characterization the effects of nanofluids and heating on

ORIGINAL PAPER Open Access

Characterization the effects of nanofluidsand heating on flow in a baffled verticalchannelAli Assim Al-Obaidi1*, Ali J. Salman1, Ali Raheem Yousif1, Dalya H. Al-Mamoori2, Mohamed H. Mussa3,Tayser Sumer Gaaz2, Abdul Amir H. Kadhum3, Mohd S. Takriff3 and Ahmed A. Al-Amiery4

Abstract

The laminar 2-D blended convection of the nanofluids at different volume fractions has gained interest in the lastdecade due to an enormous application in technology. The laminar-flow stream system can be further modified bychanging the geometry of the channel, adding an external heating source, and changing the initial conditions atwhich the stream is being influenced. The investigation of this system includes the variation of the geometricalparameters of the channel, Reynolds number, Nusselt number, and type of the nanoparticles used in preparing thenanofluid with water as the base fluid. These parameters constitute a very successful leading to utilize thenumerical solutions by using a finite volume method. Regarding heat flow, one side of the channel was suppliedby the heat while the temperature of the other side was kept steadily. The upstream walls of the regressiveconfronting step were considered as adiabatic surfaces. The nanofluids were made by adding aluminum oxide(Al2O3), copper oxide (CuO), silicon dioxide (SiO2), or zinc oxide (ZnO) nanoparticles to various volume fractions inthe scope of 1 to 4% and diverse nanoparticle diameters of 25 to 80 nm. The calculations were performed withheat flux, Reynolds numbers (Re), and step height (S) at a range of 100 < < 600 W/m2, 100 < Re < 500, and 3≤ S ≤5.8, respectively. The numerical study has shown that the nanofluid with SiO2 has the highest value of the Nusseltnumber (Nu). The distribution area and the Nu increase as Reynolds number increases and diminish as the volumefraction diminishes with the increase of the nanoparticle diameter. The outcome of this paper has shown thatassisting flow has shown superiority over the opposing flow when Nu increases.

Keywords: Blended convection, Backward-facing step, Channel flow, Nanofluids

IntroductionThe regressive confronting step stream is a basic ideathat provides a straightforward geometrical model ofcomplex solutions for stream detachment and reattach-ment (D’Adamo, Sosa, & Artana, 2014). Some applica-tion examples include cooling turbine blades, chemicalprocesses, cooling of nuclear reactors, wide angle dif-fusers, high-performance heat exchangers, energy sys-tem equipment, and flow in valves. Heat transfer inseparated flows is frequently encountered in variousengineering applications centrifugal compressor blades,gas turbine blades, and microelectronic circuit boards

(Hashim et al., 2018; Ma, Mohebbi, Rashidi, & Yang,2018a, 2019; Mohebbi & Heidari, 2017; Mohebbi, Izadi,& Chamkha, 2017; Mohebbi, Izadi, Delouei, & Sajjadi,2019; Mohebbi, Rashidi, Izadi, Sidik, & Xian, 2018;Ranjbar, Mohebbi, & Heidari, 2018). A thorough com-prehensive detail of these streams constitutes a primesignificance outlining constructing devices such as com-bustors, airfoils, turbines, and others (Bomela, 2014). Pre-vious work has utilized the geometry of a backward-facingstep to consider the partition and the possibility of reat-taching the flowing streams. In an alternative model ofmore perplexing geometries such as airfoils or otherthree-dimensional shapes, the geometric smoothness of aregressive confronting step stream guarantees the exactpurpose of detachment. A large portion of the most punc-tual investigations of the regressive confronting step

© The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made.

* Correspondence: [email protected] of Power Mechanics, Technical Institute of Babylon, Al-Furat AlAwsat Technical University, Babil, IraqFull list of author information is available at the end of the article

Al-Obaidi et al. International Journal of Mechanical and Materials Engineering (2019) 14:11 https://doi.org/10.1186/s40712-019-0105-6

http://crossmark.crossref.org/dialog/?doi=10.1186/s40712-019-0105-6&domain=pdf

http://orcid.org/0000-0003-1033-4904

http://creativecommons.org/licenses/by/4.0/

mailto:[email protected]

streams is tentatively seen in view of stream representa-tion procedures. As a rule, the essential distribution zonewas no longer effective, and the outcomes acquired forvarious geometries are strongly related to the basic stream(Denham & Patrick, 1974; Kumar & Dhiman, 2012). Oneof the techniques to deal with enhancing separatingregions in the confined areas is to use the nanofluids(NFs) (Abchouyeh, Mohebbi, & Fard, 2018; Delouei,Sajjadi, Izadi, & Mohebbi, 2019; Hasan, Sopian, Jaaz,& Al-Shamani, 2017; Izadi, Hoghoughi, Mohebbi, &Sheremet, 2018; Izadi, Mohebbi, Chamkha, & Pop,2018; Izadi, Mohebbi, Karimi, & Sheremet, 2018; Ma,Mohebbi, Rashidi, Yang, & Sheremet, 2019; Mohebbi& Heidari, 2017; Mohebbi & Rashidi, 2017). NFs arethose fluids with suspended nanoparticles commonlymetal oxides (Saidur, Leong, & Mohammad, 2011)which can be suspended in the base fluid which iscommonly water (Yu & Xie, 2012). Along these lines,there is no drop in the stream field. It is found thatmore testing exhibits that NFs enhance the propertiesof the heat flux by increasing the flux conductivityand the convective heat transfer coefficients (Al-Aswadi, Mohammed, Shuaib, & Campo, 2010; Al-Shamani et al., 2015; Jaaz et al., 2017; Jaaz, Sopian, &Gaaz, 2018; Ma, Mohebbi, Rashidi, & Yang, 2019;Mohammed, Al-Aswadi, Shuaib, & Saidur, 2011; Mo-hammed, Al-Aswadi, Yusoff, & Saidur, 2012;Mohebbi, Lakzayi, Sidik, & Japar, 2018; Mohebbi,Nazari, & Kayhani, 2016; Murshed, De Castro, Lour-enço, Lopes, & Santos, 2011; Nazari, Mohebbi, &Kayhani, 2014; Sheikholeslami & Ganji, 2016).The estimation of the flow over a regressive con-

fronting step have been broadly considered in themost recent decades for both constrained and blendedconvection, see, for instance, Armaly, Durst, Pereira,and Schönung (1983), Gartling (1990), Tylli, Kaiktsis,and Ineichen (2002), and subsequent related refer-ences therein. Likewise, a few different investigations(Ma, Mohebbi, Rashidi, Manca, & Yang, 2018; Nie &Armaly, 2002; Williams & Baker, 1997) tried the 3-Dlaminar convection stream in reverse geometrical op-posing step. Abu-Mulaweh (2003) led a broad surveyof research on laminar blended convection over abackward-facing step (BFS). The reverse confrontingstep flow while exchanging heat was investigated atuniform wall heat flux and uniform wall temperaturevariation (Nikkhah et al., 2015; Sheikholeslami &Chamkha, 2016). Blackwell and Armaly (1993) ex-plored various approaches to numerically tackle theissues for consistent 2-D-one-stage blended convec-tion flow in a vertical channel (Selimefendigil &Öztop, 2015).In another investigation, an exploratory numerical study

