.
7. M. Saleemi, N. Nikkam, S. Li, M. S. Toprak, M. Muhammed, E. B. Haghighi, R. Khodabandeh, B. Palm, Ceria nanofluids for efficient heat management, International Conference on Nanostructured Materials, Rome, Italy, 2010.
18
1 . 4 . 1 . 5 M S c t h e s i s w o r k
The following projects were conducted in relation to the research work of this thesis: 1. Mirmohammadi, S. A., Behi, M., Investigation on Thermal
Conductivity, Viscosity and Stability of Nanofluids. Energy Technology Department, Royal Institute of Technology (KTH), Stockholm, Sweden, 2012.
2. Iborra Rubio, J., Nanofluids: Thermophysical Analysis and Heat Transfer Performance. Energy Technology Department, Royal Institute of Technology (KTH), Stockholm, Sweden, 2012.
3. Ströder, S., Convective Heat Transfer with Nanofluids. Energy Technology Department, Royal Institute of Technology (KTH), Stockholm, Sweden, 2011.
4. Lumbreras Basagoiti, I., Single phase laminar convective heat transfer of nanofluids in a micro–tube. Energy Technology Department, Royal Institute of Technology (KTH), Stockholm, Sweden, 2011.
19
2 Nanof luids in the Literature
2 . 1 N a n o f l u i d s a n d t h e i r s i g n i f i c a n c e
Dilute dispersions of NPs (like metals, metal oxides, carbides, carbon nanotubes etc.) with loading less than 5 vol% in conventional heat transfer fluids (like water, ethylene glycol/water, oils etc.) are defined as nanofluids (NFs) [2]. This new class of heat transfer fluids has been suggested be used for high heat flux applications. Figure 3 shows a visual example of a NF including Al2O3 NPs dispersed in a BF (water).
Figu r e 3 : A v i su a l examp l e o f a NF
In 1993, Masuda et al., a Japanese group of scientists from Tohoku University, experimentally studied the possibility of increasing the thermal conductivity of a liquid by dispersing a small amount of ultra–fine particles in it for the first time. They showed that the thermal conductivity of 4 vol% Al2O3 in water increased up to 30% compared to pure water [3]. However, the patented concept, “nanofluid”, as a potential heat transfer coolant was promoted for the first time in 1995 by Choi and Eastman [4] from the Argonne National Lab (USA). Indeed, a considerable difference between the thermal conductivity of common liquids and solids, as shown in Figure 4, is the philosophy behind the concept of NFs as coolant alternatives. Both thermal conductivity and heat transfer coefficient of NFs were reported to significantly increase compared to those of BFs: for example, an increase of 40% in thermal conductivity of ethylene glycol was reported by dispersing 0.3 vol% Cu [5], and dispersing 0.5 vol% of carbon nanotubes in water was found to increase the heat transfer coefficient in laminar flow by 350% [6].
20
Although, it has been difficult to reproduce many of these early and astonishing results, NFs have attracted the attention of many researchers worldwide and have gained prominence as the next generation of coolants. In scientific articles in “Engineering Village”1 the word “nanofluid” was searched for as a part of article titles; the results show increasing interest from 1993 until 2013 (Figure 5).
Figu r e 4 : The rma l c o n du c t i v i t y o f s o l i d s an d l i qu i d s [7 ]
Figu r e 5 : Numbe r o f a r t i c l e s i n Eng in e e r in g Vi l la g e i n c l ud in g t h e t e rm “nano f lu i d” in t h e i r t i t l e s
1 An article database that is the information discovery platform of choice for engineering
490429
401
317
368.4 0.606 0.250 0.145
0
100
200
300
400
500
k (W
/mk)
Material
499527
396
182
130
9067
35 23 14 3 1 0 1 0 1 2 0 0 0 2
0
100
200
300
400
500
600
20
13
20
12
20
11
20
10
20
09
20
08
20
07
20
06
20
05
20
04
20
03
20
02
20
01
20
00
19
99
19
98
19
97
19
96
19
95
19
94
19
93
Re
cord
s
Year
21
2 . 2 T h e r m o p h y s i c a l p r o p e r t i e s o f n a n o f l u i d s
In order to calculate the expected heat transfer coefficients of NFs, their thermophysical properties need to be determined. These properties are thermal conductivity, viscosity, specific heat and density.
Thermal conductivity is the most widely studied thermophysical property of NFs. Effective medium theory (EMT) can be used to calculate the thermal conductivity of composites. EMT can also be used to calculate NFs’ thermal conductivity, as they are considered a kind of composite (liquid and solid). Table 1 summarizes some of the models used to predict the thermal conductivity of NFs. The most widely used EMT-based model for calculating the thermal conductivity of NFs, providing NPs are assumed spherical and uniformly distributed in BFs, is the Maxwell model [8]. Another model was suggested by Bruggeman [9], in which the effect of interactions (aggregation) among the randomly distributed particles are taken into account. The Hamilton and Crosser (HC) model is another EMT-based model appropriate also for non–
spherical particles [10]. For spherical particles 𝑛 = 3 (as stated in Table
1, 𝑛 is an empirical constant depending on the particle sphericity), and the HC model reduces to the Maxwell model. However, for elongated
particles, 𝑛 > 3; as a result, they have higher thermal conductivity than spherical particles with the same loading. Wang et al. [11] suggest a model based on the thermal conductivity of clusters. The model suggested by Nan et al. [12] takes into account the effect of interfacial thermal resistance (or Kapitza resistance), which is the source of the temperature discontinuity at the solid–liquid interface. This model always predicts the thermal conductivity of NFs to be lower than the predictions of the Maxwell model. The specific surface area and Brownian motion are taken into account in the model by Kumar et al [13]. Jang and Choi [14] and Prasher et al. [15] argue that micro/nano convection can enhance the thermal conductivity of NFs. The effect of thermal boundary layer thickness around NPs was proposed in models by Yu and Choi [16] and Mursheed et al. [17]. Accordingly different mechanisms have been suggested for explaining the deviations from the simple EMT model suggested by Maxwell. However, there is still no agreement on which mechanism is the most important or for that matter which mechanisms have any influence at all.
The experimental results reported in the literature differ considerably from one researcher to another. In several studies the thermal conductivity enhancements of NF were reported to be significantly larger than what was predicted by conventional models based on the EMT, such as the Maxwell model [5], [18], [19]. On the other hand,
22
some researchers found that the effective thermal conductivity of NFs agreed with the prediction of the Maxwell model [20], or was even lower [21], [22]. These anomalies were explained by several proposed mechanisms (Table 1). Some scientists argue that NP Brownian motion, enhances the effective thermal conductivity of NFs [13], [14], [23]; others propose models based on NP aggregation [11], [24] and liquid layering [16], [25], [26]. Though those models agree well with certain experimental data, they cannot be used as a general tool to predict other sets of experimental data.
Tabl e 1 : Mode l s f o r t h e rma l c o ndu c t i v i t y o f NFs
Author Model Remarks
Maxwell [8] 𝑘𝑒𝑓𝑓 = [𝑘𝑝 + 2𝑘𝑓 + 2(𝑘𝑝 − 𝑘𝑓)∅
𝑘𝑝 + 2𝑘𝑓 − (𝑘𝑝 − 𝑘𝑓)∅] 𝑘𝑓
For spherical particles; no interactions among particles
Bruggeman [9]
∅(𝑘𝑝 − 𝑘𝑒𝑓𝑓𝑘𝑝 + 2𝑘𝑒𝑓𝑓
) + (1 − ∅)(𝑘𝑓 − 𝑘𝑒𝑓𝑓𝑘𝑓 + 2𝑘𝑒𝑓𝑓
) = 0
𝑘𝑒𝑓𝑓 = (3∅ − 1)𝑘𝑝 + [3(1 − ∅) − 1]𝑘𝑓 + √∆
∆= (3∅ − 1)2𝑘𝑝2 + [3(1 − ∅) − 1]2𝑘𝑓
2 + 2[2 + 9∅(1 − ∅)]𝑘𝑝𝑘𝑓
NP aggregation (interactions among the randomly distributed particles)
Hamilton and Crosser (HC) [10]
𝑘𝑒𝑓𝑓 = [𝑘𝑝 + (𝑛 − 1)𝑘𝑓 + (𝑛 − 1)(𝑘𝑝 − 𝑘𝑓)∅
𝑘𝑝 + (𝑛 − 1)𝑘𝑓 − (𝑘𝑝 − 𝑘𝑓)∅] 𝑘𝑓
𝑛 = 3/𝜓
For elongated particles
Wang et al. [11]
𝑘𝑒𝑓𝑓 =
[ (1 − ∅) + 3∅∫
𝑘𝑐𝑙(𝑟)𝑛(𝑟)𝑘𝑐𝑙(𝑟) + 2𝑘𝑓
𝑑𝑟∞
0
(1 − ∅) + 3∅∫𝑘𝑓𝑛(𝑟)
𝑘𝑐𝑙(𝑟) + 2𝑘𝑓𝑑𝑟
∞
0 ]
𝑘𝑓
𝑘𝑐𝑙(𝑟) is the effective thermal conductivity of clusters, 𝑛(𝑟) radius distribution function
NP aggregation
Nan et al. [12] 𝑘𝑒𝑓𝑓 = [
(1 + 2𝛼)𝑘𝑝 + 2𝑘𝑓 + 2((1 − 𝛼)𝑘𝑝 − 𝑘𝑓)∅
(1 + 2𝛼)𝑘𝑝 + 2𝑘𝑓 − ((1 − 𝛼)𝑘𝑝 − 𝑘𝑓)∅] 𝑘𝑓
𝛼 =𝑎𝑘
𝑑𝑝/2, 𝑎𝑘 = 𝑅𝐵𝑑𝑘𝑓, 𝑅𝐵𝑑 = 10
−8𝐾𝑚2/𝑊 [20]
The effect of interfacial thermal resistance (Kapiza resistance)
Kumar et al. [13]
𝑘𝑒𝑓𝑓 = [1 + 𝐶 (2𝑘𝐵𝑇
𝜋𝜇𝑑𝑝2)(
∅𝑑𝑏𝑓𝑘𝑓(1 − ∅)𝑑𝑝
)] 𝑘𝑓
𝐶=constant
Brownian motion and temperature
Jang and Choi [14]
𝑘𝑒𝑓𝑓 = [(1 − ∅) +𝑘𝑛𝑎𝑛𝑜𝑘𝑓
∅ + 3𝐶1𝑑𝑓𝑑𝑝𝑅𝑒𝑝
2𝑃𝑟𝑓] 𝑘𝑓
𝑘𝑛𝑎𝑛𝑜=effective thermal conductivity of NP with Kapitza resistance
𝐶1=constant
Brownian motion and micro/nanoconvection
Prasher et al. [15]
𝑘𝑒𝑓𝑓 = [(1 + 𝐴𝑅𝑒𝑝𝑚𝑃𝑟𝑓
0.333∅)(1 + 2𝛼) + 2∅(1 − 𝛼)
(1 + 2𝛼) − ∅(1 − 𝛼)] 𝑘𝑓
A=40000 and m=2.5 (empirical parameters)
𝛼 =𝑎𝑘
𝑑𝑝/2, 𝑎𝑘 = 𝑅𝐵𝑑𝑘𝑓, 𝑅𝐵𝑑 = 10
−8𝐾𝑚2/𝑊 [20]
Brownian motion and micro/nanoconvection
Yu and Choi [16]
𝑘𝑒𝑓𝑓 = [𝑘𝑝𝑒 + 2𝑘𝑓 + 2(𝑘𝑝𝑒 − 𝑘𝑓)(1 + 𝛽)
3∅
𝑘𝑝𝑒 + 2𝑘𝑓 − (𝑘𝑝𝑒 − 𝑘𝑓)(1 + 𝛽)3∅] 𝑘𝑓
𝑘𝑝𝑒 =[2(1−𝛾)+(1+𝛽)3(1+2𝛾)]𝛾
−(1−𝛾)+(1+𝛽)3(1+2𝛾)𝑘𝑝, 𝛽 =
2𝛿
𝑑𝑝, 𝛾 =
𝑘𝑙
𝑘𝑝
Nanolayer
Mursheed et al. [17]
𝑘𝑒𝑓𝑓 =(𝑘𝑝 − 𝑘𝑙)∅𝑘𝑙𝑟[2𝛾𝑙
3 − 𝛾3 + 1] + (𝑘𝑝 + 2𝑘𝑙) × 𝛾13[∅𝛾3(𝑘𝑙 − 𝑘𝑓) + 𝑘𝑓]
𝛾𝑙3(𝑘𝑝 + 2𝑘𝑙) − (𝑘𝑝 − 𝑘𝑙)∅[𝛾𝑙
3 + 𝛾3 − 1]
𝛾 = 1 +𝛿
𝑑𝑝/2, 𝛾𝑙 = 1 +
𝛿
𝑑𝑝
Nanolayer
The experimental results for viscosity have consistently shown that with an increase in particle concentration, the viscosity of NFs increases [27], [28], [29], [30], [31]. Furthermore, as for BFs, an increase in temperature usually causes a decrease in viscosity [29], [32], [33], [34], [35]; however,
23
there are some contradictory results in the literature [36], [37], [38]. Only a few studies in the literature can be found that discuss the effect of particle size and shape on the viscosity of NFs. Some researchers have reported higher viscosity for smaller particles [39], [40], [41]; other studies have shown that the viscosity of NFs increases with increase of the particle size [27], [28], [42], [43], [44]. Moreover, a study even showed that particle size does not have a strong effect on viscosity [36]. Elongated particles, however, demonstrated higher viscosity in NFs [45], [46]. Several models have been suggested to predict the viscosity of NFs; they are summarised in Table 2. Some of these models - e.g. Einstein [47], Brinkman [48] , Batchelor [49], Cheng and Law [50], Krieger–Dougherty [51], and Modified Krieger–Dougherty [38] - can be used for any type of NFs, whereas others - e.g. Maiga et al. [52], Nguyen et al. [41], [53], and Williams et al. [54] - can only be used specifically for certain types of NFs. As for thermal conductivity, most of these models agree with only specific experimental data.
Tabl e 2 : Mode l s f o r v i s c o s i t y o f NFs
Author Model Remarks
Einstein [47] 𝜇𝑒𝑓𝑓 = (1 + 2.5∅)𝜇𝑓 ∅ < 0.02
Brinkman [48] 𝜇𝑒𝑓𝑓 = [1
(1 − ∅)2.5] 𝜇𝑓 ∅ < 0.04
Batchelor [49] 𝜇𝑒𝑓𝑓 = (1 + 2.5∅ + 6.2∅²)𝜇𝑓 Brownian motion of particles for an isotropic suspension of spherical and rigid particles
Cheng and Law [50] 𝜇𝑒𝑓𝑓 = 𝑒𝑥𝑝(
2.5
𝛽(
1
(1 − ∅)𝛽− 1))𝜇𝑓
𝛽=0.95 – 3.9
∅ < 0.35
Krieger- Dougherty [51]
𝜇𝑒𝑓𝑓 = [(1 −∅
∅𝑚)−2.5∅𝑚] 𝜇𝑓
∅𝑚 = 0.60 – 0.64
Semi–empirical correlation, applicable for the full range of particle volume fractions
Modified Krieger–Dougherty [38]
𝜇𝑒𝑓𝑓 = [(1 −∅𝑎∅𝑚)
−2.5∅𝑚
] 𝜇𝑓
∅𝑚 = 0.62, ∅𝑎 = ∅(𝑎𝑎/𝑎)3−𝐷, 𝐷 is typically 1.6 – 2.5 for NFs
[55], [56].
Semi–empirical correlation, applicable for the full range of particle volume fractions
Maiga et al. [52] 𝜇𝑒𝑓𝑓 = (1 + 7.3∅ + 123∅2)𝜇𝑓
𝜇𝑒𝑓𝑓 = (1 − 0.19∅+ 306∅2)𝜇𝑓
for Al2O3–Water for Al2O3–EG*
Nguyen et al. [41], [53] 𝜇𝑒𝑓𝑓 = (0.904exp (14.8∅))𝜇𝑓
𝜇𝑒𝑓𝑓 = (1 + 0.025∅+ 0.150∅2)𝜇𝑓
for Al2O3–Water (dp = 47 nm) for Al2O3–Water (dp = 36 nm)
Williams et al. [54] 𝜇𝑒𝑓𝑓 = [𝑒𝑥𝑝 (
4.91∅
0.2092−∅)]𝜇𝑓
𝜇𝑒𝑓𝑓 = [𝑒𝑥𝑝 (11.19∅
0.1960−∅)]𝜇𝑓
for Al2O3–Water for ZrO2–Water
* ethylene glycol
The density and specific heat of NFs can be calculated as the weighted average of the densities and specific heats, respectively, of NPs and BFs:
𝜌𝑒𝑓𝑓 = ∅𝜌𝑝 + (1 − ∅)𝜌𝑓 (1)
𝐶𝑃,𝑒𝑓𝑓 =∅𝜌𝑝𝐶𝑃,𝑝−(1−∅)𝜌𝑓𝐶𝑃,𝑓
𝜌𝑒𝑓𝑓 (2)
24
Most experimental studies agreed well with these predictions [43], [57], [58], [59], [60]. However, some studies reported disagreement with the specific heat predicted by Eq. (2) [61], [62]. These widely accepted
correlations for effective specific heat (𝐶𝑃,𝑒𝑓𝑓) and density (𝜌𝑒𝑓𝑓) in NFs
were used by Pak and Cho [63], Xuan and Roetzel [64] and Buongiorno [65].
2 . 3 M e t h o d o f c o m p a r i n g t h e c o o l i n g p e r f o r m a n c e o f n a n o f l u i d s
The heat transfer coefficient is not a property of a fluid. It depends on geometry, flow regime (laminar, turbulent, developing, fully developed), thermal boundary condition (constant surface heat flux, constant surface temperature), and thermophysical properties of the fluid. As with the thermophysical properties of NFs, some contradictions can also be found in the literature regarding the heat transfer coefficients of NFs.
Some data from the literature regarding the enhancement of the heat transfer coefficients of nanofluids in a straight tube with a constant heat flux at the wall are summarized in Table 3 for laminar flow and Table 4 for turbulent flow.
The heat transfer in NFs can be compared to that of BF at the same Reynolds number, the same flow velocity, and the same pumping power [63]. However in most of the works the comparison was made at the same Reynolds number. Yu et al. [66] showed that comparison at equal Reynolds numbers, commonly used in the literature, is not appropriate and distorts results.
To obtain the same Reynolds number (Re) in NFs as in their
corresponding BFs (Renf = Rebf), the viscosity increase must be compensated for by increase of the velocity. This is seen as follows: at
the same Re (unf
ubf=
μnf
μbf× (
ρnf
ρbf)−1
); as normally μnf
μbf≫
ρnf
ρbf, hence the
result is 𝑢𝑛𝑓 > 𝑢𝑏𝑓. This means that at the same Re, pressure drop and
pumping power in the flow of NFs are much higher than in their corresponding BFs. Comparison at the same Re does not consider the “cost” of increased pressure drop (or pumping power). Such a comparison may give the impression that simply increasing the viscosity (without increasing the thermal conductivity) would be favourable for heat transfer. The enhancement seen at the same Re must be compared to the cost in terms of increased pumping power. This increase could equally well, or better, be used for increasing the velocity of the BF, thereby increasing Reynolds number, Nusselt number, and heat transfer coefficient. As such, comparisons at equal Reynolds numbers - even
25
though they dominate in the literature (Table 3 and Table 4) - do not enable separation of the effect of velocity from the effect of NPs on the heat transfer coefficient, and might be very misleading.
Tabl e 3 : He a t t r an s f e r i n n an o f l u i d s i n l am inar f l ow
Author Nanofluid Dimension, Re Method of Comparison
Enhancement of hnf and comments
Wen and Ding [67] Al2O3/water 1.6 vol%
D = 4.5 mm, L = 972 mm, Re = 500 – 2100
Same Re 47 % near the inlet region, 14% near the discharge region.