of a blended convection laminar flow over a regressive

confronting step was performed by Abu-Mulaweh,Armaly, and Chen (1993). Other studies found that the in-clination angle influences both the flow and its relevantheat stream fields (Alawi, Azwadi, Kazi, & Abdolbaqi,2016; Kherbeet et al., 2015; Safaei, Togun, Vafai, Kazi, &Badarudin, 2014). It was concluded that the expansion inthe inclination edge from the vertical reduces the ad-jacent Nu estimation. This expansion is a direct resultof a lessening the streamwise caused by the extensionof the inclination edge. Hong, Armaly, and Chen(1993) and Iwai, Nakabe, Suzuki, and Matsubara(2000) have anticipated numerically that the laminarblended convection flow over a regressive confrontingadvance in two-dimensional and three-dimensionalconfigurations, respectively. They observed that thereattachment length increases as the inclination angleincreases gradually from 0° to 180° and, hence, a re-duction in the wall friction coefficient and Nu wasobserved (Nazari, Kayhani, & Mohebbi, 2013). Theopposite was looked for both reattachment length andNu as the inclination edge increases from 180° to360°. Various examinations on turbulent flow over abackward-facing step have been investigated mostly incommon and constrained convection; see, for instance(Abe, Kondoh, & Nagano, 1995; Chen, Nie, Armaly,& Hsieh, 2006; Park & Sung, 1995; Rhee & Sung,1996). A few researchers considered the convectiveheat flux exchange throughout utilizing NFs, see, forinstance, Trisaksri and Wongwises (Daungthongsuk &Wongwises, 2007; Trisaksri & Wongwises, 2007;Wang & Mujumdar, 2007), and the subsequent refer-ences therein. It ought to be noted, in any case, thatthe most investigations of a regressive confrontingstep employ regular non-NFs (Hashemi, Abouali, &Ahmadi, 2017; Ma, Mohebbi, Rashidi, & Yang, 2018b;Mohammed, Alawi, & Sidik, 2016; Mohammed, Alawi,& Wahid, 2015). Adversely, other investigations withNFs in reverse confronting step geometry have beendeveloped. The primary numerical examination to in-vestigate the stream and heat flux exchange over a re-gressive confronting step utilizing NFs was performedby Abu-Nada (2008). In this study, the volume frac-tion nanoparticles (∅) and Re were taken at 0 ≤ ∅ ≤0.2 and 200 ≤ Re ≤ 600, respectively using the nanopar-ticles of Al2O3, CuO, SiO2, or ZnO. It was suggestedthat the high Nu number inside the distribution zonegenerally depends on the thermophysical properties ofthe nanoparticles (Ma, Mohebbi, Rashidi, Yang, &Sheremet, 2019) while it shows no Re relation (Ma,Mohebbi, Rashidi, & Yang, 2018c).Numerical examination of forced and mixed convec-

tion in even and vertical pipe of various NFs was studied(Al-Aswadi et al., 2010; Mohammed et al., 2011, 2012).The effects of Re number (75 ≤ Re ≤ 225), temperature

Al-Obaidi et al. International Journal of Mechanical and Materials Engineering (2019) 14:11 of 15

difference between 0 and 30 °C using Au, Ag, Al2O3, Cu,or CuO as nanoparticles with water as the base fluidwere studied, while SiO2 and TiO2 were inspected onthe fluid stream and heat flux step characteristics. It isfound that a dispersion region develops a straightbackward-facing step between the edge of the walland within 1 mm or so before the corner where thedownstream divider is located (Alawi et al., 2016). Inthat couple of millimeters zone between the appropri-ation region and the downstream divider, the streamshows a reversing U-turn opposing the circulationstream where circulated and uncirculated streamscome together in the channel. In these systems, thehighest peak of Nu is obtained using Au as the nano-particle, while the most astonishing slightest peak inthe circulation district was obtained using diamondnanoparticles.The literature review has shown that the steady 2-

D-NF laminar mixed convection flowing over abackward-facing step in a vertical configurationunder uniform heat flux has not been thoroughly in-vestigated and this case will be a very convincing ar-gument for this study. The present examination, forinstance, oversees particular NFs such as CuO, ZnO,and SiO2 at various volume fractions and variousnanoparticle ranges. The impacts of heat flux and Reon the velocity distribution, skin friction coefficient,and Nu are analyzed and offered an explanation tothe peak under the effect of NFs on these parame-ters for facilitating the restricting streams.The aim is to study the effects of different types of

nanoparticles such as Al2O3, CuO, SiO2, and ZnOand base water and to analyze different volume frac-tions (∅) of nanoparticles in the range of 1–4%. Thecalculations were performed with heat flux, Reynoldsnumbers (Re), and step height (S) at a range of100 < < 600 W/m2, 100 < Re < 500, and 3 ≤ S ≤ 5.8,respectively.

MethodologyNumerical modelPhysical modelFigure 1 shows the geometrical arrangement for the dir-ect step backward facing where the two parameters ofthe stepping height and expansion ratio were set at 4.8mm and 2, respectively. Additionally, the upstream anddownstream walls were assembled at 24 mm and 144mm, respectively. At the wall, a uniform heat flux (qw)was applied to the step downstream wall (Xe) while theopposite wall of the channel was kept isothermally con-sistent with the fluid temperature of T0. The wallupstream is characterized by two steps: Xi and S; bothwere kept under adiabatic surface condition. The re-attachment length (Xr) is shown on the right side of the

bottom of the channel. At the channel entrance, thenanofluid stream is hydrodynamically persistent and theflow achieves the fully developed conditions at the edgeof the movement which results in zero speed at the in-ternal surface of the pipe. The nanofluids (nanoparticlesand water) were adjusted for specific heat flux to attain ano-slip condition. The flow was assumed to be incom-pressible and follows Newtonian fluid in regard to theviscosity. As an approximation, the exchange radiationheat flux, its counterpart distribution term, and theinward heat flux were dismissed. The thermophysicalproperties of the nanofluids are constant while the buoy-ancy was constrained as an opposing motion to the grav-ity. The Boussinesq equation is employed for thissystem.FLUENT solver is based on the finite volume method.