Hwang et al. [68] Al2O3/water 0.3 vol%
D = 1.8 mm, L = 2502 mm, Re = 400 – 700
Same Re 8% in the developed region, k increase by 1.44%, viscosity increase by 3%
Rea et al. [69]
Al2O3/water 6 vol% ZrO2/water 1.32 vol%
D = 4.5 mm, L = 1008 mm, Re = 140 – 1888
Same velocity
27% for alumina and 3% for zirconia. Nunf followed single–phase correlation.
Anoop et al. [42] Al2O3/water 4 wt%
D = 4.75 mm, L = 1202 mm, Re = 700 – 2000
Same Re 25% for 45 nm particle size and 11% for 150 nm particle size.
Liu and Yu [70] Al2O3/water 5 vol%
D =1.09 mm, L = 305 mm, Re=600 – 4500
Same Re
19% near the entrance region, 9% near the discharge region. Nunf followed single–phase correlation
Vafaei and Wen [71] Al2O3/water 1–7 vol%
D = 0.51 mm, L = 306 mm Same velocity
100% at high flow rate, but no enhancement at low flow rate
He et al. [40] TiO2/water 1.1 vol%
D =3.97 mm, L = 1834 mm, Re=900 – 5900
Same Re 12% in laminar flow and 40% in turbulent flow
Ding et al. [6] CNT/water 0.5 wt%
D =4.5 mm, L = 972 mm, Re=800 – 1200
Same Re 350% in the developed region
Garg et al. [72] CNT/water 1 wt%
D =1.55 mm, L = 915 mm, Re=600 – 1200
Same Re 32% in the developed region
Tabl e 4 : Hea t t r an s f e r i n n an o f l u i d s i n t u r bu l en t f l ow
Author Nanofluid Dimension, Re Method of Comparison
Enhancement of hnf and comments
Pak and Cho [63] γ-Al2O3/water and TiO2/water 1–3 vol%
D=10.66 mm, L=4800 mm, Re=104–105
Same velocity
12% lower for γ-Al2O3/water at 3 vol %
He et al. [40] TiO2/water 0.2–1.1 vol%
D=3.97 mm, L=1834 mm, Re=2000–6000
Same Re Maximum 40% enhancement for 1.1 vol % at Re=5900
Kulkarni [73] TiO2/(EG–water 60:40 wt%) 2–10 vol%
D=3.14 mm, L=1000 mm, Re=3000–12000
Same Re 16% enhancement for 10 vol % at Re=10000
Yu et al. [74] SiC/water 3.7 vol%
D=2.27 mm, L=580 mm, Re=3300–13000
Same velocity
7% lower
Duangthongsuk and Wongwises [75]
TiO2/water
0.2 – 2.0 vol%
D=9.53 mm, L=1500 mm,
Re=3000 – 18000 Same Re
20–32% enhancement at 1.0
vol %
Fotukian and Nasr
Esfahany [76]
γ–Al2O3/water
less than 0.2 vol%
D=5 mm, L=1000 mm,
Re=6000 – 31000 Same Re
48% enhancement at Re= 10000
and 0.054 vol%
Suresh et al [77] Al2O3/water
0.3 – 0.5 vol%
D=4.85 mm, L=800 mm,
Re=700 – 2050 Same Re 10 – 48% enhancement
Fotukian and Nasr
Esfahany [78]
CuO/water
less than 0.24 vol%
D=5 mm, L=1000 mm,
Re=6000 – 31000 Same Re Maximum 25% enhancement
Sajadi and Kazemi
[79]
TiO2/water
less than 0.25 vol%.
D=5 mm, L=1800 mm,
Re=5000 – 30000 Same Re
~22% enhancement at Re=5000
and 0.25 vol%
Kayhani et al [80] TiO2/water
0.1 – 2.0 vol%
D=5 mm, L=2000 mm,
Re=6000 – 16000 Same Re
8% enhancement at Re= 11800
and 2.0 vol%
26
3 Theoretical and Empirical Formulas
This chapter contains the correlations, which are used to evaluate experimental results in the following chapters.
3 . 1 P r e s s u r e d r o p a n d p u m p i n g p o w e r
The Darcy equation can be used to calculate the pressure drop in a fully developed region:
∆𝑝 = 𝑓𝜌𝑢2
2𝑑𝐿 (3)
For laminar flow, the friction factor is calculated based on the correlation expressed as in [7]:
𝑓 =64
𝑅𝑒 (4).
For turbulent flow, the friction factor is calculated using the Filonenko equation, as stated in [81]:
𝑓 = (1.82 𝑙𝑜𝑔10 𝑅𝑒 − 1.64)−2 (5).
Blasius [82] and McAdams [83] suggested another correlation for the friction factor in turbulent flow:
𝑓 = {0.316𝑅𝑒−
1
4 𝑅𝑒 ≤ 2 × 104
0.184𝑅𝑒−1
5 𝑅𝑒 ≥ 2 × 104 (6).
This equation is preferable in special circumstances due to its simpler form. Figure 6 shows the friction factor at different Reynolds numbers calculated from equations (4), (5) and (6).
27
Figu r e 6 : Fr i c t i o n f a c t o r v e r su s Re yno l d s numbe r ca l cu l a t e d w i t h Eqs . ( 4 ) , ( 5 ) , an d (6 )
Pumping power, disregarding the mechanical loss for the pump, is expressed as:
𝑃 = ∆𝑝∀̇ (7)
and pressure drop is calculated from Eq. (3).
For the sake of comparison the ratio between pumping power (at a
constant volume flow rate) with and without NPs is designated Ω.
Combining Eqs. (3), (4), (6), and (7), with Re ≤ 2 × 104 for Eq. (6), Ω is expressed as:
𝛺 =
{
𝜇𝑒𝑓𝑓
𝜇𝑓𝐿𝑎𝑚𝑖𝑛𝑎𝑟
(𝜇𝑒𝑓𝑓
𝜇𝑓)
1
4× (
𝜌𝑒𝑓𝑓
𝜌𝑓)
3
4𝑇𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡
(8).
3 . 2 C o n v e c t i v e h e a t t r a n s f e r
The local heat transfer coefficient (independent of the flow regime) can be calculated as
ℎ𝑥 =𝑞"
𝑇𝑠−𝑖𝑛,𝑥−𝑇𝑓,𝑥 (9)
𝑞"is calculated from the energy balance along the test tube (𝑞"𝜋𝑑𝐿 =
�̇�𝐶𝑝(𝑇𝑓,𝑖𝑛 − 𝑇𝑓,𝑜𝑢𝑡)). Moreover, 𝑇𝑓,𝑥 is calculated from the inlet
temperature and the known heat flux:
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 5000 10000 15000
fric
tio
n f
acto
r (-
)
Re (-)
64/ReFilonenkoBlasius
28
𝑇𝑓,𝑥 = 𝑇𝑖𝑛𝑙𝑒𝑡 +𝑞"𝜋𝑑𝑥
�̇�𝐶𝑝 (10).
The outside tube wall temperature (𝑇𝑠−𝑜𝑢𝑡,𝑥) can be measured by means
of thermocouples (Figure 7). Furthermore, the inside tube wall
temperature (𝑇𝑠−𝑖𝑛,𝑥) is calculated from the measured outside tube wall
temperature, using Fourier’s heat conduction equation with the
assumptions that the heat flux to the ambient equals zero and the tube
wall acts as a heat source:
𝑇𝑠−𝑖𝑛,𝑥 = 𝑇𝑠−𝑜𝑢𝑡,𝑥 +𝑄
4𝜋𝐿𝑘𝑡𝑢𝑏𝑒[𝜑(1−𝑙𝑛𝜑)−1
𝜑−1] (11)
and
𝜑 = (𝑑𝑜𝑢𝑡
𝑑𝑖𝑛)2 (12).
Figu r e 7 : The rmo coup l e po s i t i o n and d e s i gn a t i o n o f d i f f e r e n t t empe r a t u r e s i n Eqs . ( 10 ) and ( 11 ) [84]
The average heat transfer coefficient (h) is calculated as the length–weighted averages of the local heat transfer coefficients (hx). Moreover, the average Nusselt numbers (Nu) are calculated from the average heat transfer coefficient.
The theoretical2 values for Nusselt numbers are dependent on the flow regimes (laminar and turbulent) and are used for comparison with the Nusselt numbers calculated from experimental data.
3 . 2 . 1 L a m i n a r f l o w
In laminar flow with constant heat flux, the local Nusselt number can be calculated as a function of 𝑥∗ by Shah’s correlation [85]:
2 Nusselt numbers (and similarly heat transfer coefficients, friction factors, pressure drops, and pumping powers) calculated from classical correlations will, in the rest of the thesis, be referred to as “theoretical”.
29
𝑁𝑢𝑥 = {
1.302 (𝑥∗)−1
3⁄ − 1 𝑓𝑜𝑟 𝑥∗ ≤ 0.00005
1.302 (𝑥∗)−1
3⁄ − 0.5 𝑓𝑜𝑟 0.00005 ≤ 𝑥∗ ≤ 0.0015
4.364 + 8.68 (1000𝑥∗)−0.506𝑒−41𝑥∗
⁄ 𝑓𝑜𝑟 𝑥∗ ≥ 0.0015
} (13)
where 𝑥∗ is the non–dimensional distance from the inlet,
(𝑥 𝑑⁄ ) (𝑅𝑒𝑃𝑟)⁄ . Moreover, the average heat transfer coefficient in the entrance section for the same boundary condition can be calculated using Shah’s correlation [86]:
𝑁𝑢𝑎𝑣𝑒 = {1.953𝐿∗−1/3 𝐿∗ ≤ 0.034.364 + 0.0722𝐿∗−1 𝐿∗ > 0.03
(14)
where 𝐿∗ is the non–dimensional length, (𝐿 𝑑⁄ ) (𝑅𝑒𝑃𝑟)⁄ .
3 . 2 . 2 T u r b u l e n t f l o w
For turbulent flow in a pipe with constant heat flux, the Gnielinski correlation [87] is used for calculating theoretical values:
𝑁𝑢 =(𝑓
8)(𝑅𝑒−1000)𝑃𝑟
1+12.7(𝑓
8)0.5(𝑃𝑟0.66−1)
[1 + (𝑑
𝐿)
2
3] (
𝑃𝑟
𝑃𝑟𝑤)0.11
(15)
where 𝑓 is calculated using the Filonenko equation (5). Moreover, 𝑃𝑟𝑤 is the Prandtl number in the near–wall region calculated based on the
average of the local values of 𝑃𝑟. The range of applicability for equation (15) is Re = 2300 – 106 and Pr = 0.6 – 105.
In certain parts of this study the Dittus–Boelter equation [88] is used for
turbulent flow with constant heat flux boundary condition (0.7 ≤ 𝑃𝑟 ≤
160, 𝑅𝑒 ≥ 10000 and 𝐿
𝑑≥ 10):
𝑁𝑢 = 0.023𝑅𝑒4/5𝑃𝑟2/5 (16)
3 . 3 S u g g e s t e d m o d e l
In this work, the hottest (critical) wall temperature at the outlet is used to compare the cooling performances of nanofluids relative to those of BFs [89].
Figure 8 includes two lines representing the temperature of the surface and the bulk temperature of the coolant (fluid). The hot surface temperature line is higher than the coolant temperature. This
30
temperature difference remains the same everywhere along the length corresponding to the thermally fully developed region assumption (the local heat transfer coefficient is the same along the heat exchanger’s length). The coolant temperature increases linearly. This behaviour can easily be motivated by the assumption that the hot component has a fixed heat flux, and the specific heat is constant along the channel. Furthermore, axial conduction is neglected. Indeed, axial conduction may cause redistribution in the heat flux in real applications.
Figu r e 8 : The t empe r a tu r e s o f t h e h e a t t r an s f e r f l u i d and t h e wa l l i n a t u be w i t h c on s t an t h e a t f l ux a t t h e wa l l
[90]
From Figure 8 the critical surface temperature (wall temperature at outlet) can be calculated as:
𝑇𝑠−𝑜𝑢𝑡 = 𝑇𝑓−𝑖𝑛 + 𝛥𝑇 + 𝜗 (17)
where 𝑇𝑓−𝑖𝑛 is the coolant temperature at the inlet of the channel, 𝛥𝑇 is
the temperature change of the coolant as it passes through the heat sink,
and 𝜗 is the temperature difference between the surface and the bulk temperature of the coolant at the outlet (Figure 8). Considering heat
balances in two ways, 𝛥𝑇 and 𝜗 can be respectively expressed as:
𝛥𝑇 =𝑄
�̇�𝑐𝑝 (18)
𝜗 =𝑄
ℎ𝐴𝑝 (19)
Tf-in Tf-out
Ts-in Ts-out
Tem
pera
ture
Distance from inlet
Wall
Fluid
ΔT
ν
31
Where ℎ is the local heat transfer coefficient at the wall; therefore:
𝑇𝑠−𝑜𝑢𝑡 = 𝑇𝑓−𝑖𝑛 +𝑄
�̇�𝑐𝑝+
𝑄
ℎ𝐴𝑝 (20).
𝜆 is now defined as the difference between the wall temperatures at the outlet with NF and with BF:
𝜆 = (𝑇𝑠−𝑜𝑢𝑡)𝑏𝑓 − (𝑇𝑠−𝑜𝑢𝑡)𝑛𝑓 (21)
If NFs are better coolants, this value must be positive; the larger it is, the greater the resulting advantage from replacing BFs with NFs. The inlet
temperature (𝑇𝑓−𝑖𝑛) and the heat flow (𝑄) are assumed to be constant,
and the mass flow rate is defined as:
�̇� = 𝜌𝑢𝐴 (22)
Therefore, 𝜆 can be written as:
𝜆 = 𝑄 [1
(�̇�𝑐𝑝)𝑏𝑓(1 −
𝜌𝑏𝑓
𝜌𝑛𝑓×𝑐𝑝,𝑏𝑓
𝑐𝑝,𝑛𝑓×𝑢𝑏𝑓
𝑢𝑛𝑓) +
1
𝜋𝑑𝐿ℎ𝑏𝑓(1 −
ℎ𝑏𝑓
ℎ𝑛𝑓)] (23)
This equation includes both the thermophysical and transport properties for BFs and NFs, and gives a good criterion for evaluating the benefits of NFs.
Depending on the basis of comparison (at same Re number, same
velocity, or same pumping power), the velocity ratio (𝑢𝑏𝑓
𝑢𝑛𝑓) and heat
transfer coefficient ratio (ℎ𝑏𝑓
ℎ𝑛𝑓) of BF to NF to be used in calculating 𝜆
(Eq. 23) can be determined from the equations in Table 5 and Table 6
respectively (Re ≤ 2 × 104). The manipulation procedures for these formulas in turbulent flow (similarly in laminar flow) are explained in detail by Yu et al [66].
3 . 4 S t o k e s ’ L a w
When an object falls in a viscous fluid it experiences drag force. For a spherical and smooth object, assuming that the flow is laminar, the velocity can be determined from a balance between viscous, buoyancy and gravitational forces. The expression for this velocity is known as Stokes' Law [91]:
32
𝑢 =(𝜌𝑝−𝜌𝑓)𝑔𝑑𝑝
2
18𝜇 (24)
Based on this equation, highly stable nanofluids should have smaller particle size, more viscous BFs and a minimal difference in the density between NPs and the BF.
Tabl e 5 : The v e l o c i t y r a t i o (𝑢𝑏𝑓
𝑢𝑛𝑓)
Laminar Turbulent*
Same Re number (𝜌𝑏𝑓
𝜌𝑛𝑓)
−1
(𝜇𝑏𝑓
𝜇𝑛𝑓) (
𝜌𝑏𝑓
𝜌𝑛𝑓)
−1
(𝜇𝑏𝑓
𝜇𝑛𝑓)
Same velocity 1 1
Same pumping power (𝜇𝑏𝑓
𝜇𝑛𝑓)
−1/2
(𝜌𝑏𝑓
𝜌𝑛𝑓)
−3/11
(𝜇𝑏𝑓
𝜇𝑛𝑓)
−1/11
* [66]
Tabl e 6 : The h e a t t r an s f e r c o e f f i c i e n t r a t i o (ℎ𝑏𝑓
ℎ𝑛𝑓)
Laminar Turbulent*
Same Re number (𝑘𝑏𝑓
𝑘𝑛𝑓) (
𝐶𝑝,𝑏𝑓
𝐶𝑝,𝑛𝑓)
2/5
(𝜇𝑏𝑓
𝜇𝑛𝑓)
2/5
(𝑘𝑏𝑓
𝑘𝑛𝑓)
3/5
Same velocity (𝑘𝑏𝑓
𝑘𝑛𝑓) (
𝜌𝑝,𝑏𝑓
𝜌𝑝,𝑛𝑓)
4/5
(𝐶𝑝,𝑏𝑓
𝐶𝑝,𝑛𝑓)
2/5
(𝜇𝑏𝑓
𝜇𝑛𝑓)
−2/5
(𝑘𝑏𝑓
𝑘𝑛𝑓)
3/5
Same pumping power (𝑘𝑏𝑓
𝑘𝑛𝑓) (
𝜌𝑝,𝑏𝑓
𝜌𝑝,𝑛𝑓)
32/55
(𝐶𝑝,𝑏𝑓
𝐶𝑝,𝑛𝑓)
2/5
(𝜇𝑏𝑓
𝜇𝑛𝑓)
−26/55
(𝑘𝑏𝑓
𝑘𝑛𝑓)
3/5
* [66]
The theoretical and empirical formulas presented in this chapter are used for evaluation of experimental results.
33
4 Experimental Procedures
This chapter briefly explains the setups and procedures to measure the thermal conductivity, viscosity, convective heat transfer, sedimentation rate, and material characterisation.
4 . 1 T h e r m a l c o n d u c t i v i t y
The thermal conductivities of BFs and NFs were measured by a TPS (Transient Plane Source)–analyser (model 2500, HotDisk AB, Sweden) in the temperature range 20 – 50 ˚C. Temperature stability was maintained by a cooling bath (C50P, Thermo Haake, Germany) with readout accuracy ±0.1 ˚C. In this technique [92], a planar sensor (No. 7577 for this study) acting both as a heat source and temperature sensor is immersed in the static liquid. Based on analysis of the transient temperature response to a short heat pulse, thermal conductivity, thermal diffusivity and volumetric specific heat capacity are calculated. However, if specific heat is known, a more reliable thermal conductivity measurement can be achieved. The TPS technique has previously been used to measure the thermal conductivity of NFs in a number of studies [93], [94], [95], [96], [97]. Figure 9 shows a schematic diagram for the TPS analyser, sensor, sample holder and cooling bath.
To ensure the accuracy of the measurement data some of the tests were repeated with a THW (Transient Hot Wire)–analyser (KD2 Pro, USA) at University of Birmingham (UBHAM) at a temperature of 20 ˚C. The THW method can be expected to be influenced by natural convection at higher temperatures [94]. The same is true for the TPS method, but at slightly higher temperatures. The THW technique [98], using a similar methodology as the TPS method, was used to measure the thermal conductivity of NFs in a number of studies [21], [40], [99], [100], [101].
4 . 2 V i s c o s i t y
The viscosity of BFs and NFs were measured by a rotational viscometer (DV–II+Pro with UL adapter, Brookfield, USA), with coaxial cylinder geometry, at a primary temperature of 20 ˚C. Temperature stability was maintained by a cooling jacket connected to a cooling bath (TC–502, Brookfield model, USA) with readout accuracy ± 0.5 ˚C. In order to
34
check for Newtonian or non–Newtonian behaviour of the samples, shear rates were measured at different rotating speeds. The rotational speed of the spindle was controlled by Rheocalc 32 software, and variation in the speed led to various shear rates. Figure 10 shows a schematic diagram for the DV–II+Pro viscometer with UL adaptor and the cooling bath.
To ensure the accuracy of the measurement data some of the measurements were repeated with another rotational viscometer with plate–cone geometry (AR 1000, TA Instruments, USA) at UBHAM in the temperature range 20 – 40 ˚C.
Figu r e 9 : TPS ana l y s e r , s e n s o r , s amp l e ho l d e r an d c o o l i n g ba t h
Figu r e 10 : DV– I I+Pro v i s c ome t e r w i t h UL adap t o r an d c o o l i n g ba t h [ 102]
35
4 . 3 C o n v e c t i v e h e a t t r a n s f e r
The convective heat transfers of BFs and NFs were measured in two different test setups.
4 . 3 . 1 S c r e e n i n g s e t u p
A screening setup was used to perform the convective heat transfer experiments in laminar flow quickly. In order to make the flow hydro–dynamically developed the test section had an entrance region. Furthermore, an in-house mixer was located at the end of the test section before measuring the outlet temperature. The test setup consists of a stainless steel tube and a syringe pump. The syringe pump was used to maintain flow through the tube. The tube was resistively heated with a DC power supply. Ten T–type thermocouples were utilized for recording the outer wall temperature distribution along the length of the tube. Thermocouples were attached to the test section by thermally but not electrically conductive epoxy (Omega OB–101–1/2). In addition, two T–type thermocouples were used to record the inlet and the outlet temperatures of the test section. A differential pressure transducer was used to measure the pressure drop along the test section. The flow rate was regulated by the setting of the syringe pump, and was cross checked with a digital balance. All the data was recorded by a data logger every five seconds and the steady state data was used for calculating local heat transfer coefficients. The convective heat transfer instrumentation and its corresponding schematic diagram are shown in Figure 11. Also, Table 7 includes the important parameters of the screening setup.
Tabl e 7 : Impo r t an t p arame t e r s f o r s c r e en in g s e t u p
Parameters Screening setup
Pipe (material, din, and t) SS, 0.50 mm, 0.15 mm
Length of entrance, heating
section
50 mm, 300 mm
Temperature recording: wall,
inlet, outlet
All with thermocouples: 10 T–type (0.5 x 0.8 mm) for the wall, 1
T–type (0.5 x 0.8 mm) for the inlet and the outlet
Type of heater and power DC, 200 W
Type and thickness of
insulation
Armaflex foam (with k ≤ 0.036 W/mK), 30 mm
Heat loss* from the system Less than 15%
Pump Syringe pump (Legato 200 KDS, USA) with maximum liner
force of 34 kg and two 140 ml syringes
Differential pressure transducer
GE UNIK 5000, 0 – 2 bar, UK
* defined as the difference between the supplied electrical power (𝑉𝐼) and the measured thermal
energy (�̇�𝐶𝑝∆𝑇)
36
Figu r e 11 : S c h emat i c d i ag r am o f t h e s c r e en in g s e t up h e a t t r an s f e r me asu r emen t i n s t r umen t [103] [ 84]
4 . 3 . 2 C o n v e c t i v e t e s t s e t u p , c l o s e d – l o o p
A closed–loop system was used to perform forced convective experiments in laminar and turbulent flow. Generally it took much longer to perform experiments in the closed–loop compared to the screening setup, and a larger volume of NF was required. The test section had an entrance region in order to make the flow hydro–dynamically developed, a heated section where the wall temperatures were measured, and a mixing section in order to mix the fluid properly before measuring the temperature at the end of the test section. The test sections were heated by a DC power supply; in addition, 21 thermocouples determined the temperatures on the wall, as well as in the fluids at the inlet and the outlet. Furthermore, the test setup included a gear pump, a coriolis flow–meter, and a cooling jacket to cool down the
37
working fluid and adjust the temperature at the inlet of the test section. 250 – 280 ml of fluid was needed to run the experiments. The pressure drop over the test section, including the inlet section, was measured by a differential pressure transducer. Data acquisition units were used to collect and send the data (temperatures, pressure difference, mass flow rates and densities) to the computer when the system had reached steady state conditions. For each steady state condition the data was recorded every three seconds for about five minutes and averaged. Figure 12 shows the schematic diagram and Table 8 summarises important parameters for convective closed–loop heat transfer measurement instrumentation.
To ensure the accuracy of the measurement data, some of the measurements were repeated in a similar convective closed–loop at UBHAM. The details for this setup are reported by Utomo et. al. [104].
Tabl e 8 : Impo r t an t p arame t e r s f o r c o nv e c t i v e c l o s e d – l o o p
Parameters Convective closed–loop
Pipe (material, din, and t) SS, 3.70 mm, 1.5 mm
Length of entrance, heating,
and mixing sections
250* mm, 1468 mm, 80 mm
Temperature recording: wall,
inlet, outlet
All with thermocouples: 16 T–type (0.6 x 1.0 mm) for the wall, 2
and 3 T–type (0.5 mm) for the inlet and the outlet respectively
Type of heater and power DC, 3000 W
Type and thickness of
insulation
Armaflex foam (with k ≤ 0.036 W/mK), 10 mm and fiberglass
insulation (with k = 0.035W/mK), 30 mm
Heat loss** from the system Less than 5%
Pump Gear pump (MCP–Z, Ismatec, Switzerland) with pump head
(170–000, Micropump, USA)
Flow–meter Coriolis mass flow meter (CMFS015 with 2700 transmitter,
Micromotion, Netherlands)
Cooling jacket 1.7m double pipe and a plate heat exchangers, plus small chiller
(180 W cooling capacity)
Differential pressure transducer
GE UNIK 5000, 0 – 2 bar, UK
* effective entrance length including a T-junction was 500 mm
** defined as the difference between the supplied electrical power (𝑉𝐼) and the measured thermal
energy (�̇�𝐶𝑝∆𝑇)
38
Figu r e 12 : S c h emat i c d i ag r am o f t h e c o nv e c t i v e c l o s e d–l o o p h e a t t r an s f e r me asu r emen t i n s t r umen t [104] [ 105]
4 . 4 S e d i m e n t a t i o n r a t e
The sedimentation balance method was used to evaluate sedimentation rate of NFs in this study. In this method, an accurate scale is used to measure the weight of solid content, which accumulates on a tray submerged in the colloid. The specific gravity of a sample in many digital lab scales is measured by a density determination kit. A density kit (Figure 13–a) was modified by attaching a bowl–shaped plate (tray) (Figure 13–b). The modified kit was immersed into a container including a NF and the sedimentation rate of the NF was measured while NPs were accumulating on the tray (Figure 13–c).
Figu r e 13 : ( a ) Or i g in a l d en s i t y k i t ; ( b ) mod i f i e d d e n s i t y k i t ; ( c ) me as u r i n g s e d imen t a t i o n r a t e o f n ano f l u i d s [ 106]
To perform these measurements, a highly accurate scale (Mettler–Toledo AX205 Delta Range) with readability of 0.01/0.1 mg (for maximum load of 81/220 g) and linearity of ±0.08/0.15 mg was used. The scale was
P
HD Developing Region
thermostat bath
Gear Pump
Tubular Heat Exchanger (THE)
Plate Heat Exchanger
DC Power Supply
Differential Pressure Sensor
Insulation
Glass tube
Tube Wall’s TCs
Discharge
Tap Water
Charge
Flow Meter
Blue: Plastic pipe
Bypass
Static mixer
Inlet test section TC Outlet test section TC
39
connected to a computer using Mettler–Toledo balance software. To reduce error resulting from evaporation, environmental temperature and humidity, the sample holder area was covered by a single–glazed transparent envelope. The sample holder containing the nanofluid was placed on the stand and the whole system was set on a vibration–free table. The rate of sedimentation was then recorded. Through this measurement, the weight of particles on the submerged tray can be related to the fraction of particles still dispersed in the NF. After a period of time (some hours, days or weeks), the rate of sedimentation reached zero; at this point, it could be assumed that the particles remaining in the fluid above the tray, if any, were stably dispersed. Two interesting factors result from use of this technique: the rate of sedimentation and the time at which no more NPs settled on the platform (critical sedimentation settling time or shortly settling time). These are the criteria used to judge the shelf stability of the NFs tested. In this study 150 ml of each sample was poured in the same beaker, and the modified density kit was located in place (Figure 14). The tray, which was submerged in the samples, was indirectly connected to the scale pin. Therefore, the scale continuously measured the weight of the settled particles on the tray. The weight was recorded every minute and the moving average method was used to dampen any stochastic variations in the measured data.
Figu r e 14 : Mod i f i e d d e n s i t y k i t t o mea su r e t h e s e d imen ta t i o n r a t e o f NFs [106]
4 . 5 M a t e r i a l c h a r a c t e r i s a t i o n
The NFs in this study were synthesised by different partners, and the NPs were provided from different sources. Scanning electron microscopy (SEM) analysis or transmission electron microscopy (TEM) was performed by other partners in the project to determine the morphology and dry size of particles. Generally TEM has much higher resolution than SEM; unfortunately, TEM is also a more expensive
40
technique. In this study, SEM analysis was done at KTH (Gemini Ultra 55, Zeiss, Germany) and TEM analysis was done at UBHAM (Jeol 2100, USA). For performing SEM analysis, a two ml portion of each colloid was dried in separate glass vials for eight hours at 60 – 80 ˚C. Hydrodynamic particle size analysis was performed by dynamic light scattering (DLS) both at KTH (Delsa Nano C, Beckman Coulter, USA) and UBHAM (HPPS, Malvern, UK). For DLS measurements all samples were diluted to at least 1 wt%. Furthermore, pH vales of the samples were measured and reported, and some information about the additives were revealed. Additives or surfactants are included in NF systems to stabilize them. However, sometimes neither their exact formula, nor the amounts added were known, as they were the intellectual property of the companies that synthesised the NFs.
4 . 6 S u m m a r y o f m a t e r i a l s a n d e x p e r i m e n t s
The table in Appendix A includes materials type, source, concentration, type of BFs, pH value, SEM or TEM particle size range, most common DLS particle size, additive type or amount; in addition, it includes an ID corresponding to each of these materials that is referred to in several parts of this study, the experiments and the paper related to these materials. Furthermore, in Appendix B, SEM or TEM micrographs, the DLS size distribution and the characteristics of NPs (thermal conductivity, density, and specific heat) are summarized.
41
5 Uncer tainty Analysis
5 . 1 T h e r m a l c o n d u c t i v i t y
The thermal conductivity of distilled water (DW) was measured successively 20 times (every five minutes) at 20 ˚C, 30 ˚C, 40 ˚C and 50 ˚C to check both the validity and the repeatability of the TPS method. Furthermore, the thermal conductivity of DW was also measured at 20 ˚C by the THW method at UBHAM. The THW method is prone to inducing natural convection at higher temperatures [94], and therefore it was not used to measure the thermal conductivity of coolants at elevated temperatures. The results are compared with the reference values from the International Association for the Properties of Water and Steam (IAPWS) [107] in Figure 15. Although the manufactures of both TPS and THW analyses state that the accuracy of their instruments are better than 5%, many of the experimental data are within 2% error compared to the data from IAPWS.
Figu r e 15 : The rma l c o n du c t i v i t y o f DW
To further check the accuracy and repeatability of the TPS method, the thermal conductivity of DW was measured at 20 ˚C 400 times successively (every five minutes) with two identical sensors (200 times with each one). The results are shown in Figure 16. The first 200 data points belong to one sensor, and the latter 200 belong to the other sensor. Almost all of the experimental data in Figure 16 are within 2%
0.550
0.570
0.590
0.610
0.630
0.650
0.670
0.690
0 20 40 60 80
k (W
/m.K
)
No. of Experiments
IAPWSIAPWS +/- 3%T=20 (KTH)T=20 (UBHAM)T=30 (KTH)T=40 (KTH)T=50 (KTH)
42
error compared with the data from IAPWS. Based on the results in Figure 15 and Figure 16 the uncertainty of measuring thermal conductivity of coolants is assumed to be 2%.
Figu r e 16 : The rma l c o n du c t i v i t y o f DW a t 20 ˚C
5 . 2 V i s c o s i t y
In order to check the validity of viscosity measurements, results for DW were compared with the reference values of IAPWS [108] and the results are shown in Figure 17. As the diagram shows, in the temperature range 5˚C – 30˚C the differences between the reference line and the experimental values are between 4 and 8%.
Figu r e 17 : V i s c o s i t y o f DW
0.57
0.58
0.59
0.6
0.61
0.62
0.63
0 100 200 300 400
k (W
/m.K
)
No. of Experiments
TPSIAPWSIAPWS +/- 2%IAPWS +/- 3%
0.50
0.70
0.90
1.10
1.30
1.50
1.70
1.90
0 5 10 15 20 25 30 35
Vis
cosi
ty (
cP)
T (˚C)
DWIAPWSIAPWS +/- 8%
43
However, the accuracy of the instrumentation was improved by further insulating the tubes and the connection between the thermostat bath and the sample holder. The instrument was validated again and the results, in addition to the experimental data from UBHAM (measured with similar method), are shown in Figure 18.
Figu r e 18 : V i s c o s i t y o f DW
To further check the accuracy and repeatability of the viscometer the viscosity of DW was measured at 20 ˚C successively 50 times (every three minutes). The results are shown in Figure 19. All of the experimental data points in this plot are within 4% error compared with the data from IAPWS.
Figu r e 19 : V i s c o s i t y o f DW a t 20 ˚C
0.50
0.70
0.90
1.10
1.30
1.50
10 20 30 40 50
μ (
cP)
T (ºC)
IAPWS
IAPWS +/- 4%
KTH
UBHAM
0.9
0.95
1
1.05
1.1
0 10 20 30 40 50
μ (
cP)
T (ºC)
DWIAPWSIAPWS +/- 4%
44
5 . 3 D e n s i t y a n d s p e c i f i c h e a t
The loop to measure convective heat transfer includes a coriolis mass flow meter (Table 8). This type of flow meter can be used to measure the density of working fluids. In order to check the validity of the coriolis mass flow meter and Eq. (1), the densities of DW and water-based NFs Al2O3 (ID: 4) and TiO2 (ID: 11) with 9 wt% solid particle concentration were measured at a controlled temperature of 20 ˚C. The difference between densities measured by the coriolis mass flow meter and the ones calculated from Eq. (1) is shown in Figure 20. Based on the results, Eq. (1) can be used to predict the density of NFs with accuracy better than 1% error.
Figu r e 20 : Di f f e r e n c e i n d en s i t i e s o f c o o l an t s me asu r e d by t h e c o r i o l i s mas s f l ow me t e r an d c a l cu l a t e d u s i n g Eq .
(1 )
A proper instrument for measuring specific heat of fluids was not accessible at KTH during the time of this study. However, the measurement values in some experimental studies agreed well with the theoretical prediction from using Eq. (2) [43], [58], [59], [60], [109], [110]. In this study the accuracy of estimating the specific heat from Eq. (2) is assumed to be 1%.
5 . 4 T e m p e r a t u r e s
Temperatures are important independent parameters necessary in calculating heat transfer coefficients. In this study different types of thermocouples were used (Table 7 and Table 8). The accuracies of the thermocouples were checked with the calibration bath (ISOTECH, 936 Hyperion Plus, UK) using the RTD probe 935–14–61/DB (with accuracy better than 0.005 ˚C). Figure 21 shows as an example the results
0.0
0.2
0.4
0.6
0.8
1.0
1.2
500 4500 8500 12500 16500
Dif
fere
nce
(%
)
Re (-)
DW Al₂O₃ TiO₂
45
of such a measurement. The bath was adjusted to 20 ˚C; however, the probe showed a slightly lower temperature (~19.92 ˚C). The temperatures for 21 thermocouples and the probe were then measured for 300 s. The differences between the values of thermocouples and the probe were within ± 0.1 ˚C. The accuracies of the thermocouples were checked in the temperature range 20 – 60 ˚C, and they were better than ± 0.08 ˚C [84] for 12 thermocouples used in the screening setup (Figure 11), and better than ± 0.2 ˚C [111] and ± 0.1 ˚C [104] for 21 thermocouples (from different batches) used for the closed–loop setup (Figure 12).
Figu r e 21 : Measu r emen t b y t h e rmo cou p l e s u s e d i n c l o s e d– l o o p s e t up
5 . 5 N u s s e l t n u m b e r a n d f r i c t i o n f a c t o r
The average Nusselt number of DW versus non–dimensional length for the screening test setup is shown in Figure 22. Most of the experimental points are within ± 15% of the Shah correlation. Moreover, the calculated friction factor for DW based on the measured pressure drop is shown in Figure 23; it is compared with the theoretical (Darcy) friction factor for fully developed laminar flow. The experimental points are within ± 10% of the expected values.
In the closed–loop, the Nusselt number for DW agrees with theoretical prediction within less than 10% for laminar flow [104] and 15% for turbulent flow [105]. The friction factor for DW is accurate within 20% in laminar flow [104] and 10% in turbulent flow [105].
19.75
19.80
19.85
19.90
19.95
20.00
20.05
20.10
0 100 200 300
T (˚
C)
t (s)
T1T2T3T4T5T6T7T8T9T10T11T12T13T14T15T16T17T18T19T20T21TrefTref +/- 0.1
46
Figu r e 22 : Av e ra g e Nu s s e l t n umb e r f o r DW
Figu r e 23 : Fr i c t i o n f a c t o r f o r DW
5 . 6 E r r o r p r o p a g a t i o n
A parameter is usually a function of several variables. The uncertainty of that parameter depends on the uncertainties of those variables. For
example, if z is a function of several independent variables 𝑥𝑖, each with
their own uncertainties ∆𝑥𝑖, the overall uncertainty in z is [112]:
∆𝑧 = ±√∑ (𝜕𝑓
𝜕𝑥𝑖)2
𝑛𝑖=1 (∆𝑥𝑖)
2 (24).
The expanded uncertainty is obtained by multiplying the overall
uncertainty with the coverage factor 𝜉:
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.000 0.050 0.100 0.150 0.200 0.250 0.300
Nu
L*
Shah
Shah +/- 15%
DW
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
200 400 600 800 1000 1200
f
Re
DW
Darcy
Darcy +/- 10%
47
∆𝑍 = 𝜉𝛥𝑧 (25);
for 𝜉 = 2 the expanded uncertainty represents 95% confidence. By assuming the uncertainty of independent parameters (Table 9a), the maximum uncertainty of dependent parameters (with 95% confidence) can be calculated (Table 9b). Based on the results the uncertainty of dependent parameters for the closed–loop (Figure 12) are generally lower than the screening setup (Figure 11).
Tabl e 9 : Unc e r t a in t i e s f o r impo r t an t p ar ame t e r s
Independent parameters
Uncertainty
SS(1) CL(2)
L ± 1 mm ± 1 mm D ± 0.01 mm ± 0.01 mm k 2% 2% µ 4% 4% ρ 1% 1%
Cp 1% 1% T ± 0.08 ºC ± 0.1 ºC m 6%(3) 0.1%
ΔP(4) ± 0.0054 bar ± 0.0054 bar
(a)
Dependent parameters
Uncertainty (%)
SS CL
f 24 10(5) P 12 10(5) u 15 2
Re 18 7 h, local 16(6) 15
Nu, local 17(6) 16 h, average 11 6
Nu, average 12 7
(b) (1) Screening setup (2) Convective test setup, closed–loop (3) The accuracy of the digital balance was ± 0.01 g. (4) Given by the manufacturer (combining standard, zero offset and line pressure effect uncertainties) (5) For 70% of experimental data
(6) With 68% confidence 𝜉 = 1 in Eq. (25)
48
6 Summary of Results and Discussion
6 . 1 P a p e r s 1 , 2 a n d 3 : T h e r m o p h y s i c a l a n d t r a n s p o r t p r o p e r t i e s o f t h r e e N F s
The thermal conductivity, viscosity and its effect on pumping power in cooling systems were investigated in these papers [102], [103], [111]. Convective heat transfer in the screening setup (Figure 11) and the closed–loop (Figure 12) was also reported for water based Al2O3, TiO2, and ZrO2 NFs (all 9 wt%). These NFs had ID numbers 1, 8 and 13 (Appendix A).