In this case, domain of the model to be examined is dis-cretized into a finite set of the control volumes, whichare termed meshes or cells. Then, the general conserva-tion equations for mass, momentum, and energy solvedon this set control volumes. Other transport equationssuch as the equations for species may also be applied.Subsequently, partial differential equations are discre-tized into a system of algebraic equations. All algebraicequations are solved numerically to render the solution

Fig. 1 Schematic diagram for 2D BFS in a vertical channel


field. Computational fluid dynamic (CFD) theories, theCFD modeling process, physical model, and assumptionssuch as model, governing equations and boundary con-ditions, thermophysical properties of nanofluids, finitevolume method (FVM), and fluid computation by theSIMPLE algorithm are presented in the following sec-tions. CFD techniques are used to study and solve com-plex fluid flow and heat transfer problems in thebackward and forward double steps. CFD is acomputer-based tool for simulating the behavior ofsystems involving fluid flow, heat transfer, and otherphysical-related processes. It works by solving theequations of fluid flow (in a special form) over a re-gion of interest, with specified (known) conditionson the boundary of that region. CFD has facilities inthe industry as it can solve several system configura-tions in the same time and at a cheaper cost com-pared with other experimental studies. In the currentstudy, a CFD technique is used to investigate the ef-fect of using nanofluids as work fluid instead of theconventional fluids over backward and forwarddouble steps. The interest region where flow simula-tion is to be done is the computational domain ofthe problems.

Cost analysis of using nanofluids To investigate thecost-effectiveness of using nanofluids as coolants,computational fluid dynamics method is employed todirectly simulate the flow and heat transfer of thenanofluids in a 2-dimensional micro channel in thepresent paper. There are two different numericalmethods for doing these. One is based on moleculardynamics which directly focuses on the molecular be-haviors of the nanoparticles. This method needs moreCPU time and computer memory. The other is basedon Navier-Stokes questions introducing the thermaland dynamic parameters of the nanofluids obtainedfrom the mixture fluid theory and experimental mea-surements. Nanofluids are prepared by either one-stepor two-step methods. Both methods require advancedand sophisticated equipment. This leads to higherproduction cost of nanofluids. Therefore, high cost ofnanofluids is a drawback of nanofluid applications(Xu, Pan, & Yao, 2007).

Governing equations To prepare the CFD investigationof the reverse confronting step, it is imperative to setup the basic three equations which describe the con-tinuity (Eq. 1), momentum (Eq. 2), and the energy(Eq. 3). It is also important to set the non-dimensionalvariables. In addition, the Boussinesq equation was usedto deal with the viscous dispersal and compressibilityimpact. The conditions for two-dimensional laminar

incompressible streams can be composed as suggestedby (Abu-Nada, 2008):

The continuity equation :∂U∂X

þ ∂V∂Y

¼ 0 ð1Þ

The momentum equations

X‐motion : U∂U∂X

þ V∂V∂Y

¼ −∂P∂X

þ μnfρnυnf

1Re

∂2U∂X2 þ

∂2U∂Y 2

� �

Y ‐motion : U∂U∂X

þ V∂V∂Y

¼ −∂P∂Y

þ μnfρnυnf

1Re

∂2U∂X2 þ

∂2U∂Y 2

� �þ ρβð Þnf

ρnf βnf

Gr

Re2θ

ð2Þ

The energy equation : U∂θ∂X

þ V∂θ∂Y

¼ αnfα f RePr

∂2θ∂X2 þ

∂2θ∂Y 2

� �

ð3ÞThe dimensionless variables are defined as follows,

X ¼ xS

Y ¼ yS

θ ¼ T−T 0

Tw−T 0

U ¼ uU0

V ¼ vV 0

Re ¼ ρu0Dh

μ

Boundary conditions The boundary conditions as shownbelow reflect the limiting situations at the walls in regard tothe flow, no-slip condition, and temperature. The conditionsat the channel segment include the temperature and thespeed. The overall arrangement is governed by the followingconditions (Ghasemi & Aminossadati, 2010; Öztop, 2006):

Upstream inlet:

X ¼ − XiDh

SDh

≤Y≤ HDh

U1 ¼ uiuo

V = 0 θ = 0

Downstream exit:

X ¼ XeDh

0≤Y≤ HDh

∂2U∂X2 ¼ 0 ∂2V

∂X2 ¼ 0 ∂2θ∂X2

¼ 0

Top wall:

− 1Dh

≤X≤ XeDh

Y ¼ HDh

U = 0 V = 0 θ = 0

Sidewalls:

− XiDh

≤X≤ XeDh

0≤Y≤ HDh

U = 0 V = 0 θ = 0

Stepped wall condition: (a) Upstream:

− XiDh

≤X≤0 Y ¼ SDh

U = 0 V = 0 ∂θ∂Y ¼ 0

Stepped wall condition: (b) At the step:

X = 0 0≤Y≤ SDh

U = 0 V = 0 ∂θ∂Y ¼ 0

Stepped wall condition: (c) Downstream:

0 < X≤ XiDh

Y = 0 U = 0 V = 0 ∂θ∂Y ¼ −1

Code validations and grid testingi. Preliminary evaluation of the grid


A preliminary evaluation was adopted to coordinatethe grid geometrical conditions and the ability of thegrid to show the impact of heat transfer of the fluidswith various NFs. The cross investigation was drivenwith the working fluids, NFs, at Re = 50 and 175, whilekeeping the downstream wall and the channel stream attemperature difference of ΔT = 15 °C. Three grid size of140 × 50, 128 × 50, and 140 × 60 were used for testing aself-governance system while a fourth grid size of 128 ×50 was maintained for self-governing independence tri-als. Several local trials have shown that using other gridsizes reduces the performance of the grid up to 4% inevaluating speed and temperature. The partition be-tween the center points was extended to reach 14 in thex-direction while it reaches 3.5 in the y-direction. Thecurrent examination has adopted a non-uniform struc-ture and quadrilateral sides. The system was specificallytested near the steps at the edge and the walls to guaran-tee the precision of the numerical deviation which helpsremarkably to save both the computational time andcross assessment.The second cross tests have improved the situation of

air flow at Re = 100 while a uniform heat flux progressof qw = 200 W/m2 was applied to the downstream wall.The points of the cross-sectional center are set at dif-ferent sizes of the grid while the framework numbers inthe x-direction were 100, 120, and 140 and 50, 60, and70 in the y-heading to ensure the system flexibility test.A grid size of 100 × 50 was used to examine and thento validate the cross self-sufficient course of action. Itshows under 3% reduction in Nu and other grid sizesthat are mentioned in Table 1, a fine structure is usedas a part of the x-coordinate which is close to the div-ider motion section, while it increases with expansionof 0.1 in x-bearing along the way from the wall pos-ition. Other fine grids of the improvement extents atthe ratio of 0.285 in the y-heading are utilized veryclose to the base divider and the edge of the wall to

ensure the accuracy of the framework free course ofaction.

ii. Validation of the code

The numerical approval strategy that comprises thenumerical code under particular conditions was testedand then used as a benchmark for afterward contrasting.The main experiment was performed by creating theconstrained convective nanofluids stream over an evenBFS in a pipe (Al-Aswadi et al., 2010). For this stream,Re numbers for the laminar flow were taken at 50 and175. Figures 2, 3, and 4 demonstrate the consequencesof the correlation with the findings of the various NFs aspresented by Al-Aswadi et al. (2010). The velocity distri-bution for different stepped wall increments (X/S) in thedistribution along the pipe is shown in Figs. 2 and 3 forAl2O3 and CuO under same conditions, respectively.The distribution location shows up and the measure ofthe local distribution diminishes as the separation betweenthe step X/S achieves the reattachment condition at zero-speed flow as shown in Figs. 2a–d and 3a–d. Figures 2a–cand 3a–c demonstrate that a distribution location grewcontinuously downstream. Additionally, the downstreamof flow begins to end up completely by creating fluidstream toward the pipe exit as shown in Figs. 2 and 3d.The skin friction coefficients shown in Fig. 4 were

demonstrated at the base of the wall step showing thatthey achieve the separation downstream from the stepshowing the highest extreme base peak until achieving aconsistent friction coefficient along the rest of the basewall. The condition of the flow to reach fully developedflow depends on the asymptotic variation of the skincoefficient. The second experiment was prepared toreproduce blended convective wind stream over BFS inthe channel according to the work performed by Honget al. (1993). The conditions of this experiment includesetting Re at 100 and applying a uniform wall heat fluxat 200 W/m2. The velocity distribution and Nu at thepoint where θ° = 0 are explained in Fig. 5a, b.

Procedure of numerical calculation The procedure ofthe numerical calculations was executed throughgoverning equations and the conditions alongside thelimit as depicted in Eqs. (1) to (3). The conditions forthe strong and fluid stage were considered as a singledomain. The discretization of the conditions in theliquid and strong regions has come to an end byutilizing FVM. The diffusion term under energy andmomentum conditions is approximated continuously byarranging the focal distinction until achieving a steadystate condition. However, a second-arranged upstreamprocedure was prepared to show the relation to the con-vective terms. The calculation of the stream field was

Table 1 Grid tests for the Nusselt number at Re = 100

Grid no. Expansion factor (first/last) Nusseltnumberx-direction y-heading x-direction y-heading

100 50 0.1 0.285 1.75485

60 1.77592

70 1.80250

120 50 1.75856

60 1.77922

70 1.80828

140 50 1.76701

60 1.78369

70 1.81702


completely utilized by the SIMPLE calculation (John &Anderson, 1995). This was an iterative arrangement meth-odology where the calculation is introduced throughspeculating the weight field. At this point, the momentumequations were utilized to determine the speed partsfollowed by refreshing the weight factor to reach the con-tinuity state. Despite the fact that the steady state does notcontain any weight factor, it can be changed effortlesslyinto a weight adjustment condition (Patanker, 1980).

Thermophysical characteristics of nanofluids The zincoxide (ZnO) nanoparticles were synthesized using asimple precipitation method with zinc sulfate and sodiumhydroxide as starting materials. The synthesized samplewas calcined at different temperatures for 2 h (Kumar,Venkateswarlu, Rao, & Rao, 2013); copper oxide (CuO) isthe inorganic compound with the formula CuO. As ablack solid, it is one of the two stable oxides of copper, theother being Cu2O or cuprous oxide. As a mineral, it isknown as tenorite. It is a product of copper mining andthe precursor to many other copper-containing productsand chemical compounds (Richardson, 2002). Silicondioxide (SiO2), also known as silica, is an oxide of siliconwith the chemical formula SiO2, most commonly found in

nature as quartz and in various living organisms (Fernández,Lara, & Mitchell, 2015; Iler, 1979). In many parts of theworld, silica is the major constituent of sand. Silica is one ofthe most complex and most abundant families of materials,existing as a compound of several minerals and as a syn-thetic product. Notable examples include fused quartz,fumed silica, silica gel, and aerogels. It is used in structuralmaterials and microelectronics (as an electrical insulator)and as components in the food and pharmaceutical indus-tries. Aluminium oxide (Al2O3) (IUPAC name) oraluminum oxide (American English) is a chemical com-pound of aluminum and oxygen with the chemical formula(Al2O3). It is the most commonly occurring of severalaluminum oxides and specifically identified as aluminum(III) oxide. It is commonly called alumina and may also becalled aloxide, aloxite, or alundum depending on particularforms or applications. It occurs naturally in its crystallinepolymorphic phase α-Al2O3 as the mineral corundum, var-ieties of which form the precious gemstones ruby and sap-phire. Al2O3 is significant in its use to produce aluminummetal, as an abrasive owing to its hardness and as a refrac-tory material owing to its high melting point (Davis, 1993).With a specific end goal to complete simulation for

NFs, the compelling thermophysical characteristics of

a b

c d

Fig. 2 Comparison of velocity distribution with the results of Al-Aswadi et al. (2010) in the recirculation region for S = 4.8mm, and ER= 2 at Re=175.For Al2O3 at different X/S: a 1.04, b 1.92, c 2.6, d 32.8


Fig. 3 Comparison of velocity distribution with the results of Al-Aswadi et al. (2010) in the recirculation region for S = 4.8mm, and ER= 2 at Re=175.For CuO at different X/S: a 1.04, b 1.92, c 2.6, d 32.8

a b

Fig. 4 Comparison of skin friction coefficient of SiO2 nanofluids for different Reynolds numbers a Re = 50 and b Re = 175 at the bottom walldownstream the step


NFs must be first determined. For this situation, thenanoparticles are Al2O3, CaO, ZnO, and SiO2. Therequired properties for the recreations are to set theeffective heat conductivity (keff), to calculate the effectiveviscosity (μeff) and effective density (ρeff), and to assumethat the effective coefficient of heat expansion (βeff) andeffective particular heat capacity (cpeff) are following theincompressible fluid and their estimation depends onthe volume fraction of their nanofluid (∅). By utilizingBrownian movement of nanoparticles in reverseconfronting step, the effective heat flux conductivity canbe acquired as following mean experimentalrequirements (Ghasemi & Aminossadati, 2010; Heidari,Mohebbi, & Safarzade, 2016):

keff ¼ kstatic þ kBrownian ð4Þ

where kstatic is defined as,

kstatic ¼ kbfknp þ 2kbf −2 kbf −knp

� �∅

knp þ 2kbf þ 2 kbf −knp� �

∅

" #ð4:1Þ

and the Brownian thermal conductivity,

kBrownian ¼ 5� 104β∅cp;bf

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikT

2ρnpRnp

sf T ;∅ð Þ ð4:2Þ

where Boltzmann constant:

k ¼ 1:3807� 10−23 J=KβAl2O3 ¼ 8:4407 100∅ð Þ−1:07304βCuO ¼ 9:881 100∅ð Þ−0:9446

Modeling function, β (Vajjha & Das, 2009):