The measured thermal conductivity of the NFs and the values predicted by Maxwell’s equation (Table 1) in the temperature range 20 – 50 ˚C are shown in Figure 24. The thermal conductivity of NFs increases with the temperature. However, in this temperature range the relative thermal conductivity (thermal conductivity compared to water) is almost independent of temperature, as shown in Figure 25. Based on the results, adding NPs to the BFs improves their thermal conductivity, but only by a few percent. The highest value is associated with Al2O3 and is around 7% at T = 20 ˚C (Figure 25). The Maxwell equation predicts experimental results within 3% error.
The rheological behaviour of the NFs was studied in the temperature range 5 – 30 ˚C by changing shear rates while measuring the viscosity of the samples. It was concluded that adding solid NPs up to 9 wt% does not change the Newtonian behaviour of the BF.
The viscosity and the relative viscosity of the NFs were measured in the temperature range 5 – 30 ˚C, and the results are shown in Figure 26 and Figure 27 respectively. The results show that the viscosity of the NFs decreased with increasing temperature. However, the relative viscosity in the temperature range 5 – 30 ˚C is the same. The TiO2 NF has the lowest viscosity of the three tested NFs, though the reason for this observation is not completely clear.
49
Figu r e 24 : The rma l c o n du c t i v i t y o f t h e NFs ( a l l 9 w t%) [103]
Figu r e 25 : Re l a t i v e t h e rma l c o ndu c t i v i t y f o r t h e NFs ( a l l 9 w t%) [ 103]
The pressure drop ratio for a given geometry, with the same volume
flow rate for BF and NF, is equal to the ideal pumping power ratio Ω (Eq. 8). This ratio is shown in Figure 28 for the laminar flow (a) and the turbulent flow (b). As NFs are more viscous, their pumping power is always larger compared to that of the BF. The results show, as expected,
a higher value of Ω in the laminar flow region than in the turbulent flow region. This is because of the higher dependency of this factor on the relative viscosity (power of 1 compared to ¼ in Eq. 8). The average values of the ratio in this temperature range for Al2O3, ZrO2 and TiO2
0.550
0.570
0.590
0.610
0.630
0.650
0.670
0.690
10 20 30 40 50 60
k (W
/mK
)
T (ºC)
Distilled WaterAl2O3 (Exp)ZrO2 (Exp)TiO2 (Exp)Maxwell Eq. For Al2O3Maxwell Eq. For ZrO2Maxwell Eq. For TiO2
1.00
1.02
1.04
1.06
1.08
10 20 30 40 50 60
k r (
-)
T (ºC)
Al2O3ZrO2TiO2
50
NFs are 2.05, 1.98 and 1.31 in the laminar regime, and 1.26, 1.26 and 1.13 in the turbulent flow regime respectively.
Figu r e 26 : V i s c o s i t y o f t h e N Fs ( a l l 9 w t%) [102]
Figu r e 27 : Re l a t i v e v i s c o s i t y f o r t h e NFs ( a l l 9 w t%) [102]
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0 5 10 15 20 25 30 35
µ (
cP)
T (˚C)
Al2O3ZrO2TiO2
1.00
1.40
1.80
2.20
2.60
0 5 10 15 20 25 30 35
µr
(-)
T (˚C)
Al2O3ZrO2TiO2
51
( a )
(b )
F i g u r e 28 : The r a t i o b e tw e en i d e a l pumpi ng powe r w i t h and w i t ho u t NPs (Eq . 8 ) f o r NFs ( a l l 9 w t%) i n
l am inar ( a ) an d t u r bu l e n t f l o w ( b ) ( a t a g i v e n v o l ume f l o w r a t e ) [ 102]
The heat transfer coefficients in the screening setup were measured for water and NFs at different volume flow rates (10 – 30 ml/min). The experimental results of the three NFs and DW are compared with the Shah correlation (Eq. 14) in Figure 29. As is shown, the experimental data points at low Reynolds numbers are lower than the predicted values. Axial conduction is the main reason for this deviation as it causes to underestimate the heat flux at the inlet and overestimate it at the outlet, and thereby also under- and overestimate the heat transfer coefficients at these locations in the same way. Furthermore, non-laminar flow at the
0.00
0.50
1.00
1.50
2.00
2.50
0 5 10 15 20 25 30 35
Ωla
min
ar (
-)
T (˚C)
Al2O3
ZrO2
TiO2
0.00
0.50
1.00
1.50
2.00
2.50
0 10 20 30 40
Ω T
urb
ule
nt
(-)
T (˚C)
Al2O3ZrO2TiO2
52
inlet and ill-defined starting points for the heating are some other possible explanations for this difference.
Figu r e 29 : Nus s e l t numb e r v s . Re f o r DW and NFs
The pressure drops measured are used to calculate the friction factors. These friction factors are compared with the conventional friction factor for laminar flow (Eq. 4) in Figure 30. Based on the results for DW, TiO2 and Al2O3 NFs, the difference is within 10%. However for ZrO2 the difference is slightly greater. The friction factor calculated form Eq. 4 seems to be valid for NFs as well as for BFs.
Figu r e 30 : Exp e r ime n t a l v a l u e s f o r t h e f r i c t i o n fa c t o r f o r DW and t h e NFs c ompar e d w i t h t h e Dar c y f r i c t i o n
f a c t o r [ 103]
The average heat transfer coefficients for DW and the NFs in the screening setup are compared using different criteria in Figure 31
0
2
4
6
8
10
12
0 500 1000 1500 2000
Nu
(-)
Re (-)
Shah DW Shah TiO2Shah ZrO2 Shah Al2O3DW TiO2ZrO2 Al2O3
0.00
0.05
0.10
0.15
0.20
0.25
0 500 1000 1500 2000
f (-
)
Re (-)
DWTiO2ZrO2Al2O364/Re64/Re (+/-) 10%
53
(plotted versus Reynolds number in Figure 31–a, versus volume flow rate in Figure 31–b, versus mass flow rates in Figure 31–c, versus pressure drop in Figure 31–d and versus pumping power in Figure 31–e). To facilitate the interpretation of the data the results for DW (+/-) 10% are plotted in the same diagram.
The results demonstrate that the heat transfer coefficient at any given Reynolds number increases up to roughly 30% for Al2O3 and ZrO2 NFs, and up to around 10% for TiO2 NF. The NFs with higher viscosity (Al2O3 and ZrO2) show higher heat transfer coefficients at the same Reynolds number, as they need the higher flow velocity and thereby considerably higher pressure drop to achieve the same Reynolds number. Therefore this method of comparison is deceptive. Unfortunately, comparison at the same Reynolds number is very common in the literature in the field of NFs.
The differences between the heat transfer coefficients of DW and the tested NFs measured in the screening setup when compared at equal volume flow rates (Figure 31–b) or mass flow rates (Figure 31–c) are very small. The heat transfer coefficients of NFs when compared at equal pressure drop (Figure 31–d) or pumping power (Figure 31–e) are lower than those of DW. Therefore, these alternative presentations of the experimental results do not show any advantage from using NFs for cooling applications.
(a ) h v s R e yno l d s numbe r
3000
4000
5000
6000
7000
8000
9000
200 600 1000 1400 1800
h (
W/m
2 K)
Re (-)
TiO2ZrO2Al2O3DWDW (+/-) 10%
54
(b ) h v s v o lume f l ow r a t e
( c ) h v s mas s f l ow r a t e
3000
4000
5000
6000
7000
8000
9000
10.00 15.00 20.00 25.00 30.00 35.00
h (
W/m
2 K)
Q (ml/min)
TiO2ZrO2Al2O3DWDW (+/-) 10%
3000
4000
5000
6000
7000
8000
9000
0.500 1.000 1.500 2.000
h (
W/m
2 K)
m (kg/hr)
TiO2ZrO2Al2O3DWDW (+/-) 10%
55
(d ) h v s p r e s su r e d r o p
( e ) h v s pumpi ng powe r
F i g u r e 31 : Hea t t r an s f e r c o e f f i c i e n t h f o r DW and NFs c ompar ed w i t h d i f f e r en t c r i t e r i a [103]
The average heat transfer coefficients of DW and NFs were measured in the closed–loop (Figure 12) for a wide range of Reynolds numbers (150 – 8000), covering both the laminar and turbulent flow regimes. The results were compared with the conventional flow correlations - Shah for laminar flow (Eq. 14) and Gnielinski for turbulent flow (Eq. 15). Figure 32 shows the deviations from the classical correlations. Based on the results, the classical equations slightly over–predict NF heat transfer performance in laminar flow but under–predict it in turbulent flow. However, the deviation for most of the measured data is within ± 15 %.
3000
4000
5000
6000
7000
8000
9000
0.2000 0.4000 0.6000 0.8000 1.0000 1.2000
h (
W/m
2 K)
ΔP (Bar)
TiO2ZrO2Al2O3DWDW (+/-) 10%
3000
4000
5000
6000
7000
8000
9000
0.0 10.0 20.0 30.0 40.0 50.0 60.0
h (
W/m
2 k)
P (mW)
TiO2ZrO2Al2O3DWDW (+/-) 10%
56
It seems that the classical equations can be used to predict the heat transfer coefficients of the tested NFs with reasonable accuracy.
Figu r e 32 : Dev ia t i o n in t h e av e r a g e ex pe r imen t a l c o nv e c t i v e h ea t t r an s f e r c o e f f i c i e n t s f r om t h e p r e d i c t i o n s o f Shah ( l am inar f l ow ) and Gn i e l i n sk i ( t u r bu l e n t f l ow )
equa t i o n s [111]
The measured average convective heat transfer coefficients in the closed–loop are plotted versus Reynolds number for DW and NFs in Figure 33. The results show that in both laminar and turbulent flow regimes, the NFs have higher heat transfer coefficients compared with distilled water at any given Reynolds number. The greatest increase is found for Al2O3, which is the NF with the highest increase in viscosity.
The heat transfers coefficients for NFs and water measured in the closed–loop are shown versus pumping power in Figure 34. Based on the result at the same ideal pumping power, the heat transfer coefficients are clearly lower for NFs compared with DW. The lowest value corresponds to the NF with the highest viscosity (Al2O3).
In summary, based on the results of this section the Maxwell model predicted the thermal conductivity of NFs with acceptable accuracy. Moreover, the relative viscosity of NFs were much higher than their relative thermal conductivity. Furthermore, experiments in both the screening setup and the closed–loop showed classical correlations can be used to predict convective heat transfer of NFs similar to BFs.
-20
-15
-10
-5
0
5
10
15
20
0 2000 4000 6000 8000 10000
De
viat
ion
(%
)
Re (-)
DW
Al₂O₃
TiO₂
ZrO₂
(+/-) 15%
57
Figu r e 33 : h v s Re yno ld s n umbe r f o r wa t e r an d NFs [111]
Figu r e 34 : h v s pump in g pow e r f o r wa t e r an d NFs [111]
58
6 . 2 P a p e r 4 : C o o l i n g p e r f o r m a n c e o f N F s i n a s m a l l – d i a m e t e r t u b e
This article reports the measurement results for thermal conductivity, viscosity and convective heat transfer performance in laminar flow in the screening setup for five selected NFs with 9 wt% (Al2O3 (I), Al2O3 (II), TiO2 (I), TiO2 (II), CeO2). These NFs have IDs 2, 3, 9, 10, and 15 respectively (Appendix A). The preparation and characterisation of the NFs, as well as their thermophysical properties, are reported in details by Haghighi et al. [84].
Based on the results, the maximum difference between the measured thermal conductivity and the values predicted by the Maxwell model was 5.8%. Furthermore, the enhancement in thermal conductivity of the NFs compared to the BF was independent of temperature. The viscosity results also showed Newtonian behaviour for these NFs and a higher increase (compared to water) for viscosity (24 – 65%) than for thermal conductivity (2 – 6%).
The average Nusselt numbers versus the non–dimensional tube length (L*) for DW and the NFs are plotted in Figure 35; most of the results are within ± 15% of the Shah correlation (Eq. 14). Based on the pressure drop measured, the friction factors for DW and these NFs were calculated, and the results are shown in Figure 36. The difference between the experimental results and the theoretical (Darcy) friction factor (Eq. 4) for fully developed laminar flow is in the range of ± 15%. No unexpected behaviour for NFs was demonstrated, as the classical correlation for DW still predicts the data for the NFs.
Figu r e 35 : Av e ra g e Nu s s e l t n umb e r f o r d i s t i l l e d wa t e r an d NFs [84]
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.000 0.050 0.100 0.150 0.200 0.250 0.300
Nu
L*
Shah
Shah +/- 15%
DW
Al2O3 (I)
Al2O3 (II)
TiO2 (I)
TiO2 (II)
CeO2
59
Figu r e 36 : Fr i c t i o n f a c t o r f o r d i s t i l l e d wa t e r an d NFs [84]
Average heat transfer coefficients for NFs and DW are compared using different criteria: same Reynolds numbers, mass flow rates, inlet velocities, and pumping power. The average heat transfer coefficient of DW and NFs are shown in Figure 37–a (plotted vs. Reynolds number), Figure 37–b (vs. mass flow rate), Figure 37–c (vs. inlet velocity), and Figure 37–d (vs. pumping power). The straight dashed lines in these graphs, which are linear regression fits pass as accurately as possible through the DW data points to make interpretation of the results easier. Although at equal Reynolds numbers some increase can be seen for NFs, with few exceptions no enhancement in the heat transfer of these NFs can be observed through comparison with other factors. The results included a maximum enhancement of 11.2% at equal Reynolds numbers, 2% at the same mass flow rate, 4.9% at equal velocity and 3.9% at the same pumping power for these NFs. Again, the results show that NFs offer no advantage over water in laminar flow except when compared at the same Reynolds numbers, which is very common in the literature.
( a ) Ave r ag e h e a t t r an s f e r c o e f f i c i e n t v s Re yno ld s numb e r
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
200 400 600 800 1000 1200
f
Re
DW
Al2O3 (I)
Al2O3 (II)
TiO2 (I)
TiO2 (II)
CeO2
Darcy
Darcy +/- 15%
4000
4500
5000
5500
6000
6500
7000
200 400 600 800 1000 1200
h (
W.m
-2.K
-1)
Re
DW
Al2O3 (I)
Al2O3 (II)
TiO2 (I)
TiO2 (II)
CeO2
60
(b ) Ave r ag e h e a t t r an s f e r c o e f f i c i e n t v s mas s f l ow r a t e
( c ) Av e r ag e h e a t t r an s f e r c o e f f i c i e n t v s v e l o c i t y
(d ) Ave r ag e h e a t t r an s f e r c o e f f i c i e n t v s pump ing pow e r
F i g u r e 37 : Av e ra g e h e a t t r an s f e r c o e f f i c i e n t s f o r NFs and wat e r c ompar e d w i t h d i f f e r en t c r i t e r i a [84]
4000
4500
5000
5500
6000
6500
7000
0.5 0.7 0.9 1.1 1.3 1.5
h (
W.m
-2.K
-1)
m (kg/hr)
DW
Al2O3 (I)
Al2O3 (II)
TiO2 (I)
TiO2 (II)
CeO2
4000
4500
5000
5500
6000
6500
7000
0.5 1.0 1.5 2.0 2.5
h (
W.m
-2.K
-1)
V (m/s)
DW
Al2O3 (I)
Al2O3 (II)
TiO2 (I)
TiO2 (II)
CeO2
4000
4500
5000
5500
6000
6500
7000
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0
h (
W.m
-2.K
-1)
P (mW)
DW
Al2O3 (I)
Al2O3 (II)
TiO2 (I)
TiO2 (II)
CeO2
61
6 . 3 P a p e r 5 : H e a t t r a n s f e r i n l a m i n a r f l o w : c o m p a r i s o n o f r e s u l t s f r o m t w o u n i v e r s i t i e s
Heat transfer coefficients were investigated in straight tubes with constant heat flux at the wall in laminar flow for five water-based NFs with Al2O3 (ID: 4, 5), TiO2 (ID: 11, 12) and CNT3 NPs [104]. The main objective of this study was to clarify whether classical correlations for single phase fluids in laminar flow in standard close–loops (similar to practical applications) can be used to predict the heat transfer coefficients of NFs, or if the addition of NPs to BFs might improve the heat transfer coefficients of NFs over and above the predictions of these correlations. The heat transfer coefficients of identical NFs were measured independently in near-identical experimental setups4, in order to ensure the accuracy of experimental results, at the University of Birmingham, UK (UB) and at KTH. The heat transfer coefficients of NFs calculated from experimental data are compared with the values predicted by classical correlations at equal mass flow rate, velocity, Reynolds number, and pumping power. The materials synthesis and characterisation along with the thermophysical properties of these NFs were reported separately by Utomo et al. [104].
The Nusselt numbers calculated based on the experimental data are compared to the Shah correlation (Eq. 14), as shown in Figure 38 for water and the NFs. The experimental data from KTH agree very well with theoretical predictions; however, the experimental data from UB include slightly lower values. This might be because at KTH the heating section was longer than that in UB, and the first thermocouple was much closer to the inlet. Most of the experimental data points are in agreement with the Shah correlation for average Nusselt numbers within ± 10%.
The wall friction factors calculated from the pressure drop measured in the tube (only at the KTH setup) were compared with the classical correlation for liquids (Eq. 4) as shown in Figure 39. Most of the experimental data points are in agreement with the classical correlation for the friction factor within ± 20%. In this study, as the fluctuation of pressure drop data is rather large, when comparing the heat transfer coefficients at equal pressure drop, the pressure drops of water and NFs were calculated based on the theoretical friction factor (Eq. 4) to ensure the consistency of data treatment between UB and the KTH.
3 not included in the experiments done at the KTH, and therefore not covered here in detail
4 The setup at UB included a heated section (L = 1220 mm, din = 4.57 mm, and t = 0.89 mm), a pump, a flow meter and a cooler [104].
62
Figu r e 38 : Compar i s o n o f av e r ag e exp e r im en t a l Nus s e l t numbe r s (wa t e r an d N Fs ) t o t h e p r e d i c t i o n s o f t h e Shah
c o r r e l a t i o n f o r av e r ag e Nus s e l t numbe r s [ 104]
Figu r e 39 : Fr i c t i o n f a c t o r s o f wa t e r and N Fs [104]
The fact that the experimental data of all investigated NFs agree with the classical correlations (Eq. 4 and Eq. 14) suggests that the heat transfer coefficient and pressure drop enhancements of NFs relative to those of BF can be predicted based on these correlations if the correct thermophysical properties of NFs are used.
The comparisons of the average heat transfer coefficient enhancement of Al2O3 NF (NF with ID: 4 in Appendix A) calculated from experimental data and from the theoretical correlation (Eq. 14) at equal mass flow rate, average velocity, pumping power and Reynolds number are shown in Figure 40. The upper and lower limits are calculated based on the average thermophysical properties ± uncertainties. As shown,
63
nearly all experimental data agree with the theoretical predictions within the experimental uncertainty.
Figu r e 40 : Av e ra g e h e a t t r an s f e r c o e f f i c i e n t e nhan c em en t s o f ITN–AL 9 w t% (NF w i t h ID: 4 i n Append ix A ) a t e qua l mas s f l ow r a t e ( a ) , e q ua l v e l o c i t y ( b ) , e qua l pump in g
powe r ( c ) , e qua l Re y no l d s numbe r ( d ) [ 104]
6 . 4 P a p e r 6 : H e a t t r a n s f e r i n t u r b u l e n t f l o w : c o m p a r i s o n o f r e s u l t s f r o m t w o u n i v e r s i t i e s
This article investigates convective heat transfer with NFs in turbulent flow [105]. The thermal conductivity and viscosity of Al2O3 and TiO2 NFs (IDs: 4 and 12 respectively in Appendix A) at 20 and 40 ˚C were measured, and the results are summarised in Table 10. The thermal conductivity calculated from the Maxwell model (Table 1) is also shown in this table. The differences between the thermal conductivities measured at KTH and at UBHAM, and values calculated from the Maxwell model, are below 2%; however, viscosity differs by 5 – 12%. The relative thermal conductivity and viscosity of these NFs are summarised in Table 11. For almost all measurements, the differences between the KTH and UBHAM results are within experimental error (Table 9).