βSiO2 ¼ 1:9526 100∅ð Þ−1:4594βZnO ¼ 8:4407 100∅ð Þ−1:07304

Modeling function

f T ;∅ð Þ ¼ 2:8217� 10−2∅� �þ 3:917� 10−3Þ T

T0

� �þ −3:0699� 10−2∅−3:91123� 10−3� �

and μeff can be empirically estimated (Corcione, 2010):

μeff ¼μ f

1−34:87 dpd f

� �−0:3∅1:03

ð5Þ

where,

The equivalent diameter is deff ¼ 6MNπρbt

� �1=3

ð6Þ

The density of NF 68½ � is ρnf¼ 1−∅ð Þρ f þ∅ρnf ð7Þ

The effective heat capacity at constant pressure of NF(Ghasemi & Aminossadati, 2010) is:

cp� �

nf ¼ 1−∅ð Þ cp� �

f þ∅ cp� �

np ð8Þ

The effective coefficient of thermal expansion ofnanofluid (Ghasemi & Aminossadati, 2010):

βð Þnf ¼ 1−∅ð Þ βð Þ f þ∅ βð Þnp ð9Þ

The experimental values of the thermophysicalproperties for pure water with different NFs at 300 K arelisted in Table 2.

Fig. 5 Comparison of the present results with the results of Hong et al. (1993) (S = 4.8 mm, and ER = 2) for Re=100, and qw = 200 W/m2 (X = 3) at0° angle. a Velocity distribution. b Nusselt number


Results and discussionReattachment zoneThe zone was allocated to display the numerical resultsto test the 2-D vertical mixed convective stream bystanding up the step. The results of speed distributionand skin friction coefficient were taken at differentvalues of Nu at various nanofluids at hand, variousnanoparticle volume fractions, Reynolds numbers, andvarying heat flux and the height of the wall, and finallywith varying nanoparticle diameters. The Reynolds num-ber was taken between 100 and 500 while the heat fluxwas considered between 100 and 600 W/m2. The streamreaches out from a totally developed upstream to outlinea basic circulation region. Starting forward, the speedprofile is reattached and redeveloped pushing toward atotally developed stream as fluid streams toward chan-nels exit.

Nanofluid parameters’ impactsThe nanoparticles with water as a base fluid of Al2O3,CaO, ZnO, and SiO2 were used. The impact of variousnanofluids on the heat transfer enhancement was testedunder the following parameters of ∅ = 0.04, dp = 25 nm,Re = 100, and qw = 500 W/m2 along the channel.Figure 6a shows that Nu acquires the highest value nearthe wall due to an increasing heating of the wall whichdecreases steadily as the detachment continues. This is aresult of the temperature refinement when the exchangedstream is joined to the essential separated stream which

has a lower temperature. It is found that SiO2 nanofluidhas the highest Nu peak followed by Al2O3, CuO, andfinally ZnO. The results mentioned can be explained interms of how much is the reduction in the fluid viscosityand the effect of the heat flux since the viscosity is verycritical to these two factors.This study also shows the effect of ∅ between 1 and

4% on the characteristics of the heat transfer asillustrated in Fig. 6b under the conditions ofnanoparticle dp = 25 nm, Re = 100, and qw = 500 W/m2.As ∅ increases, the Nu of SiO2 nanofluids ends uphigher than that of unadulterated fluids. This is becauseof the density increasing which prompts the heattransfer enhancement as showed in Fig. 6b. A possibleexplanation to this could be referred to the effect of thedecreasing temperature refinement as ∅ increases whichresults in increasing the heat transfer improvement. Theimpact of the diameter of nanoparticles on the heattransfer reveals that the heat transfer varies significantlywith the mean nanoparticle diameter between 25 and 80nm, at Re = 100, ∅ = 4%, and qw = 500 W/m2.Figure 6c shows the eventual outcome of Nu when

SiO2 nanofluids were used. It has been shown that themean nanofluid diameter increases due to the increasingNu. This is because the nanofluid properties such asdensity and heat capacity increase with a decreasingnanoparticle volume ratio which affects the surface area.Thus, the small diameter of the nanoparticles results inincreasing the heat transfer improvement. Consequently,

Table 2 Thermophysical properties for pure water and different nanofluids at T = 300 K (Corcione, 2010)

Thermophysical properties Water Al2O3 CuO ZnO SiO2

Density, ρ (kg/m3) 998.203 3970 6500 5600 2200

Dynamic viscosity, μ (Ns/m2) 2.01 × 10−3 – – – –

Thermal conductivity, k (W/m K) 0.613 40 20 13 1.2

Specific heat, Cp (J/kg K) 4182.2 765 535.6 495.2 703

Coefficient of thermal expansion, β (1/K) 2.06 × 10−4 5.8 × 10–6 4.3 × 10–6 4.3 × 10–6 5.5 × 10–6

a b c

Fig. 6 The effect of nanofluid parameters along the downstream wall at Re = 100, qw = 500 W/m2, ∅ = 4%, and dp = 25 nm for a differentnanoparticle type, b different volume fractions, and c different nanoparticle diameters


Nu increases as the diameter of the nanoparticlesincreases.

Different Reynolds numbers’ impactsDistribution of the velocityFigure 7 shows the speed circulations of SiO2 nanofluid atRe numbers in the scope of 100 ≤ Re ≤ 500, qw = 500 W/m2, dp = 25 nm, and ∅ = 4% at various X/S sections alongthe stepped wall. In Fig. 7a, as Re increases, the speedprofile for SiO2 nanofluid becomes more profound andillustrative. The speed increases as Re increases untilreaching the distribution at which the flow reached thereattachment. It has been noted that as the separationbetween the step and the stepped wall increase, the flowachieves the reattachment faster and the span of thedistribution area diminishes as Re expands further asshown in Fig. 7b, c. Beyond this point, the downstreamshows that the flow begins to redevelop until reachingcompletely developed flow at the exit as shown in Fig. 7d.

Coefficient of skin frictionFigure 8a explains the behavior of the skin frictioncoefficient of the SiO2 nanofluid at Re in the scope of

100 ≤ Re ≤ 500, ∅ = 4%, qw= 500 W/m2, and dp = 25 nmalong the downstream wall. It is shown that the skinfriction coefficient decreases rapidly as Re increases.Additionally, it is seen that the crests at and close to theessential local distribution are displaced along the way fromthe wall divider in the streamwise bearing as Re increases.This increase comes with the increasing of the lengthdifferential of the essential distribution region. The behaviorof the coefficient of friction is inversely proportional.