64
Tabl e 10 : The rma l c o n du c t i v i t y and v i s c o s i t y o f NFs a t T=20˚C ( a ) an d T=40˚C ( b )
T=20˚C k (Wm-1K-1) µ (cP)
Material KTH UBHAM Maxwell KTH UBHAM
Al2O3 0.642 0.638 0.641 1.225 1.074
TiO2 0.636 0.626 0.636 1.315 1.152
(a)
T=40˚C k (Wm-1K-1) µ (cP)
Material KTH UBHAM Maxwell KTH UBHAM
Al2O3 0.688 – 0.675 0.804 0.741
TiO2 0.672 – 0.670 0.865 0.821
(b)
Tabl e 11 : Re l a t i v e t h e rma l c o n du c t i v i t y an d r e l a t i v e v i s c o s i t y o f N F s a t T=20˚C ( a ) an d T=40˚C ( b )
T=20˚C krel µrel
Material KTH UBHAM Maxwell KTH UBHAM
Al2O3 1.072 1.070 1.070 1.186 1.110
TiO2 1.078 1.050 1.062 1.273 1.191
(a)
T=40˚C krel µrel
Material KTH UBHAM Maxwell KTH UBHAM
Al2O3 1.090 – 1.070 1.184 1.109
TiO2 1.062 – 1.062 1.274 1.230
(b)
Nusselt numbers as a function of Reynolds numbers at two inlet temperatures (25 ˚C and 40 ˚C) measured at the KTH and UBHAM for Al2O3 and TiO2 NFs, respectively, are shown in Figure 41 and Figure 42. In these figures, the theoretical values were obtained from Eq. (15) with densities, specific heats, and thermal conductivities calculated from Eqs. (1), (2) and the Maxwell model (Table 1) respectively. In addition, experimental viscosity values measured at KTH (Table 10) were used. The theoretical predictions of the UBHAM experiments are not shown in these figures for clarity, as the difference with respect to the KTH results was less than 3%. The results reveal that the differences between the experimental data and the Gnielinski correlation for most of the experimental data points are below 10%; however, for a few data points, the difference is higher but still below 20%.
65
The agreement with the Gnielinski correlation is better at the lower inlet temperature for both NFs than at higher temperature; however, the exact cause of this behaviour is not clear. In summary, the results show that the Gnielinski correlation can predict the Nusselt number for the tested NFs with accuracy better than 20% in the temperature range 25 – 40 ˚C. The Gnielinski correlation, according to the literature, predicts the Nu number of single phase fluids within ± 20% [113]. The results (Figure 41 and Figure 42) show that if the correct properties of the NFs are used, the heat transfer coefficients in NFs in turbulent flow can also be accurately predicted using the same correlation. This confirms that mechanisms such as NP migration due to Brownian motion or thermophoresis that are frequently used in literature to explain alleged NF heat transfer enhancement have a negligible effect on heat transfer in turbulent flow within pipes.
Friction factors calculated from the flow rate measured and the pressure drop along the KTH test section are compared with the values calculated with the Filonenko equation (Eq. 5), and the results are shown in Figure 43 as a function of Reynolds number for DW and NFs in the range 25 – 55 ˚C. Based on the results, at Reynolds number higher than 4000, the Filonenko equation (Eq. 5) can predict the friction factors with a maximum deviation of ± 10%. Again, the conventional equation developed for simple (single phase) fluids can be used to predict pressure drop for NFs if the correct thermophysical properties of the NFs are used.
66
(a )
(b )
F i g u r e 41 : Compar i s o n b e tw e e n t h e expe r ime n t a l and ca l cu l a t e d av e r ag e Nus s e l t numbe r s (Eq . 15 ) f o r A l 2O 3
NF a t 25 ˚C (a ) and 40 ˚C ( b ) [105]
0
20
40
60
80
2000 4000 6000 8000 10000
Nu
(-)
Re (-)
KTH (Al₂O₃)
UBHAM (Al₂O₃)
Gnielinski
Gnielinski +/- 10%
0
20
40
60
80
2000 4000 6000 8000 10000
Nu
(-)
Re (-)
KTH (Al₂O₃)UBHAM (Al₂O₃)GnielinskiGnielinski +/- 10%
67
(a )
(b )
F i g u r e 42 : Compar i s o n b e tw e e n t h e expe r ime n t a l and ca l cu l a t e d av e r ag e Nus s e l t numbe r s (Eq . 15 ) f o r T iO 2
NF a t 25 ˚C (a ) an d 40 ˚C ( b ) [105]
0
20
40
60
80
2000 4000 6000 8000 10000
Nu
(-)
Re (-)
KTH (TiO₂)UBHAM (TiO₂)GnielinskiGnielinski +/- 10%
0
20
40
60
80
2000 4000 6000 8000 10000
Nu
(-)
Re (-)
KTH (TiO₂)UBHAM (TiO₂)GnielinskiGnielinski +/- 10%
68
Figu r e 43 : Fr i c t i o n f a c t o r s ba s ed on expe r ime n t a l r e su l t s c ompar ed t o t h e F i l o n e nko e qua t i o n (Eq . 5 ) [105]
Convective heat transfer coefficients in TiO2 and Al2O3 NFs are compared with the heat transfer coefficient in DW at the same Reynolds numbers and at equal pumping power. However, only the results for Al2O3/Water NFs are shown in this section, as the results for the other NFs were identical. Figure 44 compares heat transfer coefficients at equal Reynolds numbers for Al2O3 NF with that of DW at 25 ˚C and 40 ˚C, whilst Figure 45 compares the heat transfer coefficient for these NFs at equal pumping power. In these graphs the Gnielinski correlation was used to calculate the theoretical values of the Nusselt numbers and heat transfer coefficients.
In both the KTH and UBHAM experiments, the heat transfer coefficients in the NF at the same Reynolds numbers are clearly higher than those in the BF (Figure 44). In the UBHAM experiments, however, the increase is slightly lower (4 – 8% in the UBHAM results compared to 10 – 15% in the KTH results).
The differences between measured and predicted heat transfer coefficients in NFs at equal pumping power are significantly lower (Figure 45) than the differences at equal Reynolds number (Figure 44) in both the KTH and UBHAM results.
Using the correct method for comparing the heat transfer performance of NFs with that of their BFs is obviously very important. Both the effects of heat transfer and pressure drop in the system must be taken into account at the same time. Therefore, the heat transfer coefficients in NFs must be compared with the heat transfer coefficient in BFs at equal pumping power. Comparing heat transfer coefficients of NFs and BFs at
0.02
0.03
0.04
0.05
0.06
4000 6000 8000 10000
f (-
)
Re (-)
KTH (DW)KTH (Al₂O₃) KTH (TiO₂)FilonenkoFilonenko +/- 10%
69
equal Reynolds numbers, although common in the literature, is misleading.
(a )
(b )
F i g u r e 44 : Chang e i n h e a t t r an s f e r c o e f f i c i e n t s f o r Al 2O 3 NF compar e d t o DW a t 25 ˚C ( a ) an d 40 ˚C ( b ) , a t
equa l Re [ 105]
-5
0
5
10
15
20
3000 4500 6000 7500 9000
Incr
eas
e (
%)
Re (-)
KTH (Al₂O₃)UBHAM (Al₂O₃)Theoretical prediction± 10%
-5
0
5
10
15
20
3000 4500 6000 7500 9000
Incr
eas
e (
%)
Re (-)
KTH (Al₂O₃)
UBHAM (Al₂O₃)
Theoretical prediction
± 10%
70
(a )
(b )
F i g u r e 45 : Chang e i n h e a t t r an s f e r c o e f f i c i e n t s f o r Al 2O 3 NF compar e d t o DW a t 25 ˚C ( a ) an d 40 ˚C ( b ) , a t
equa l pumpi ng powe r [ 105]
6 . 5 P a p e r 7 : A m e t h o d p r e d i c t i n g t h e c o o l i n g e f f i c i e n c y o f N F s c o m b i n i n g t h e e f f e c t o f p h y s i c a l a n d t r a n s p o r t p r o p e r t i e s
In this article, the measured thermal conductivity and viscosity of the NFs ITN–AL, EVO–AL, AA–AL, ITN–TI, EVO–TI, LEVASIL–SI, AA–CI (IDs: 4, 5, 6, 11, 12, 14, 16 respectively in Appendix A) are
-25
-20
-15
-10
-5
0
5
10
0 200 400 600 800 1000 1200
Incr
eas
e (
%)
P (mW)
KTH (Al₂O₃)UBHAM (Al₂O₃)Theoretical prediction± 10%
-25
-20
-15
-10
-5
0
5
10
0 200 400 600 800 1000 1200
Incr
eas
e (
%)
P (mW)
KTH (Al₂O₃)UBHAM (Al₂O₃)Theoretical prediction± 10%
71
analysed at various solid particle concentrations and temperatures [90]. The experiments were done at two universities (KTH and UBHAM) and the samples were taken from the same batch to ensure the accuracy of the measurements. Moreover, any advantage or disadvantage of replacing the BF with a selected NF is predicted analytically, considering both thermophysical and transport properties. The results are compared against three relevant factors (at the same Reynolds number, flow velocity, and pumping power), for both laminar and turbulent flow regimes.
6 . 5 . 1 T h e r m a l c o n d u c t i v i t y
The thermal conductivity of these NFs was measured at 20 ˚C independently at KTH and UBHAM. The results were compared with each other and with the Maxwell model (Table 1). The relative thermal conductivity of these NFs at concentrations 3 – 45 wt%, calculated from the data measured, are shown in Figure 46–a. Furthermore, the data is compared to the prediction of the Maxwell model (Figure 46–b). As expected, the NFs with higher particle concentrations have higher thermal conductivity (Figure 46–a). For almost all NPs concentrations, the ITN–AL NF showed the highest thermal conductivity compared to the BF in both the KTH and UBHAM measurements. The experimental results from KTH and UBHAM are in good agreement. Furthermore, the Maxwell model, with the exception of a few points, predicts the thermal conductivity of these NFs within ±10% error (Figure 46–b). Large differences in the thermal conductivity of the same material from different sources (particularly Al2O3 NFs) were observed. Different methods of synthesizing NPs and NFs, in addition to differences in additives and in crystal structure, might be the cause of this inconsistency.
The thermal conductivities of these NFs (all at 9 wt%) were measured at temperatures 20 ˚C, 30 ˚C, 40 ˚C and 50 ˚C at KTH in order to investigate the effect of temperature. The relative thermal conductivity versus temperature is shown in Figure 47–a, and the deviation of the measured values from the Maxwell model is depicted in Figure 47–b. The Maxwell model can predict the thermal conductivity of these NFs within ± 10% uncertainty, even at elevated temperatures. Very small increases in the thermal conductivity at higher temperatures could be due to stronger natural convection at higher temperatures (Figure 47–a). ITN–AL NF showed the highest thermal conductivity among these NFs.
72
(a )
(b )
F i g u r e 46 : Re l a t i v e t h e rma l c o ndu c t i v i t y o f NFs (3 – 45 w t%) a t 20 ˚C ( a ) c ompar e d w i t h t h e Maxwe l l mode l ( b )
[90]
1.0
1.1
1.2
1.3
1.4
1.5
1.6
0.0 10.0 20.0 30.0 40.0
kr-E
xp
wt.%
EVO-AL (KTH)EVO-AL (UBHAM)ITN-AL (KTH)ITN-AL (UBHAM)AA-AL (KTH)AA-AL (UBHAM)EVO-TI (KTH)EVO-TI (UBHAM)ITN-TI (KTH)ITN-TI (UBHAM)LEVASIL-SI (KTH)LEVASIL-SI (UBHAM)
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.0 1.1 1.2 1.3 1.4 1.5 1.6
kr-E
xp
kr-Maxwell
EVO-AL (KTH)EVO-AL (UBHAM)ITN-AL (KTH)ITN-AL (UBHAM)AA-AL (KTH)AA-AL (UBHAM)EVO-TI (KTH)EVO-TI (UBHAM)ITN-TI (KTH)ITN-TI (UBHAM)LEVASIL-SI (KTH)LEVASIL-SI (UBHAM)AA-CI (KTH)AA-CI (UBHAM)kr-Exp=kr-Maxwell(+/-) 10%
73
(a )
(b )
F i g u r e 47 : Re l a t i v e t h e rma l c o ndu c t i v i t y o f NFs (9 w t%) a t d i f f e r e n t t empe r a t u r e s (a ) c ompar e d w i t h t h e Maxwe l l
mode l (b ) [ 90]
1.00
1.05
1.10
1.15
10 20 30 40 50 60
kr-E
xp
T (˚C)
EVO-ALITN-ALAA-ALEVO-TIITN-TILEVASIL-SI
1.00
1.05
1.10
1.15
1.00 1.05 1.10 1.15
kr-E
xp
kr-Maxwell
EVO-ALITN-ALAA-ALEVO-TIITN-TILEVASIL-SIAA-CIkr-Exp=kr-Maxwell
74
6 . 5 . 2 V i s c o s i t y
The viscosity of all the NFs was measured at 20˚C independently at KTH and UBHAM, and the results are compared with each other and with the modified Krieger–Dougherty model (Table 2). The relative viscosity calculated from the measured data at concentrations 3 – 40 wt% is shown in Figure 48. The viscosity of the NFs increased with increasing particle concentration. For the ITN–TI NF, the experimental results at KTH were much higher (5.3 – 28.1%) than the results from the UBHAM experiments. This NF was treated by tip ultrasonication at UBHAM, probably explaining the difference. The data measured is compared with the modified Krieger–Dougherty model in Figure 48–a. The experimental results from KTH and UBHAM are in good agreement, and with the exception of a few points the modified Krieger–Dougherty model predicts the viscosity of these NFs within ± 10% error. It should be pointed out that the good agreement is achieved only after the fractal index (D) (in Table 2) was adjusted to fit the experimental data. For EVO–AL, ITN–AL, AA–AL, ITN–TI, EVO–TI, LEVASIL–SI and AA–CI the values of D were 2.4, 1.6, 1.9, 2.3, 1.8, 2.5 and 2.3 respectively.
The effect of temperature was investigated by measuring the viscosity of all the NFs (9 wt%) at temperatures 20 ˚C, 30 ˚C and 40 ˚C at UBHAM. The relative viscosity from the measured data at different temperatures is shown in Figure 49–a, and the experimental data is compared to the modified Krieger–Dougherty model in Figure 49–b. Based on the results, the modified Krieger–Dougherty model was able to predict the viscosity of the NFs within 10% error. Furthermore, temperature had no effect on the relative viscosity of the NFs. Relative viscosity from experiments ranged from 1.09 to 1.48, which is indeed in broader range than that generated by the thermal conductivity results (1.03 – 1.11). Again, the accuracy of the Krieger–Dougherty model in the present study depends heavily on the experimental determination of the fractal index.
75
(a )
(b )
F i g u r e 48 : Re l a t i v e dyn am i c v i s c o s i t y o f NFs (3 – 45 w t%) a t 20˚C ( a ) c ompar e d w i t h t h e mo d i f i e d KD mod e l
(b ) [ 90]
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.0 10.0 20.0 30.0 40.0
µr-
Exp
wt.%
EVO-AL (KTH)EVO-AL (UBHAM)ITN-AL (KTH)ITN-AL (UBHAM)AA-AL (KTH)AA-AL (UBHAM)EVO-TI (KTH)EVO-TI (UBHAM)ITN-TI (KTH)ITN-TI (UBHAM)LEVASIL-SI (KTH)LEVASIL-SI (UBHAM)AA-CI (KTH)AA-CI (UBHAM)
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
1.0 3.0 5.0 7.0
µr-
Exp
µr-KD
EVO-AL (KTH)EVO-AL (UBHAM)ITN-AL (KTH)ITN-AL (UBHAM)AA-AL (KTH)AA-AL (UBHAM)EVO-TI (KTH)EVO-TI (UBHAM)ITN-TI (KTH)ITN-TI (UBHAM)LEVASIL-SI (KTH)LEVASIL-SI (UBHAM)AA-CI (KTH)AA-CI (UBHAM)µr-Exp=µr-KD(+/-) 10%
76
(a )
(b )
F i g u r e 49 : Re l a t i v e v i s c o s i t y o f NFs (9 w t%) a t d i f f e r e n t t emp e ra t u r e s ( a ) c ompar e d w i t h t h e mo d i f i e d KD mode l
(b ) [ 90]
1.0
1.1
1.2
1.3
1.4
1.5
1.6
10 20 30 40 50
µ-r
el-
Exp
T (˚C)
EVO-ALITN-ALAA-ALEVO-TIITN-TILEVASIL-SIAA-CI
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.0 1.2 1.4 1.6
µ-r
el-
Exp
µ-rel-KD
EVO-ALITN-ALAA-ALEVO-TIITN-TILEVASIL-SIAA-CIµr-Exp=µr-KD(+/-) 10%
77
6 . 5 . 3 T h e e f f e c t o n t h e c r i t i c a l w a l l t e m p e r a t u r e
o f r e p l a c i n g B F w i t h N F
As stated in chapter 3 the hottest (critical) wall temperature at the outlet can be used to compare the cooling performances of nanofluids relative
to those of BFs. Therefore, λ was defined as the difference between the wall temperatures at the outlet with NF and with BF (Eq. 21). In an imaginary cooling loop (a straight tube heat sink, L = 1.5 m and d = 4
mm), the applicability of the derived equation for 𝜆 (Eq. 23) is demonstrated. Water is circulated as a coolant with an inlet temperature of 20 ˚C, and it is assumed that the flow is adjusted such that the temperature difference between the inlet and outlet is around 5 ˚C. The flow is assumed to be both hydro-dynamically and thermally fully developed. The average flow velocity for water is assumed to be 0.25 m/s for the laminar (Re ≈ 970), and 4 m/s for the turbulent (Re ≈ 15500) flow regimes. The heat dissipated as coolants pass through the uniformly heated tube is assumed to be 60 W for laminar flow and 1000 W for turbulent flow. ITN–AL NF is selected as a potential NF, due to its highest relative thermal conductivity (~10% at 9 wt%) and its lowest relative viscosity (~10% at 9 wt%), to replace the BF (water) in this
cooling system. The values for 𝜆 (Eq. 23) are calculated using three different bases of comparison: at equal Reynolds number, flow velocity, and pumping power. The thermophysical property ratios are calculated at 20 ˚C, and are assumed to be constant along the tube. For thermal conductivity and viscosity, experimental values from KTH are used; however, for density and specific heat, Eqs. (1) and (2) are used. The results are shown in Figure 50 for laminar flow and in Figure 51 for turbulent flow for ITN–AL NF with particle concentrations of 3 – 30 wt%.
The values for 𝜆, at the same Reynolds numbers, are positive (0.4 – 2.5 ˚C for laminar and 0.5 – 2.1 ˚C for turbulent flow); as a result, the critical wall temperature with NFs is lower than with BF. At equal flow velocity,
the 𝜆 value for laminar flow is also positive, but lower; the value ranges from 0.1 ˚C to 1.2 ˚C with solid particle concentrations of 3 – 30 wt%.
For turbulent flow, the 𝜆 value is between -0.1 ˚C and 0 ˚C. At equal
pumping power, for both laminar and turbulent flow, the values of 𝜆 are all negative and decrease with increasing particle concentration.
The reason for this discrepancy between the results for the three bases of comparison lies in the physical characteristics that give rise to them. For example, to compare the NF with the BF at equal Reynolds number, higher NF velocity should be used in the calculations to compensate for the higher viscosity of the NF compared to the BF. As such, this basis of comparison, which is common in the literature, is misleading - increasing
78
the velocity would be beneficial even without using a NF. At equal pumping power the thermal behaviour of the system is evaluated while considering the increased pressure drop caused by the viscosity increment. The flow regime also affects the thermal performance of the system. Based on the results, the NFs did not show any benefit in turbulent flow at equal flow rates or equal pumping power; however, in laminar flow, the NF demonstrated a maximum decrease of 1.2 ˚C (at equal flow velocity) in the critical wall temperature of the heat sink compared to the performance of water.