Nusselt numberThe Nu of SiO2 nanofluid at Re between 100 and 500,∅ = 4%, qw = 500 W/m2, and dp = 25 nm along thedownstream wall is plotted in Fig. 8b. It is shown thatNu increases as Re increases exhibiting strongerconvective current which is caused by the reduction inthe isotherms. The behavior of Nu shows an exponentialreduction from its optimal level until the vortex isstarted forming. At the highest Re, the stream decreasesto the minimum apex of the Nu number at the regionwhere the flows are mixed. Along this zone, the Nu SiO2

nanofluid was found to possess higher values as Renumber increases.

a b

c d

Fig. 7 Velocity distributions of SiO2 nanofluid with ∅ = 4%, and dp = 25 nm at different Re for qw = 500 W/m2 at a X/S = 0, b X/S = 1.8, c X/S =12.82, and d exit


Various heat fluxes’ impactsDistribution of the velocityFigure 9 shows the speed distribution of SiO2

nanofluid at qw varies between 100 and 600W/m2,Re = 100, dp = 25 nm, and ∅ = 4% along the X/Ssections. It seems that there is an insignificant effectat the edge region, as the stream profiles show nopattern difference as shown in Fig. 9a.However, the degree of the circulation area expands as

the heat transfer increases between the heated steppedwall and the stream of the nanofluid as shown in Fig. 9b,c. It was also found that the buoyancy force slightlypushes up the fast stream and cutting down heat fluxand increasing the reattachment length. As the divisions,X/S along the wall increases the circulation zonedecreases as shown in Fig. 9b, c. At this location, theflow starts to redevelop approaching full developingstream flow at the exit according to Fig. 9d.

Skin friction coefficientThe testing of the skin friction of SiO2 nanofluid wascarried out with ∅ = 4%, and dp = 25 nm, heat flux in thescope of 100≪ qw≪ 600 W/m2, and Re = 100 along thedownstream divider are shown in Fig. 10a. It is observedthat the increase in the heat flow enhances the skinfriction coefficient. However, at a particular heat flux ofqw = 600 W/m2, the skin friction coefficient shows highervalues due to the diminishing shear stress at the vortex.

Nusselt numberFigure 10b explains the behavior of Nu-SiO2 with ∅ =4%, dp = 25 nm, heat flux of 100≪ qw≪ 600 W/m2, and

Re = 100 along the downstream divider. As qw increases,it was noticed that the highest value of Nu decreases dueto the increasing effect of the expanding buoyancy force.It is important to note that the reduction of optimized

Nu continues until roughly the exiting point. The resultsshow that the stream with high heat flow possesses themost astounding Nu least peak in the region where theflows are mixed. It was also found that alongside thisterritory, Nu with SiO2 nanofluid possesses the highestvalue when the heat flow is at the highest value.

ConclusionsNumerical simulation for laminar blended convectionstream in a vertical 2-D backward-facing step channelconfiguration was investigated under a variety of param-eters and initial conditions. This topic has recentlygained special importance especially due to consolidatingRe and nanofluids such as aluminum, copper(II) oxide,zinc oxide, and silicon dioxide with water. Reynoldsnumber was chosen within 100≪ Re ≤ 500, diameter ofnanoparticles dp: [25, 80] nm, and ∅: [1%, 4%]. Thebackward-facing step downstream flow has reached itsuniform condition at the uniform heat flux between 100and 600W/m2 while the channel particular propel stat-ures were taken in the extent of 3.0≪ S≪ 5.8 mm. Thegoverning equations have shown very good agreementwith the solution using FVM with specific suppositionscoupled with proper limit conditions. The current inves-tigation examined the influence of the stream and itsrelevant opposing flow on the properties of the heat flux.The following conclusions are drawn from thisinvestigation:

a b

Fig. 8 The effect of Re of SiO2 nanofluid with ∅ = 4%, and dp = 25, qw = 500 W/m2 along the downstream wall. a Skin friction coefficient. bNusselt number


Fig. 10 The effect of heat flux of SiO2 nanofluid with∅= 4%, and dp= 25, Re= 100 along the downstream wall. a Skin friction coefficient. b Nusselt number

Fig. 9 Velocity distributions of SiO2 nanofluid with φ = 4%, and dp = 25 nm at different heat fluxes for Re= 100 at a X/S = 0, b X/S = 1.8, c X/S = 12.82,and d exit


1. SiO2 nanoparticles show the most astounding Nufollowed by Al2O3, CaO, and ZnO.

2. Nu increased continuously by expanding Re and byincreasing the step height as well. It was alsoobserved that Nu increases as the heat fluxincreases. However, Nu is slowly diminishing as thenanofraction diminishes.

3. The present work creates a region of a straightdownstream distribution for blended convectionstream at various Re and heat flux. It was foundthat this distribution is highly dependent onincreasing Re. The best location of this distributingregion was allocated at the interface of the cornerwhere the stepping height joins the downstreamwall.

4. The heat flux was found very dependent on theconditions that correlate the preferred fluxexchange rate over restricting stream condition.

NomenclatureA Area (m2)Al2O3 Aluminum oxideAr Aspect ratioBFS Backward-facing stepcp Specific heat (kJ/kg K)CFD Computational fluid dynamicCuO Copper oxidedp Diameter of nanofluid particles (nm)FVM Finite volume methodDh Hydraulic diameter at inlet (m)ER Expansion ratio, H/Se Expansion successive ratioFFS Forward-facing stepf Elliptic relaxation functionGr Grashof number, gβΔTS3/v2

g Gravitational acceleration (m/s2)H Total channel height (m)h Inlet channel height (m)h Convective heat transfer coefficient (W/m2 K)H2O Waterk Thermal conductivity (W/m K)k Turbulent kinetic energy (m2/s2)S Step height (m)SiO2 Silicon dioxideL Total length channel (m)Nu Nusselt number, hs/kNus, max Maximum Nusselt number, hs/kP Nodal point number of processorsp Pressure (pa)pa Pressure at the outlet (pa)Pr Prandtl number, μ Cp/kqw Wall heat flux (W/m2)Re Reynolds number, ρuo Dh/μRi Richardson number, Gr/Re2

T Temperature (K)Tw Heat wall temperature (K)To Temperature at the inlet, outlet, or top wall (K)UHF Uniform heat fluxU Dimensionless streamwise velocity component, u/uou Velocity component x-direction (m/s)uo Average velocity for inlet flow (m/s)u∞ Free-stream velocity (m/s)V Dimensionless transverse velocity component, v/uov Velocity component y-direction (m/s)X Dimensionless length at x-coordinate, x/Sx x-Coordinate direction (m)Xe Downstream wall length (m)Xi Upstream wall length (m)Xn Nusselt number peak length (m)Xo Secondary recirculation length (m)Xr Reattachment length (m)Y Dimensionless length at y-coordinate, y/Sy y-Coordinate direction (m)ZnO Zinc oxide

Greek symbolsρ Density (kg/m3)β Thermal expansion coefficient, (1/K)υ Kinematic viscosity (m2/s)φ Volume fraction (%)μ Dynamic viscosity (N m/s)α Thermal diffusivity of the fluid (m2/s)Δ Amount of difference

Dimensionless temperature, (T − To)/(Tw − To)

Subscriptsbf Base fluidi Inleto Outletf Fluidnf Nanofluids Solid (nanoparticles)W Wall

AcknowledgementsThe authors gratefully acknowledge the Al-Furat Al Awsat TechnicalUniversity ‘Iraq’ for supporting this work.