Figu r e 50 : Ca l c u l a t e d v a lu e f o r λ (Eq . 23 ) a t e q ua l Re yno l d s n umbe r , f l ow v e l o c i t y , pump ing pow e r ( l am inar
f l o w ) [ 90]
Figu r e 51 : Ca l c u l a t e d v a lu e f o r λ (Eq . 23 ) a t e q ua l Re yno l d s n umbe r , f l ow v e l o c i t y , pump ing pow e r
( t u r bu l e n t f l ow ) [ 90]
-1.0
0.0
1.0
2.0
3.0
0 5 10 15 20 25 30
λ (˚
C)
wt%
Equal Re
Equal V
Equal P
-1.0
0.0
1.0
2.0
3.0
0 5 10 15 20 25 30
λ (˚
C)
wt%
Equal Re
Equal V
Equal P
79
6 . 6 P a p e r 8 : S h e l f s t a b i l i t y o f N F s a n d i t s e f f e c t o n t h e r m a l c o n d u c t i v i t y
The shelf stability of NFs and its effect on thermal conductivity are investigated in this article [106]. Specifically, the shelf stability of the NFs with IDs 19, 20, 21, and 7 (in Appendix A), identified in the content and the graphs of this section respectively as clay (I), (II), (III) and Al2O3, is discussed in details. All the NFs were water-based with concentrations of 9, 9, 1.75, and 9 wt% respectively for clay (I), (II), (III) and Al2O3. The thermal conductivities of these NFs were also measured in order to illustrate the effect of shelf stability on this thermophysical property.
For around 12000 minutes (approximately eight days), the sedimentation rates for the clay NFs were measured. The results of these measurements are also compared with the results using the straightforward photography method. Figure 52–a and Figure 52–b show the sedimentation behaviour of these NFs for the entire study, and the first 1000 minutes respectively. As these graphs indicate, the total sedimentation during the 12000 minutes varies considerably between the clays. The difference is partially explained by the difference in particle density (Appendix B). Moreover, the sedimentation rate for all clays is below 0.002 gr/min after the first 200 minutes. Generally, these NFs (particularly clay (III)) have a tendency to sediment rapidly. Clay (III) required only 80 minutes (settling time - the time at which no more NPs settled accordingly the rate of sedimentation approaches zero) to sediment thoroughly. For Clay (I) and (II), the settling times were nearly 2500 and 1500 minutes respectively. For Clay (II), some sedimentation did occur in the subsequent 3500 minutes at a very low rate (less than 0.0002 gr/min).
As noted in Appendix B, the smallest hydro–dynamic particle size is found in Clay (III); based on Stokes’ Law (Eq. (24)), it should have the lowest sedimentation rate despite its highest density. The results, however, show the opposite regardless of its lower concentration. Comparing the most common hydro–dynamic particle size for Clays (I) and (II) from Appendix B (1420 nm and 490 nm respectively), and using different values for density (Appendix B), it is expected that the sedimentation rate for Clay (I) would be faster. Based on Stokes’ Law the sedimentation speed for Clay (I) should be roughly 1.7 times faster than that of Clay (II); however, the experiments show precisely the reverse (1.7 times slower). As a result, Stokes’ Law evidently cannot predict the sedimentation rate for these NFs, comparatively or quantitatively. Stokes’ Law does not take into account factors such as the effect of surfactants, concentrations, particle shapes and other time-dependent agglomerations. Furthermore, predicting viscous drag on irregular shapes
80
(the reasonably correct assumption for NFs due to their particle agglomeration/aggregation) is difficult, and might be another shortcoming of Stokes’ Law for predicting the sedimentation rate of NFs.
Figu r e 52 : S e d im en t a t i o n and s e d imen ta t i o n r a t e o f C l ay ( I ) , ( I I ) an d ( I I I ) NFs f o r t h e en t i r e exp e r im en t ( a ) an d
t h e f i r s t 1000 minu t e s ( b ) [106]
A digital camera was employed to carry out the photography method. The camera was adjusted to take photos of these three clay NFs samples every ten minutes. Figure 53 shows some selected photos from the first 40 hours, and Figure 54 is a photo of these samples after eight days. The photos in Figure 53, in agreement with the graphs in Figure 52, show Clay (II) has the slowest sedimentation rate, and Clay (III) the fastest. All the photographs, which were taken after the first five hours for Clay (I), show a transparent layer on top; the average agglomerated particle sizes were approximately 3 and 4.5 times bigger than Clays (II) and (III). However, for Clay (II) for the first 20 hours and for Clay (III) during the entire recording time, a murky layer is evident on top due to the presence of some small particles. These can be distinguished in SEM micrographs in Appendix B.
The obvious higher sediment volume of Clay (I) compared to Cay (II) in Figure 54, even with the same solid concentrations, might be because of
81
the different hydro–dynamic particle size and shape of Clay (I). Furthermore, the photo of the samples after eight days (Figure 54) and the curves for sedimentation behaviour (Figure 52) clearly demonstrate that Clay (III) had a much lower concentration.
Figu r e 53 : A s amp l e o f pho t o g r aphs o f C l ay ( I ) , ( I I ) an d ( I I I ) NFs a t t h e b e g inn in g ( a ) , a f t e r 30 m inu t e s (b ) , 1
hou r ( c ) , 5 hou r s ( d ) , 10 hou r s ( e ) , 20 hou r s ( f ) , 30 hou r s ( g ) an d 40 hou r s ( h ) o f meas u r emen t [106]
Figu r e 54 : A s amp l e o f pho t o g r aphs f o r o f C l ay ( I ) , ( I I ) an d ( I I I ) NFs a f t e r e i gh t d ay s [106]
82
The stability of Al2O3 NF was monitored for 25000 minutes (approximately 17 days), and the results are presented in Figure 55. The amount of sediment on the tray during the measurement varies from 0 to around 1.7 gr. Based on this result, the sedimentation rate for this NF is below 0.0002 gr/min (nearly ten times less than the rate for the clays in Figure 52). Moreover, the sedimentation rate decreases over time; this may be due to the reduction in the amount of bigger particles in the colloid. However, the exact settling time cannot be determined. Based on the results, the rate of sedimentation is quite small and nearly zero after around 20000 minutes (approximately 14 days). Even so, after this amount of time clear phase separation between solid and liquid was not observed. The experimental results, compared to what Stokes’ Law predicts, reveal a significantly lessened amount of time necessary for the complete settling of particles in this NF (600 minutes lower). Surface modification might be the reason for the high stability of this NF.
Figu r e 55 : S e d im en t a t i o n and s e d imen ta t i o n r a t e o f Al 2O 3 NF [ 106]
The thermal conductivity of Al2O3 NF (a NF with good shelf stability) and Clays (I), (II), and (III) (NFs with poor shelf stability) at 20˚C were measured every ten minutes by the TPS (Transient Plane Source)–analyser (Figure 9) for around 33 hours; the results are shown in Figure 56. Based on the results, the first measuring points reveal an increase of 5.9%, 7.9% and 4.2% for Clay (I), (II), and (III) NFs respectively. However, after nearly 130 minutes for Clay (I), 270 minutes for Clay (II) and 70 minutes for Clay (III), the values for the thermal conductivity of the NFs approached the constant value of 0.591 W/mK. This value is approximately 1% lower than the corresponding value of water [107], which is within the measurement error of 2% (Table 9). The results are in agreement with the results of the sedimentation rate measurements in Figure 52 and the results of the photography method in Figure 53.
On the contrary, as shown in Figure 56, the thermal conductivity of the Al2O3 NF shows only a negligible reduction in thermal conductivity during the entire experimental time. The average value of thermal
83
conductivity for Al2O3 NF is 0.645 W/mK, about 8% higher compared to the reference value of thermal conductivity of water as the base liquid at 20˚C [107].
Figu r e 56 : The rma l c o n du c t i v i t y o f C l ay ( I ) , ( I I ) , ( I I I ) NFs ( a ) , and A l 2 O 3 NF ( b ) [ 106]
6 . 7 O t h e r R e s u l t s
During the NanoHex project [1] many NFs were tested including water based Al2O3, TiO2, ZrO2, SiC, CeO2, SiO2, China clay, carbon black, CNT, Ag, diamond, and Fe2O3 and EG–water solution based Al2O3, TiO2, CeO2, Ag, and SiC (approximately 88 NFs in total). For most of the NFs the relative viscosity was higher than the relative thermal conductivity at the same temperature and loading. Furthermore, the Maxwell model could predict the thermal conductivity of all of these NFs within acceptable error. Despite a huge effort, only in one NF
system (SiC‐α in EG–water 50:50 wt%) did the thermal conductivity increase overcome the viscosity increase, which is briefly discussed in this section. Furthermore, the effect of particle size and surfactants on the thermal conductivity and viscosity of NFs are discussed.
6 . 7 . 1 S i C – α i n E G – w a t e r 5 0 : 5 0 w t %
SiC–α NPs were dispersed in an EG–water mixture (50-50 wt%) by an ultrasonication method. The average SEM and DLS size of the NPs were ~30 nm and ~50 nm [114] respectively. NFs with three different concentrations were prepared, the thermal conductivity and viscosity were measured at 20 °C and the results are shown in Table 12. As the relative viscosity is lower than the relative thermal conductivity, the results show some potential for EG based SiC–α NF. The thermal conductivity experiments for BF and NFs (out of the same batch) were repeated in three other laboratories belonging to the NanoHex project
84
partners (University of Birmingham, Division of Functional Materials (FNM) at KTH, and University of Twente) where instruments (Transient Hot Wire, KD2 Pro, USA in all cases) were available. These results are summarised in Figure 57. Moreover, the reference value for the BF [115], the average values, and prediction from the Maxwell model, all with 5% error bars, are shown in this figure. This showed varying enhancement values in different laboratories from 14% to 19% for NF with 9 wt% loading. The results confirmed the reproducibility of these results according to the 5% measurement error, which is applicable to most of the commercial instruments. Small differences in the results can be related to different handling and possibly time dependent agglomeration in different samples.
Tabl e 12 : The rma l c o n du c t i v i t y and v i s c o s i t y o f BF and NFs a t 20°C
Material k (Wm-1K-1) µ (cP) krel µrel
BF (EG–water 50:50 wt%) 0.378 3.923 ‐ ‐
SiC‐α (3 wt%) 0.409 4.190 1.082 1.068
SiC‐α (6 wt%) 0.429 4.360 1.135 1.111
SiC‐α (9 wt%) 0.450 4.520 1.190 1.152
Figu r e 57 : The rma l c o n du c t i v i t y o f BF (EG–wat e r
50 :50 w t%) and S iC–α NFs a t 20 °C
6 . 7 . 2 T h e e f f e c t o f p a r t i c l e s i z e
The effect of particle size on thermal conductivity and viscosity was investigated broadly in the NanoHex project [1]. For example, two NF systems: Al2O3 in EG–water 50:50 wt% and DW with different
0.3890.382
0.399
0.416
0.437
0.350
0.370
0.390
0.410
0.430
0.450
0.470
k (W
m-1
K-1
)
RefKTH–EnergyKTH–FNMUBHAMUTwenteAveMaxwell
85
hydrodynamic particle size were fabricated by Dispersia, one of the project partners. In the first NF system, NPs had diameters of 40 nm, 150 nm, and 250 nm and the results in terms of thermal conductivity and viscosity are shown in Table 13 and Figure 58. The experiments for thermal conductivity were cross-checked at University of Twente (UTwente) and the results are depicted in Figure 58 as well. The difference between the KTH and Utwente was within 4% error. In the second system, three Al2O3 water based NFs with hydro-dynamical diameters of 200 nm, 250 nm, and 300 nm were synthesised. The results for the thermal conductivity and viscosity are shown in Table 14 and Figure 59.
Based on the results, the effect of NP’s size on the thermal conductivity of NFs is small and the Maxwell model can still predict the values with an acceptable uncertainty. However, the difference in the viscosity by changing NP size are huge, changing from 10% to 40%. However, the trend corresponding to the particle size was different.
Tabl e 13 : The rma l c o n du c t i v i t y and v i s c o s i t y o f BF and Al 2O 3 -NFs ( a l l 9 w t%) a t 20 °C
Material k (Wm-1K-1) µ (cP) krel µrel
BF (EG–water 50:50 wt%) 0.378 3.923 ‐ ‐
NF (40 nm) 0.427 5.896 1.128 1.503
NF (150 nm) 0.416 5.244 1.101 1.337
NF (250 nm) 0.417 4.864 1.102 1.240
NF (Maxwell) 0.419 ‐ 1.108 ‐
Tabl e 14 : The rma l c o n du c t i v i t y and v i s c o s i t y o f BF and Al 2O 3 -NFs ( a l l 9 w t%) a t 20 °C
Material k (Wm-1K-1) µ (cP) krel µrel
BF (DW) 0.596 1.03 ‐ ‐
NF (200 nm) 0.622 1.446 1.645 1.404
NF (250 nm) 0.624 1.864 1.650 1.810
NF (300 nm) 0.626 1.730 1.657 1.680
NF (Maxwell) 0.641 ‐ 1.696 ‐
86
(a )
(b )
F i g u r e 58 : The rma l c o n du c t i v i t y ( a ) an d v i s c o s i t y ( b ) o f BF (EG–wat e r 50 :50 w t%) and Al 2O 3 -NFs ( a l l 9
w t%) a t 20 °C
0.340
0.360
0.380
0.400
0.420
0.440
0.460
k (W
m-1
K-1
)
KTHUTwenteMaxwell ±5%
2.000
3.000
4.000
5.000
6.000
µ (
cP)
87
(a )
(b )
F i g u r e 59 : The rma l c o n du c t i v i t y ( a ) an d v i s c o s i t y ( b ) o f BF (DW) and A l 2O 3 -NFs ( a l l 9 w t%) a t 20 °C
6 . 7 . 3 T h e e f f e c t o f s u r f a c t a n t
NFs generally are stabilised by adjusting pH and/or by addition of surfactants. The surfactants are organic compounds with hydrophobic tails and hydrophilic head groups added to NFs to improve their stability. Different surfactants and concentrations were used to optimise the NFs in the NanoHex project [1] including G-Arabic, sodium citrate, ATPMS, CTAB, PVP, DMF, ATPMS, SDS, and octysilane. Based on the results in general adding surfactants had negative effect as it caused increase in the viscosity and a decrease in the thermal conductivity. The
0.500
0.540
0.580
0.620
0.660
0.700
k (W
m-1
K-1
)
Maxwell ±5%
0.000
0.400
0.800
1.200
1.600
2.000
µ (
cP)
88
effect of octysilane on the thermal conductivity and viscosity of EG–water 50:50 wt% based Al2O3-NFs (all 9 wt%)is reported in this section.
The thermal conductivity and viscosity of samples without surfactant and with 1 wt%, and 3.5 wt% (g surfactant/g solid) surfactants were measured and the results are reported in Table 15 and Figure 60. Based on the results, 3.5 wt% octysilane as a surface modifier has slight reverse impact on the thermal conductivity of NFs; however, as the decrease is so small the Maxwell model can still predict the thermal conductivity of these NFs. In reverse, the effect of adding octysilane surfactant on the viscosity of NFs is huge. For example, adding 1 wt%, and 3.5 wt% surfactant increased the viscosity of NF by 27.5% and 138% respectively.
Tabl e 15 : The rma l c o n du c t i v i t y and v i s c o s i t y o f BF (EG–wat e r 50 :50 w t% ) and Al 2O 3 -NFs ( a l l 9 w t%) a t
20 °C
Material k (Wm-1K-1) µ (cP) krel µrel
BF (EG–water 50:50 wt%) 0.378 3.923 ‐ ‐
NF (w/o surfactant) 0.439 4.390 1.162 1.119
NF (1 wt% surfactant) 0.441 5.470 1.167 1.394
NF (3.5 wt% surfactant) 0.425 9.790 1.125 2.496
NF (Maxwell) 0.419 ‐ 1.108 ‐
89
(a )
(b )
F i g u r e 60 : The rma l c o n du c t i v i t y ( a ) an d v i s c o s i t y ( b ) o f BF (EG–wat e r 50 :50 w t%) and Al 2O 3 -NFs ( a l l 9
w t%) a t 20 °C
0.340
0.360
0.380
0.400
0.420
0.440
0.460
k (W
m-1
K-1
)
Maxwell ±5%
0.0
2.0
4.0
6.0
8.0
10.0
12.0
µ (
cP)
90
7 Conclusion and Future Work
Nanofluids (NFs) are fabricated by homogeneously dispersing solid nanoparticles (NPs) in base fluids (BFs). Due to an exponential increase in the heat flux of electronics and their miniaturisation, conventional cooling technologies (such as adding fins or extended surfaces) and common heat transfer fluids (usually using water, ethylene glycol, and oil) seem to have reached their performance limits. Improving the thermal qualities of common heat transfer fluids, as conceptually suggested by NFs, might be an answer to this bottleneck. A better heat transfer fluid is characterized by higher thermal conductivity and specific heat, and lower viscosity and density. Due to the characteristics of NPs (like higher thermal conductivity), adding NPs to common BFs essentially changes the thermophysical properties of BFs in either a positive (+) or a negative (-) way: thermal conductivity increases (+), viscosity increases (-), density increases (-), and specific heat decreases (-). The heat transfer coefficient depends not only on thermophysical properties but also on the geometry and flow regime. The effects of all of the thermophysical properties (not just one) must be taken into consideration while discussing the advantages or disadvantages of replacing NFs with BFs in cooling systems. Finally, the shelf stability of NFs, a very important parameter in practical applications, must be assessed carefully to avoid unwanted sedimentation in equipment, facilities, and piping. This comprehensive overview, unfortunately, was not covered by many studies in the NF field. In this respect, this thesis is a unique study with the aim of encouraging further research towards employing NFs in single phase flow for cooling applications.
The thermal conductivity of different NFs was measured in the temperature range of 20 to 50 ˚C, and with solid particle concentrations of 3 – 45 wt%. The results show that the Maxwell model, which was introduced 140 years ago, can predict thermal conductivity of most of the NFs tested within 10% uncertainty.
The viscosity of these NFs under the same experimental conditions was measured as well. The modified Krieger–Dougherty model can predict the viscosity of most of these NFs within 10% error; however, the
91
success of this model is highly dependent on knowing the ratio of aggregated to primary particles, as well as on an experimental determination of another variable called the fractional index. As such, viscosity is a more complicated property than thermal conductivity. For the same type of NPs, many other parameters - such as size, surface area, shape, production method and type and amount of surfactant - were proven to have small effect on thermal conductivity, but seem to be relevant for viscosity.
The heat transfer coefficients of several NFs were measured in both a screening setup (with the test section d = 0.5 mm and L = 30 cm) in laminar flow, and a convective closed–loop (with the test section d = 3.7 mm and L = 1.5 m) in both laminar and turbulent flow. It was found that when correct thermophysical properties, either from experiments or trustable models, are used, the classical correlations traditionally used for common fluids are still valid for NFs with acceptable error. For example,
the results show that the Shah correlation and friction factor (𝑓 =64/𝑅𝑒) in laminar flow are valid for NFs within 10 – 15% and 10 – 20% uncertainty, respectively. In turbulent flow, the Gnielinski correlation (for Nusselt number) and the Filonenko correlation (for friction factor) are valid for NFs within 20% and 10% uncertainty, respectively.
The relative thermal conductivity and the relative viscosity of the NFs were unchanged, even in elevated temperatures within the temperature range of this study. Furthermore, the convective heat transfer experiments at higher inlet temperature (40 ˚C) did not show results different than the ones observed at room inlet temperature (20 – 25 ˚C). Therefore, mechanisms such as nanoparticle migration due to Brownian motion or thermophoresis seem to have negligible effects on thermophysical and transport properties of NFs.
Choosing the appropriate method of comparing the convective heat transfer coefficients of the NFs to those of BFs is very important, and is the source of many contradictory results. In this study it is shown that comparing the results at the same Reynolds numbers, although the most popular method employed in the literature, is not relevant. To achieve the same Reynolds number, due to the higher viscosity for NFs, higher volumetric flow and therefore a higher pressure drop and pumping power are needed for NFs. This is not a relevant comparison from a practical point of view, as the heat transfer of any fluid can be increased by increasing the flow rate. This enhancement (at equal Reynolds number criterion), as such, cannot be due to the presence of NPs. The evaluation of the heat transfer performance of the NFs at equal pumping power is the most appropriate and correct approach from an industrial point of view. Based on this criterion, the experimental results of this
92
study show only a small benefit for some NFs in laminar flow for cooling applications. In turbulent flow, however, NFs evidenced no benefit at all. It seems that the positive results claimed in some of the literature should be attributed to a non–realistic basis of comparison (equal Reynolds number), or to using unproven equations for the thermal conductivity and viscosity of NFs.
To quickly check the feasibility of replacing BFs with NFs, a method of analysis was suggested based on the calculation of the highest wall temperature in a heat sink. This model also showed that the experiments in terms of no or very small benefit can be expected with NFs in cooling systems if the comparison is done at equal pumping power.
The applicability of the sedimentation balance method to analysing the sedimentation behaviour of NFs, which is an important parameter in real applications, was illustrated successfully. Much greater detail can be found from this method compared with the traditional photography method; as expected, the results are consistent with one another. Additionally, due to complexity in shape, structure and synthesis of NFs, Stokes’ Law - the traditionally accepted equation used to predict sedimentation rate for normal colloids - cannot be used for NFs.
Based on this study, the commercialisation of NFs for cooling applications is still a relevant question; some potential for improvement was observed. The focus of future research must move towards the material synthesis of NFs. Material scientists should make an effort to understand the effect of additives and NPs characteristics on the viscosity of NFs. They should try to reduce the viscosity increases experienced by BFs due to the addition of NPs. We believe that this is the key success factor necessary in future research to unlock the potential of NFs for cooling purposes.
93
8 Nomenclature
Roman
𝐴 cross sectional area, m2
𝐴𝑝 perimetrical area, m2
𝑎 radius of primary particles, m
𝑎𝑎 radius of aggregates, m
𝑐𝑝 specific heat capacity, J/(kgK)
𝑑 pipe diameter, m
𝑑𝑝 diameter of a spherical particle, m
𝑑𝑏𝑓 diameter of bf molecule , m
𝐷 fractal index, –
𝑓 friction factor, –
𝐺𝑧 Graetz number, (𝑅𝑒𝑃𝑟) (𝑥 𝑑⁄ )⁄
𝑔 gravitational constant, m/s2
ℎ heat transfer coefficient, W/(m2K)
𝐼 electric current, A
𝑘 thermal conductivity, W/(mK)
𝑘𝑙 thermal conductivity of nanolayer, W/(mK)
𝐿 length, m
94
𝐿∗ non–dimensional length, (𝐿 𝑑⁄ ) (𝑅𝑒𝑃𝑟)⁄
�̇� mass flow rate, kg/s
𝑁𝑢 Nusselt number, hd/k
𝑃𝑟 Prandtl number, (Cp μ)/k
𝑅𝑒 Reynolds number, (ρud)/μ
𝑅𝑒𝑝 Reynolds number based on NP Brownian
motion (Table 1), (ρu𝑑𝑝)/μ
∆𝑝 pressure drop, Pa
𝑄 heat flow, W
𝑞′′ heat flux, W/m2
𝑃 pumping power, W
𝑇 temperature, ˚C
𝑡 thickness, mm
𝑉 electric voltage, V
𝑢 velocity, m/s
∀̇ volume flow rate, m3/s
𝑥 axial direction, m
𝑥∗ non–dimensional length, (𝑥 𝑑⁄ ) (𝑅𝑒𝑃𝑟)⁄
BF base fluid
DC direct electric current
DW distilled water
EG ethylene glycol
EMT Effective medium theory
95
Exp expermental
HC Hamilton and Crosser
IAPWS International Association for the Properties of Water and Steam
KTH Kungliga Tekniska Högskolan
N/A not available
NF nanofluid
NP nanoparticle
SS stainless steel
UBHAM, UB University of Birmingham
WP work package
vol volume
wt weight
Greek
𝛼 thermal diffusivity, m2/s
𝛿 nanolayer thickness, nm
𝜌 density, kg/m3
𝜆 temperature difference, °C
𝜇 dynamic viscosity, cP
𝜈 kinematic viscosity, m2/s
∅ solid particle volume concentration, –
∅𝑚 maximum particle packing fraction (Table 2), –
𝜓 particle sphericity, –
96
Subscripts
𝑒𝑓𝑓 effective
𝑓 fluid
𝑠 surface
𝑤 wall
𝑖𝑛 inner
𝑜𝑢𝑡 outer
𝑝 nanoparticle
𝑥 axial direction, m
𝑎𝑣𝑒 average
97
9 Appendix A
This appendix contains information about materials type, source, concentration, type of BFs, pH value, SEM or TEM particle size range, most common DLS particle size, additive type or amount, and an ID corresponding to each of these materials, and the paper related to these materials.
98
ID NFs’ source Solid
concentration (wt%/vol%)
BF pH SEM or TEM
particle size (nm) Most common DLS particle size (nm)
Additives, type and/or amount (g surfactant/g
solid) Experiments Paper No.
Alumina
1 Dispersia Ltd, UK 9 / 2.4 DW* 3.6 20 68 No info TC1, Visc2, HTC/S3, HTC4 1, 2 , 3
2 Dispersia Ltd, UK 9 / 2.4 DW 5 ~ 10 180 Polyacrylic acid copolymer
sodium salt (0.5 %) TC, Visc, HTC/S 4
3 Dispersia Ltd, UK 9 / 2.4 DW 5 ~ 10 60 No additives TC, Visc, HTC/S 4
4 ItN Nanovation, Germany 3 – 40 / 1 – 14 DW 9.1 100 – 200 200 1.5% – 1.8% TC, Visc 5, 6, 7
5 Evonik (Aerodisp 440) 3 – 40 / 1 – 17 DW 4.1 10 – 20 150 1.4 % TC, Visc 5, 7
6 Alafa Aesar (Nanodur X1121W) 3 – 40 / 1 – 14 DW 4.0 10 – 80 160 12.7 % TC, Visc 7
7 ItN Nanovation, Germany 9 / 2.4 DW No info 40 – 200 220 No info Shelf Stability 8
Titania
8 ItN Nanovation, Germany 9 / 2.3 DW 8.1 20 – 30 160 Ammonium polyacrylate TC, Visc, HTC (Sc), HTC 1, 2 , 3
9 Dispersia Ltd 9 / 2.3 DW 8 20 – 30 145 polyacrylic acid ammonium
salt (0.5 %) TC, Visc, HTC/S 4
10 ItN Nanovation 9 / 2.3 DW 7.4 20 – 25 170 polyacrylic acid ammonium
salt (10.45 %) TC, Visc, HTC/S 4
11 ItN Nanovation 3 – 20 / 1 – 6 DW 7.8 15 – 50 220 nm or
140 nm (ultrasonicated)
20.8 % TC, Visc 5, 7
12 Evonik (Aerodisp W740X) 3 – 40 / 1 – 15 DW 6.7 15 – 50 130 3.0 % TC, Visc 5, 6, 7
Zirconia
13 ItN Nanovation, Germany 9 / 1.7 DW 8.1 30 – 40 237 Ammonium polyacrylate TC, Visc, HTC (Sc), HTC 1, 2 , 3
Silica
14 Eka Chemical Levasil 100 3 – 45 / 1 – 27 DW 10 30 nm spherical 90 0 % TC, Visc 7
Ceria
15 Nano Grade, Switzerland 9 / 1.3 DW 7 –8 50 – 100 200 No additives TC, Visc, HTC/S 4
16 Alfa Aesar (Nanotek CE6042) 3 – 20 / 0.5 – 3 DW 2.5 30 nm (cubic) 160 0.5 % TC, Visc 7
17 KTH–Lab–01 1&2 / 0.2&0.3 EG No info 10 – 50 45 No additives Shelf Stability 8
18 KTH–Lab–02 9 / 1.4 EG–DW (50% Vol)
No info 10 – 50 45 No additives Shelf Stability 8
Clay
19 Clay I (CPI, UK) 9 / 3.8 DW 8 – 8.5 20 – 40** 1420 No info Shelf Stability 8
20 Clay II (CPI, UK) 9 / 2.7 DW 8 – 8.5 40 – 400 490 No info Shelf Stability 8
21 Clay III (ItN Nanovation, Germany) 1.75 / 0.4 DW 7 80 – 250 320 No additives Shelf Stability 8
* distilled water ** normal to the elongated direction 1: thermal conductivity, 2: viscosity, 3: screening setup, 4: convective test setup, closed–loop
99
10 Appendix B
ID NFs SEM or TEM DLS
Alumina
1 Dispersia Ltd, UK
k = 36 W/mK, ρ = 3970 kg/m3, Cp = 0.765 kJ/kgK [7]
2 Dispersia Ltd, UK
k = 36 W/mK, ρ = 3970 kg/m3, Cp = 0.765 kJ/kgK [7]
3 Dispersia Ltd, UK
k = 36 W/mK, ρ = 3970 kg/m3, Cp = 0.765 kJ/kgK [7]
0 100 200In
ten
sity
(a.
u)
Diameter (nm)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 250 500 750
Dif
f. In
ten
sity
(%
)
Diameter (nm)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 75 150 225
Dif
f. In
ten
sity
(%
)
Diameter (nm)
100
4 ItN Nanovation,
Germany
k = 36 W/mK, ρ = 3970 kg/m3, Cp = 0.765 kJ/kgK [7]
5 Evonik (Aerodisp
440)
k = 36 W/mK, ρ = 3270* kg/m3, Cp = 0.765 kJ/kgK [7]
6 Alafa Aesar (Nanodur
X1121W)
k = 36 W/mK, ρ = 3970 kg/m3, Cp = 0.765 kJ/kgK [7]
7 ItN Nanovation,
Germany
k = 36 W/mK, ρ = 3970 kg/m3, Cp = 0.765 kJ/kgK [7]
0
5
10
15
20
25
0 500
Inte
nsi
ty (
%)
Diameter (nm)
0
5
10
15
20
0 500In
ten
sity
(%
)Diameter (nm)
0
5
10
15
0 200 400
Inte
nsi
ty (
%)
Diameter (nm)
0
2
4
6
8
10
0 200 400 600
%In
ten
sity
Diameter (nm)
101
Titania
8 ItN Nanovation,
Germany
k = 8.4 W/mK, ρ = 4157 kg/m3, Cp = 0.710 kJ/kgK [7]
9 Dispersia Ltd
k = 8.4 W/mK, ρ = 4157 kg/m3, Cp = 0.710 kJ/kgK [7]
10 ItN Nanovation
k = 8.4 W/mK, ρ = 4157 kg/m3, Cp = 0.710 kJ/kgK [7]
11 ItN Nanovation
k = 8.4 W/mK, ρ = 4157 kg/m3, Cp = 0.710 kJ/kgK [7]
0 500 1000 1500
Inte
nsi
ty (
a.u
)
Diameter (nm)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0 200 400 600In
ten
sity
(%
)Diameter (nm)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
0 250 500
Inte
nsi
ty (
%)
Diameter (nm)
0
5
10
15
0 500
Inte
nsi
ty (
%)
Diameter (nm)
102
12 Evonik (Aerodisp
W740X)
k = 8.4 W/mK, ρ = 3800* kg/m3, Cp = 0.710 kJ/kgK [7]
Zirconia
13 ItN Nanovation,
Germany
k = 2* W/mK, ρ = 5680* kg/m3, Cp = 0.418* kJ/kgK
Silica
14 Eka Chemical Levasil
100
k = 1.38 W/mK, ρ = 2220 kg/m3, Cp = 0.745 kJ/kgK [7]
Ceria
15 Nano Grade, Switzerland
k = 12 W/mK, ρ = 7220 kg/m3, Cp = 0.460 kJ/kgK [116]
0
5
10
15
0 500
Inte
nsi
ty (
%)
Diameter (nm)
0 250 500 750
Inte
nsi
ty (
a.u
)
Diameter (nm)
0
5
10
15
0 500
Inte
nsi
ty (
%)
Diameter (nm)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 250 500 750
Inte
nsi
ty (
%)
Diameter (nm)
103
16 Alfa Aesar (Nanotek
CE6042)
k = 12 W/mK, ρ = 7220 kg/m3, Cp = 0.460 kJ/kgK [116]
17 KTH–Lab–01
18 KTH–Lab–02
k = 12 W/mK, ρ = 7220 kg/m3, Cp = 0.460 kJ/kgK [116] Clay
19 Clay I (CPI, UK)
k = N/A W/mK, ρ = 2530* kg/m3, Cp = N/A kJ/kgK
20 Clay II (CPI, UK)
k = N/A W/mK, ρ = 3500* kg/m3, Cp = N/A kJ/kgK
0
5
10
15
20
-100 100 300 500
Inte
nsi
ty (
%)
Diameter (nm)
0
1
2
3
4
5
6
0 50 100 150 200
Inte
nsi
ty (
%)
Diameter (nm)
0
1
2
3
4
5
0 2000 4000 6000
Inte
nsi
ty (
%)
Diameter (nm)
0
2
4
6
8
10
0 200 400 600 800
Inte
nsi
ty (
%)
Diameter (nm)
104
21 Clay III (ItN Nanovation, Germany)
k = N/A W/mK, ρ = 4000* kg/m3, Cp = N/A kJ/kgK
* stated by the manufacturer
0
2
4
6
8
10
12
0 200 400
Inte
nsi
ty (
%)
Diameter (nm)
105
11 References
[1] NanoHex (Enhanced Nanofluid Heat Exchange), EU project, FP7, grant agreement 22882, 2010-2013.
[2] S. K. Das, S. U. S. Choi, W. Yu, and T. Pradeep, Nanofluids - Science and Technology.: John Wiley & Sons, 2008.
[3] Masuda, H.; Ebata, A; Teramae, K.; Hishinuma, N., "Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles. Dispersion of Al2O3, SiO2 and TiO2 Ultra-Fine Particles," Netsu Bussei, vol. 7, no. 4, pp. 227-233, 1993.
[4] S. U. S Choi and J. A. Eastman, "Enhancing thermal conductivity of fluids with nanoparticles," in International mechanical engineering congress and exhibition, 12-17 Nov, San Francisco, CA, 1995.
[5] Eastman, J. A.; Choi, S. U. S.; Li, S.; Yu, W.; Thompson, L. J., "Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles," Appl. Phys. Lett., vol. 78, pp. 718-720, 2001.
[6] Ding, Y.; Alias, H.; Dongsheng W.; Williams, R. A., "Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids)," Int. J. Heat Mass Transf., vol. 49, pp. 240–250, 2006.
[7] Bergman, T. L.; Lavine, A. S.; Incropera, F. P.; DeWitt, D. P., Fundamentals of Heat and Mass Transfer.: John Wiley & Sons, Inc., 2011.
[8] Maxwell, J. C., A treatise on electricity and magnetism. Oxford: Clarendon Press, 1873.
[9] "Berechnung Verschiedener Physikalischer Konstanten von Heterogenen Substanzen, I. Dielektrizitatskonstanten und Leitfahigkeiten der Mischkorper aus Isotropen Substanzen,"
106
Annalen der Physik, vol. 24, pp. 636–679, 1935.
[10] Hamilton, R. L. ; Crosser, O. K., "Thermal conductivity of heterogeneous two component systems," I&EC Fundamentals, vol. 1, pp. 187-191, 1962.
[11] Wang, B. X.; Zhou, L. P.; Peng, X. F., "A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles," Int. J. Heat Mass Transf., vol. 46, pp. 2665–2672, 2003.
[12] Nan, Ce-Wen; Birringer, R.; Clarke, D.R.; Gleiter, H., "Effective thermal conductivity of particulate composites with interfacial thermal resistance," J. Appl. Phys., vol. 81, no. 10, pp. 6692-9, 1997.
[13] Kumar, D. H.; Patel, H. E.; Kumar, V. R. R.; Sundararajan, T.; Pradeep, T.; Das, S. K., "Model for heat conduction in nanofluids," Phys Rev Lett, vol. 93, pp. 144301-1-4, 2004.
[14] Jang, S. P.; Choi, S. U. S., "Role of Brownian motion in the enhanced thermal conductivity of nanofluids," Appl. Phys. Lett., vol. 84, pp. 4316-4318, 2004.
[15] Prasher, R.; Bhattacharya, P.; Phelan, P. E., "Thermal conductivity of nanoscale colloidal solutions (nanofluids)," Phys. Rev. Lett., vol. 94, pp. 025901-1–025901-4.
[16] Yu, W.; Choi, S. U. S., "The role of interfacial layers in the enhanced thermal conductivity of nanofluids: A renovated Hamilton-Crosser model," J. Nanoparticle Res., vol. 6, pp. 355-361, 2004.
[17] Murshed, S. M. S.; Leong, K. C.; Yang, C., "Investigations of thermal conductivity and viscosity of nanofluids," Int J Therm Sci, vol. 47, pp. 560–568, 2008.
[18] Kang, H. U.; Kim, S. H.; Oh, J. M., "Estimation of thermal conductivity of nanofluid using experimental effective particle volume," Exp. Heat Transf., vol. 19, pp. 181-191, 2006.
[19] Shaikh, S.; Lafdi, K.; Ponnappan, R., "Thermal conductivity improvement in carbon nanoparticle doped PAO oil: An
107
experimental study," J Appl Phys, vol. 101, p. 064302, 2007.
[20] Buongiorno, J. et al., "A benchmark study on the thermal conductivity of nanofluids," J. Appl. Phys., vol. 106, p. 094312, 2009.
[21] Timofeeva, E. V.; Gavrilov, A. N.; McCloskey, J. M.; Tolmachev, Y. V.; Sprunt, S.; Lopatina, L. M.; Selinger, J. V., "Thermal conductivity and particle agglomeration in alumina nanofluids: experiment and theory," Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. , vol. 76, p. 061203, 2007.
[22] Wong, K. F. V.; Kurma, T., "Transport properties of alumina nanofluids," Nanotechnol., vol. 19, p. 345702, 2008.
[23] Bhattacharya, P.; Saha, S. K.; Yadav, A.; Phelan, P. E.; Prasher, R. S., "Brownian dynamics simulation to determine the effective thermal conductivity of nanofluids," J Appl Phys, vol. 95, pp. 6492–6494, 2004.
[24] Xuan, Y.; Li, Q.; Hu, W., "Aggregation structure and thermal conductivity of nanofluids," AIChE J., vol. 49, pp. 1038–1043, 2003.
[25] Xue, Q.; Xu, W. M., "A model of thermal conductivity of nanofluids with interfacial shells," Mater. Chem. Phys., vol. 90, pp. 298–301, 2005.
[26] Xie, H.; Fujii, M.; Zhang, X., "Effect of interfacial nanolayer on the effective thermal conductivity of nanoparticle-fluid mixture," Int. J. Heat Mass Transf., vol. 48, pp. 2926-2932, 2005.
[27] Chevalier, J.; Tillement, O.; Ayela, F., "Rheological properties of nanofluids flowing through microchannels," Appl. Phys. Lett., vol. 91, p. 233103, 2007.
[28] Lu, W.; Fan, Q., "Study for the particle’s scale effect on some thermophysical properties of nanofluids by a simplified molecular dynamics method," Eng. Anal. Boundary Elem., vol. 32, pp. 282–289, 2008.
[29] Anoop, K. B.; Kabelac, S.; Sundararajan, T.; Das, S. K., "Rheological and flow characteristics of nanofluids: influence of
108
electroviscous effects and particle agglomeration," J. Appl. Phys., vol. 106, p. 034909, 2009.
[30] Chen, H.; Ding, Y.; Lapkin, A.; Fan, X., "Rheological behaviour of ethylene glycol-titanate nanotube nanofluids," J. Nanopart. Res., vol. 11, pp. 1513–1520, 2009.