Authors’ contributionsAAA-O and AJC carried out the experiments. ARY, MHM, and DHA collectedthe data and did the validation. AAH and MST supervised the project. AAAwrote the manuscript with support from TSG. All authors read and approvedthe final manuscript.

FundingUKM-YSD Grant 020–2017

Availability of data and materialsAll data generated or analyzed during this study are included in thispublished article.

Competing interestsThe authors declare that they have no competing interests.


Author details1Department of Power Mechanics, Technical Institute of Babylon, Al-Furat AlAwsat Technical University, Babil, Iraq. 2Technical College Al-Musaib, Al-FuratAl Awsat Technical University, Al-Musaib, Babil 51009, Iraq. 3Faculty ofEngineering & Built Environment, Universiti Kebangsaan Malaysia, 43600Bangi, Selangor, Malaysia. 4Energy and Renewable Energies TechnologyCenter, University of Technology, Baghdad 10001, Iraq.

Received: 8 March 2019 Accepted: 8 July 2019

ReferencesAbchouyeh, M. A., Mohebbi, R., & Fard, O. S. (2018). Lattice Boltzmann simulation

of nanofluid natural convection heat transfer in a channel with a sinusoidalobstacle. International Journal of Modern Physics C, 29, 1850079.

Abe, K., Kondoh, T., & Nagano, Y. (1995). A new turbulence model forpredicting fluid flow and heat transfer in separating and reattachingflows—II. Thermal field calculations. International Journal of Heat andMass Transfer, 38, 1467–1481.

Abu-Mulaweh, H. (2003). A review of research on laminar mixed convection flowover backward-and forward-facing steps. International Journal of ThermalSciences, 42, 897–909.

Abu-Mulaweh, H., Armaly, B. F., & Chen, T. (1993). Measurements of laminarmixed convection in boundary-layer flow over horizontal and inclinedbackward-facing steps. International Journal of Heat and Mass Transfer, 36,1883–1895.

Abu-Nada, E. (2008). Application of nanofluids for heat transfer enhancement ofseparated flows encountered in a backward facing step. International Journalof Heat and Fluid Flow, 29, 242–249.

Al-Aswadi, A., Mohammed, H., Shuaib, N., & Campo, A. (2010). Laminar forcedconvection flow over a backward facing step using nanofluids. InternationalCommunications in Heat and Mass Transfer, 37, 950–957.

Alawi, O., Azwadi, C. N., Kazi, S., & Abdolbaqi, M. K. (2016). Comparative study onheat transfer enhancement and nanofluids flow over backward and forwardfacing steps. Journal of Advanced Research in Fluid Mechanics and ThermalSciences, 23, 25–49.

Al-Shamani, A. N., Sopian, K., Mohammed, H., Mat, S., Ruslan, M. H., & Abed, A. M.(2015). Enhancement heat transfer characteristics in the channel withtrapezoidal rib–groove using nanofluids. Case Studies in Thermal Engineering,5, 48–58.

Armaly, B. F., Durst, F., Pereira, J., & Schönung, B. (1983). Experimental andtheoretical investigation of backward-facing step flow. Journal of FluidMechanics, 127, 473–496.

Blackwell, B., & Armaly, B. (1993). Computational aspects of heat transferbenchmark problems. ASME HTD, 258, 1–10.

Bomela, C. L. (2014). The effects of inlet temperature and turbulence characteristicson the flow development inside a gas turbine exhaust diffuser. Charlotte: TheUniversity of North Carolina.

Chen, Y., Nie, J., Armaly, B., & Hsieh, H.-T. (2006). Turbulent separated convectionflow adjacent to backward-facing step—effects of step height. InternationalJournal of Heat and Mass Transfer, 49, 3670–3680.

Corcione, M. (2010). Heat transfer features of buoyancy-driven nanofluids insiderectangular enclosures differentially heated at the sidewalls. InternationalJournal of Thermal Sciences, 49, 1536–1546.

D’Adamo, J., Sosa, R., & Artana, G. (2014). Active control of a backward facing stepflow with plasma actuators. Journal of Fluids Engineering, 136, 121105.

Daungthongsuk, W., & Wongwises, S. (2007). A critical review of convective heattransfer of nanofluids. Renewable and Sustainable Energy Reviews, 11, 797–817.

Davis, J. R. (1993). Aluminum and aluminum alloys: ASM international.Delouei, A. A., Sajjadi, H., Izadi, M., & Mohebbi, R. (2019). The simultaneous effects

of nanoparticles and ultrasonic vibration on inlet turbulent flow: anexperimental study. Applied Thermal Engineering, 146, 268–277.

Denham, M., & Patrick, M. (1974). Laminar flow over a downstream-facing step ina two-dimensional flow channel. Transactions of the Institution of ChemicalEngineers, 52, 361–367.

Fernández, L. D., Lara, E., & Mitchell, E. A. (2015). Checklist, diversity anddistribution of testate amoebae in Chile. European Journal of Protistology, 51,409–424.

Gartling, D. K. (1990). A test problem for outflow boundary conditions—Flowover a backward-facing step. International Journal for Numerical Methods inFluids, 11, 953–967.

Ghasemi, B., & Aminossadati, S. (2010). Brownian motion of nanoparticles in atriangular enclosure with natural convection. International Journal of ThermalSciences, 49, 931–940.

Hasan, H. A., Sopian, K., Jaaz, A. H., & Al-Shamani, A. N. (2017). Experimentalinvestigation of jet array nanofluids impingement in photovoltaic/thermalcollector. Solar Energy, 144, 321–334.

Hashemi, Z., Abouali, O., & Ahmadi, G. (2017). Direct numerical simulation ofparticle–fluid interactions: a review. Iranian Journal of Science and Technology,Transactions of Mechanical Engineering, 41, 71–89.

Hashim, W. M., Shomran, A. T., Jurmut, H. A., Gaaz, T. S., Kadhum, A. A. H., & Al-Amiery, A. A. (2018). Case study on solar water heating for flat plate collector.Case Studies in Thermal Engineering, 12, 666–671.

Heidari, H., Mohebbi, R., & Safarzade, A. (2016). Parameter estimation infractional convection-diffusion equation. PONTE International ScientificResearch Journal, 72, 55–68.

Hong, B., Armaly, B. F., & Chen, T. (1993). Laminar mixed convection in a ductwith a backward-facing step: The effects of inclination angle and Prandtlnumber. International Journal of Heat and Mass Transfer, 36, 3059–3067.

Iler, R. K. (1979). The chemistry of silica (pp. 30–62). New York: Wiley.Iwai, H., Nakabe, K., Suzuki, K., & Matsubara, K. (2000). The effects of duct

inclination angle on laminar mixed convective flows over a backward-facingstep. International Journal of Heat and Mass Transfer, 43, 473–485.