[31] Yu, W.; Xie, H.; Li, Y.; Chen, L., "Experimental investigation on thermal conductivity and viscosity of aluminum nitride nanofluid," Particuology, vol. 9, pp. 187–191, 2011.
[32] Yang, Y.; Zhang, Z. G.; Grulke, E. A.; Anderson, W. B.; Wu, G., "Heat transfer properties of nanoparticle-in-fluid dispersions (nanofluids) in laminar flow," Int. J. Heat Mass Transfer, vol. 48, pp. 1107–1116, 2005.
[33] Haisheng C.; Wei Y.; Yurong H.; Yulong D.; Lingling Z.; Chunqing T.; Lapkin, A. A.; Bavykin, D.V., "Heat transfer and flow behaviour of aqueous suspensions of titanate nanotubes (nanofluids)," Powder Technol., vol. 183, pp. 63–72, 2008.
[34] Duangthongsuk, W.; Wongwises, S., "Measurement of temperature-dependent thermal conductivity and viscosity of TiO2–water nanofluids," Exp. Therm Fluid Sci, vol. 33, pp. 706–714, 2009.
[35] Chen, L.; Xie, H.; Li, Y.; Yu, W., "Nanofluids containing carbon nanotubes treated by mechanochemical reaction," Thermochim. Acta, vol. 477, pp. 21–24, 2008.
[36] Prasher, R.; Song, D.; Wang, J.; Phelan, P., "Measurements of nanofluid viscosity and its implications for thermal applications," Appl. Phys. Lett., vol. 89, p. 133108, 2006.
[37] Chen, H.; Ding, Y.; He, Y.; Tan, C., "Rheological behaviour of ethylene glycol based titania nanofluids," Chem. Phys. Lett., vol. 44, pp. 333–337, 2007.
[38] Chen, H.; Ding, Y.; Tan, C., "Rheological behaviour of nanofluids," New J. Phys., vol. 9, pp. 367-1-24, 2007.
[39] Nguyena C. T.; Desgranges, F.; Roy, G.; Galanis, N.; Maré, T.; Boucher, S.; Mintsa, H. A., "Temperature and particle-size
109
dependent viscosity data forwater-based nanofluids – hysteresis phenomenon," Int. J. Heat Fluid Flow, vol. 28, pp. 1492–1506, 2007.
[40] He, Y.; Jin, Y.; Chen, H.; Ding, Y., Cang, D.; Lu, H., "Heat transfer and flow behaviourof aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe," Int. J. Heat Mass Transfer, vol. 50, pp. 2272–2281, 2007.
[41] Nguyen, C. T.; Desgranges, F.; Galanis, N.; Roy, G.; Mare, T.; Boucher, S.; Angue, M. H., "Viscosity data for Al2O3–water nanofluid—hysteresis: is heat transfer enhancement using nanofluids reliable?," Int J. Therm. Sci, vol. 47, pp. 103–111, 2008.
[42] Anoop, K. B.; Sundararajan, T.; Das, S. K., "Effect of particle size on the convective heat transfer in nanofluid in the developing region," Int. J. Heat Mass Transfer, vol. 52, pp. 2189–2195, 2009.
[43] Namburu, P. K.; Kulkarni, D. P.; Dandekar, A.; Das, D. K., "Experimental investigation of viscosity and specific heat of silicon dioxide nanofluids," Micro & Nano Letters, vol. 2, pp. 67–71, 2007.
[44] Pastoriza-Gallego, M. J.; Casanova, C.; Legido, J. L.; Piñeiro, M. M., "CuO in water nanofluid: influence of particle size and polydispersity on volumetric behaviour and viscosity," Fluid Phase Equilib., vol. 300, pp. 188–196, 2011.
[45] Timofeeva, E. V.; Yu, W.; France, D. M.; Singh, D.; Routbort, J. L., "Nanofluids for heat transfer: an engineering approach," Nanoscale Res. Lett., vol. 6, p. 182, 2011.
[46] Timofeeva, E. V.; Routbort, J. L.; Singh, D., "Particle shape effects on thermophysical properties of alumina nanofluids," J. Appl. Phys., vol. 106, p. 014304, 2009.
[47] Einstein, A., "Eine neue bestimmung der moleküldimensionen," Annalen der Physik, vol. 324, pp. 289–306, 1906.
[48] Nagarajan R., Gorai P., Chawla N., "Modeling of thermodynamic and trasport phenomena in CVD processes for nano-scale applications," ECS Trans. , vol. 13, no. 9, pp. 7-18, 2008.
[49] Batchelor G. K., "The effect of Brownian motion on the bulk stress in a suspension of spherical particle," Fluid Mech., vol. 83, pp.
110
97-117, 1977.
[50] Cheng, N. S.; Law, A. W. K., "Exponential formula for computing effecti veviscosity," Powder Techno, vol. 129, pp. 156–160, 2003.
[51] Krieger, I. M., "A mechanism for non Newtonian flow in suspensions of rigid spheres," J. Rheol., vol. 3, pp. 137–152, 1959.
[52] Maïga S. E. B., Nguyen C. T., Galanis N., Roy G., Maré T., Coqueux M., "Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension," Int. J. Numer. Methods Heat Fluid Flow, vol. 16, pp. 275–292, 2006.
[53] Nguyen C. T., Desgranges F., Roy G., Galanis N., Maré T., Boucher S., Mintsa H. A., "Temperature and particle size deepndent viscosity data for water-based fluids - hysterisis phenomenon," Int. J. Heat Fluid Flow, vol. 28, no. 6, pp. 1492-1506, 2007.
[54] Williams W. C., "Experimental and theoretical investigation of transport phenomena in nanoparticle colloids (nanofluids)," Massachusetts Institute of Technology, 2006.
[55] H. Chen, S. Witharna, Y. Jin, C. Kim, Y. Ding, "Predicting thermal conductivity of liquid suspensions of nanoparticles (nanofluids) based on rheology," Particuology, vol. 7, pp. 151–157, 2009.
[56] Gharagozloo, P. E.; Goodson, K. E., "Aggregate fractal dimensions and thermal conduction in nanofluids," J. Appl. Phys., vol. 108, p. 074309, 2010.
[57] Vajjha, R. S.; Das, D. K.; Mahagaonkar, B. M., "Density measurement of different nanofluids and their comparison with theory," Petrol Sci Technol, vol. 27, pp. 612–624, 2009.
[58] Vajjha, R. S.; Das, D. K., "Measurements of specific heat and density of Al2O3 nanofluid," in AIP Conf. Proc., vol. 1063, 2008, pp. 361-370.
[59] Zhou, S. Q.; Ni, R., "Measurement of the specific heat capacity of water-based Al2O3 nanofluid," Appl. Phys. Lett., vol. 92, p. 093123, 2008.
111
[60] Sohel Murshid, S. M., "Simultaneous measurement of thermal conductivity, thermal diffusivity, and specific heat of nanofluids," Heat Transfer Eng., vol. 33, pp. 722–731, 2012.
[61] Donghyun, S.; Banerjee, D., "Enhancement of specific heat capacity of high-temperature silica-nanofluids synthesized in alkali chloride salt eutectics for solar thermal-energy storage applications," Int. J. Heat Mass Transfer, vol. 54, pp. 1064–1070, 2011.
[62] Vajjha, R. S.; Das, D. K., "Specific heat measurement of three nanofluids and development of new correlations," J. Heat Transf., vol. 131, p. 071601, 2009.
[63] Pak, B. C.; Cho, Y. I., "Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles," Exp. Heat Transf., vol. 11, pp. 151-170, 1998.
[64] Xuan, Y.; Roetzel, W., "Conceptions for heat transfer correlations," Int. J. Heat Mass Transfer, vol. 43, pp. 3701–3707, 2000.
[65] Buongiomo, J., "Convective transport in nanofluids," J. Heat Transf., vol. 128, pp. 240-250, 2006.
[66] Yu, W.; France, D. M.; Timofeeva, E. V.; Singh, D.; Routbort, J. L., "Thermophysical property-related comparison criteria for nanofluid heat transfer enhancement in turbulent flow," Appl Phys Lett, vol. 96, p. 213109 (3 pp.), 2010.
[67] Wen, D.; Ding, Y., "Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions," Int. J. Heat Mass Transfer, vol. 47, pp. 5181–5188, 2004.
[68] Hwang, K. S., Jang, S. P., and Choi, S. U. S., "Flow and convective heat transfer characteristics of water-based Al2O3 nanofluids in fully developed laminar flow regime," Int. J. Heat Mass Transfer, vol. 52, pp. 193-199, 2009.
[69] Rea, U.; McKrell, T.; Hu, L. W.; Buongiorno, J., "Laminar convective heat transfer and viscous pressure loss of alumina-water and zirconia-water nanofluids," Int. J. Heat Mass Transf., vol. 52, pp.
112
2042-8, 2009.
[70] D. Liu and L. Yu, "Experimental investigation of single-phase convective heat transfer of nanofluids in a minichannel," in IHTC 14, vol. 6, 2010, pp. 641-652.
[71] Vafaei, S.; Wen, D. S., "Convective heat transfer of alumina nanofluids in a microchanne," in Proceedings of the 14th International Heat Transfer Conference (IHTC 14), 2010.
[72] Garg, P.; Alvarado, J. L.; Marsh, C.; Carlson, T. A.; Kessler, D. A.; Annamalai, K., "An experimental study on the effect of ultrasonication on viscosity and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids," Int. J. Heat Mass Transfer, vol. 52, pp. 193-199, 2009.
[73] D. Kulkarni, P. Namburu, H. Bargar and D. Das, "Convective heat transfer and fluid dynamic characteristics of SiO2-ethylene glycol/water nanofluid," Heat Transfer Eng, vol. 29, pp. 1027–1035, 2008.
[74] W. Yu, D. M. France, D. S. Smith, D. Singh, E. V. Timofeeva and J. L. Routbort, "Heat transfer to a silicon carbide/water nanofluid," Int J Heat Mass Transfer, vol. 52, pp. 3606–3612 , 2009.
[75] Duangthongsuk, W.; Wongwises, S., "An experimental study on the heat transfer performance and pressure drop of TiO2-water nanofluids flowing under a turbulent flow regime," Int J Heat Mass Transfer, vol. 53, pp. 334–344, 2010.
[76] Fotukian, S. M.; Nasr Esfahany, M., "Experimental investigation of turbulent convective heat transfer of dilute γ-Al2O3/water nanofluid inside a circular tube," Int J Heat Fluid Fl, vol. 31, pp. 606–612, 2010.
[77] Suresh, S.; Selvakumar, P.; Chandrasekar, M.; Srinivasa Raman, V., "Experimental studies on heat transfer and friction factor characteristics of Al2O3/water nanofluid under turbulent flow with spiraled rod inserts," Chem Eng Process, vol. 53, pp. 24–30, 2012.
[78] Fotukian, S. M.; Nasr Esfahany, M., "Experimental study of turbulent convective heat transfer and pressure drop of dilute
113
CuO/water nanofluid inside a circular tube," Int Commun Heat Mass, vol. 37, pp. 214–219, 2010.
[79] Sajadi, A. R.; Kazemi, M. H., "Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube," Int Commun Heat Mass, vol. 38, pp. 1474–1478, 2011.
[80] M. H. Kayhani, H. Soltanzadeh, M. M. Heyhat, M. Nazari, and F. Kowsary, "Experimental study of convective heat transfer and pressure drop of TiO2/water nanofluid," Int Commun Heat Mass, vol. 39, pp. 456–462, 2012.
[81] Karlekar, B. V; Desmond, R. M., Engineering Heat Transfer.: West Publishing Company, 1977.
[82] Blasius H. , "Das Aehnlichkeitsgesetz bei Reibungsvorgängen in Flüssigkeiten," Mitteilungen über Forschungsarbeiten auf dem Gebiete des Ingenieurwesens, vol. 131, pp. 1-41, 1913.
[83] McAdams, W. H., Heat Transmission. New York, USA: McGraw Hill Book Co., 1942.
[84] Haghighi, E. B.; Saleemi, M.; Nikkam, N.; Anwar, Z.; Lumbreras, I.; Behi, M.; Mirmohammadi, S. A.; Poth, H.; Khodabandeh, R.; Toprak, M. S.; Muhammed, M.; Palm, B., "Cooling performance of nanofluids in a small diameter tube," Exp. Therm. Fluid Sci., vol. 49, pp. 114-122, 2013.
[85] Shah, R K; London, A L, Laminar flow forced convection in ducts : a source book for compact heat exchanger analytical data. New York: Academic Press, 1978.
[86] Shah, R. K., "Thermal entry length solutions for the circular tube and parallel plates," in 3rd National Heat and Mass Transfer Conference, 1975, pp. HMT-11-75.
[87] V. Gnielinski, "New correlations for heat and mass transfer in turbulent pipe and channel flow," Forsch Ingenieurwes, vol. 41, pp. 8-16, 1975.
[88] Winterton, R. H. S., "Where did the Dittus and Boelter equation come from?," Int. J. Heat Mass Transfer, vol. 41, pp. 809-810, 1998.
114
[89] Vanapalli, S.; ter Brake, H. J. M., "Assessment of thermal conductivity, viscosity and specific heat of nanofluids in single phase laminar internal forced convection," Int. J. Heat Mass Transf., vol. 64, pp. 689–693, 2013.
[90] Haghighi, E. B.; Utomo, A. T.; Ghanbarpour, M.; Zavareh, A. I. T.; Nowak, E.; Khodabandeh, R.; Pacek, A. W.; Palm, B., "Combined Effect of Physical Properties and Convective Heat Transfer Coefficient of Nanofluids on Their Cooling Efficiency ," Submitted to Int. J. Therm. Sci., 2014.
[91] Hiemenz, P. C.; Dekker, M., Principles of colloid and surface chemistry. New York: Dekker, 1986.
[92] Gustafsson, S. E., "Transient plane source techniques for thermal conductivity and thermal diffusivity measurements of solid materials," Rev. Sci. Instrum., vol. 62, pp. 797-804, 1991.
[93] Hu, P.; Shan, W. L.; Yu, F.; Chen, Z. S., "Thermal conductivity of AlN–Ethanol nanofluids," Int J Thermophys, vol. 29, pp. 1968-1973, 2008.
[94] Li, X. F.; Zhu, D. S.; Wang, X. J.; Wang, N.; Gao, J. W.; Li, H., "Thermal conductivity enhancement dependent pH and chemical surfactant for Cu-H2O nanofluids," Thermochimic Acta, vol. 469, pp. 98–103, 2008.
[95] Wang, X. J.; Li, X. F., "Influence of pH on nanofluids’ viscosity and thermal conductivity," Chin. Phys. Lett., vol. 26, p. 056601, 2009.
[96] Dongsheng, Z.; Xinfang, L.; Nan, W.; Xianju, W.;Jinwei, G.; Hua, L., "Dispersion behavior and thermal conductivity characteristics of Al2O3–H2O nanofluids," Curr. Appl Phys., vol. 9, pp. 131–139, 2009.
[97] Nikkam, N.; Salimi, M.; Toprak, M. S.; Li, S.; Muhammed, M.; Haghigh, E B.; Khodabandeh, R.; Palm, B., "Novel nanofluids based on mesoporous silica for enhanced heat transfer," J. Nanopart. Res., vol. 13, pp. 6201-6206, 2011.
[98] Horrocks, J. K.; McLaughlin, E., "Non-steady state measurements of thermal conductivities of liquids polyphenyls," Proc R Soc Lond,
115
vol. 273(A), pp. 259–74, 1963.
[99] Hong, K. S.; Hong, T. K.; Yang, H. S., "Thermal conductivity of Fe nanofluids depending on the cluster size of nanoparticles," Appl Phys Lett, vol. 88, p. 031901, 2006.
[100] Kwak, K; Kim, C., "Viscosity and thermal conductivity of copper oxide nanofluid dispersed in ethylene glycol," Korea–Aust Rheo J, vol. 17, pp. 35–40, 2005.
[101] Lee, J. H.; Hwang, K. S.; Jang, S. P.; Lee, B. H.; Kim, J. H.; Choi, S. U. S., "Effective viscosities and thermal conductivities of aqueous nanofluids containing low volume concentrations of Al2O3 nanoparticles," Int J Heat Mass Transfer, vol. 51, pp. 2651–6, 2008.
[102] Haghighi, E. B.; Saleemi, M.; Nikkam, N.; Ghadamgahi, M.; Khodabandeh, R.; Palm, B.; Toprak, M. S.; Muhammed, M., "Measurement of temperature-dependent viscosity of nanofluids and its effect on pumping power in cooling systems," in International Conference on Applied Energy, Pretoria, 2013.
[103] Haghighi, E. B.; Anwar, Z.; Lumbreras, I.; Mirmohammadi, S. A.; Behi, M.; Khodabandeh, R.; Palm, B., "Screening single phase laminar convective heat transfer of nanofluids in a micro-tube," J. Phys. Conf. Ser., vol. 1, p. 2036, 2012.
[104] Utomo, A. T.; Haghighi, E. B.; Zavareh, A. I. T.; Ghanbarpour, M.; Poth, H.; Khodabandeh, R.;Palm, B.; Pacek, A. W. , "The effect of nanoparticles on laminar heat transfer in a horizontal tube," Int. J. Heat Mass Transfer, vol. 69, pp. 77-91, 2014.
[105] Haghighi, E. B.; Utomo, A. T.; Ghanbarpour, M.; Zavareh, A. I. T.; Poth, H.; Khodabandeh, R.; Pacek, A. W.; Pam, B., "Experimental Study on Convective Heat Transfer of Nanofluids in Turbulent Flow: Methods of Comparing Their Performance," Submitted to Int. J. Heat Mass Transfer, 2014.
[106] Haghighi, E. B.; Nikkam, N.; Saleemi, M.; Behi, M.; Mirmohammadi, S. A.; Poth, H.; Khodabandeh, R.;Toprak, M. S.; Muhammed, M; Palm, B., "Shelf Stability of Nanofluids and Its Effect on Thermal Conductivity and Viscosity," Meas. Sci. Technol., vol. 24, p. 105301, 2013.
116
[107] Release on the IAPWS Formulation 2011 for the Thermal Conductivity of Ordinary Water Substance (September 2011). [Online]. http://www.iapws.org
[108] Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance (September 2008). [Online]. http://www.iapws.org.
[109] B. Barbes et al., "Thermal conductivity and specific heat capacity measurements of Al2O3 nanofluids," J Therm Anal Calorim, vol. 111, pp. 1615–1625, 2013.
[110] B. Barbes, R. Paramo, E. Blanco, and C. Casanova, "Thermal conductivity and specific heat capacity measurements of CuO nanofluids," J Therm Anal Calorim, vol. 115, pp. 1883–1891, 2014.
[111] Haghighi, E. B.; Saleemi, M.; Nikkam, N.; Khodabandeh, R.; Toprak, M. S.; Muhammed, M.; Palm, B., "Accurate basis of comparison for convective heat transfer in nanofluids," Int. Commun. Heat Mass, vol. 52, pp. 1-7, 2014.
[112] Andraos, J., "On the propagation of statistical errors for a function of several variables," Journal of Chemical Education, vol. 73, no. 2, p. 150, 1996.
[113] Ji, W. T.; Zhang, D. C.; He, Y. L.; Tao, W. Q., "Prediction of fully developed turbulent heat transfer of internal helically ribbed tubes – An extension of Gnielinski equation," Int J Heat Mass Transfer, vol. 55, pp. 1375–1384, 2012.
[114] Nanofluid Characterization and Optimization (Final Report for NanoHex Project), 2013.
[115] Melinder, Å, Properties of Secondary Working Fluids for Indirect Systems (Secondary Refrigerants or Coolants, Heat Transfer Fluids). Paris, France: International Institute of Refrigeration, 2010.
[116] Mogensen, M.; Sammes, N. M. ;Tompsett G. A., "Physical, chemical and electrochemical properties of pure and doped ceria," Solid State Ion. Diffus. React. (Netherlands), vol. 129, no. 1-4, pp. 63-94, 2000.