Izadi, M., Hoghoughi, G., Mohebbi, R., & Sheremet, M. (2018). Nanoparticlemigration and natural convection heat transfer of Cu-water nanofluid insidea porous undulant-wall enclosure using LTNE and two-phase model. Journalof Molecular Liquids, 261, 357–372.

Izadi, M., Mohebbi, R., Chamkha, A., & Pop, I. (2018). Effects of cavity and heatsource aspect ratios on natural convection of a nanofluid in a C-shapedcavity using Lattice Boltzmann method. International Journal of NumericalMethods for Heat & Fluid Flow, 28, 1930–1955.

Izadi, M., Mohebbi, R., Karimi, D., & Sheremet, M. A. (2018). Numerical simulationof natural convection heat transfer inside a ┴ shaped cavity filled by aMWCNT-Fe3O4/water hybrid nanofluids using LBM. Chemical Engineering andProcessing-Process Intensification, 125, 56–66.

Jaaz, A., Hasan, H., Sopian, K., Kadhum, A., Gaaz, T., & Al-Amiery, A. (2017). Outdoorperformance analysis of a photovoltaic thermal (PVT) collector with jetimpingement and compound parabolic concentrator (CPC). Materials, 10, 888.

Jaaz, A. H., Sopian, K., & Gaaz, T. S. (2018). Study of the electrical and thermalperformances of photovoltaic thermal collector-compound parabolicconcentrated. Results in Physics, 9, 500–510.

John, D., & Anderson, J. (1995). Computational fluid dynamics: the basics withapplications. In Mechanical Engineering Series. Sydney: McGraw-Hill.

Kherbeet, A. S., Mohammed, H., Salman, B., Ahmed, H. E., Alawi, O. A., & Rashidi,M. (2015). Experimental study of nanofluid flow and heat transfer overmicroscale backward- and forward-facing steps. Experimental Thermal andFluid Science, 65, 13–21.

Kumar, A., & Dhiman, A. K. (2012). Effect of a circular cylinder on separated forcedconvection at a backward-facing step. International Journal of ThermalSciences, 52, 176–185.

Kumar, S. S., Venkateswarlu, P., Rao, V. R., & Rao, G. N. (2013). Synthesis,characterization and optical properties of zinc oxide nanoparticles.International Nano Letters, 3, 30.

Ma, Y., Mohebbi, R., Rashidi, M., & Yang, Z. (2018a). Study of nanofluid forcedconvection heat transfer in a bent channel by means of lattice Boltzmannmethod. Physics of Fluids, 30, 032001.

Ma, Y., Mohebbi, R., Rashidi, M., & Yang, Z. (2019). MHD forced convection ofMWCNT–Fe 3 O 4/water hybrid nanofluid in a partially heated τ-shapedchannel using LBM. Journal of Thermal Analysis and Calorimetry, 136(4),1723–1735.

Ma, Y., Mohebbi, R., Rashidi, M., & Yang, Z. (2018b). Simulation of nanofluidnatural convection in a U-shaped cavity equipped by a heating obstacle:Effect of cavity's aspect ratio. Journal of the Taiwan Institute of ChemicalEngineers, 93, 263–276.

Ma, Y., Mohebbi, R., Rashidi, M., & Yang, Z. (2018c). Numerical simulation of flow overa square cylinder with upstream and downstream circular bar using latticeBoltzmann method. International Journal of Modern Physics C, 29, 1850030.

Ma, Y., Mohebbi, R., Rashidi, M., Yang, Z., & Sheremet, M. A. (2019). Numericalstudy of MHD nanofluid natural convection in a baffled U-shaped enclosure.International Journal of Heat and Mass Transfer, 130, 123–134.

Ma, Y., Mohebbi, R., Rashidi, M. M., Manca, O., & Yang, Z. (2018). Numericalinvestigation of MHD effects on nanofluid heat transfer in a baffled U-shaped


enclosure using lattice Boltzmann method. Journal of Thermal Analysis andCalorimetry, 135(6), 3197–3213.

Ma, Y., Mohebbi, R., Rashidi, M. M., & Yang, Z. (2019). Effect of hot obstacleposition on natural convection heat transfer of MWCNTs-water nanofluid inU-shaped enclosure using lattice Boltzmann method. International Journal ofNumerical Methods for Heat & Fluid Flow, 29, 223–250.

Mohammed, H., Al-Aswadi, A., Shuaib, N., & Saidur, R. (2011). Convective heattransfer and fluid flow study over a step using nanofluids: a review.Renewable and Sustainable Energy Reviews, 15, 2921–2939.

Mohammed, H., Al-Aswadi, A., Yusoff, M., & Saidur, R. (2012). Mixed convectiveflows over backward facing step in a vertical duct using various nanofluids-buoyancy-assisting case. Thermophysics and Aeromechanics, 42, 1–30.

Mohammed, H., Alawi, O., & Sidik, N. C. (2016). Mixed convective nanofluids flowin a channel having forward-facing step with baffle. Journal of AdvancedResearch in Applied Mechanics, 24, 1–21.

Mohammed, H., Alawi, O. A., & Wahid, M. (2015). Mixed convective nanofluid flowin a channel having backward-facing step with a baffle. Powder Technology,275, 329–343.

Mohebbi, R., & Heidari, H. (2017). Lattice Boltzmann simulation of fluid flow andheat transfer in a parallel-plate channel with transverse rectangular cavities.International Journal of Modern Physics C, 28, 1750042.

Mohebbi, R., Izadi, M., & Chamkha, A. J. (2017). Heat source location and naturalconvection in a C-shaped enclosure saturated by a nanofluid. Physics ofFluids, 29, 122009.

Mohebbi, R., Izadi, M., Delouei, A. A., & Sajjadi, H. (2019). Effect of MWCNT–Fe 3 O4/water hybrid nanofluid on the thermal performance of ribbed channelwith apart sections of heating and cooling. Journal of Thermal Analysis andCalorimetry, 135, 3029–3042.

Mohebbi, R., Lakzayi, H., Sidik, N. A. C., & Japar, W. M. A. A. (2018). LatticeBoltzmann method based study of the heat transfer augmentationassociated with Cu/water nanofluid in a channel with surface mountedblocks. International Journal of Heat and Mass Transfer, 117, 425–435.

Mohebbi, R., Nazari, M., & Kayhani, M. (2016). Comparative study of forcedconvection of a power-law fluid in a channel with a built-in square cylinder.Journal of Applied Mechanics and Technical Physics, 57, 55–68.

Mohebbi, R., & Rashidi, M. (2017). Numerical simulation of natural convectionheat transfer of a nanofluid in an L-shaped enclosure with a heatingobstacle. Journal of the Taiwan Institute of Chemical Engineers, 72, 70–84.

Mohebbi, R., Rashidi, M., Izadi, M., Sidik, N. A. C., & Xian, H. W. (2018). Forcedconvection of nanofluids in an extended surfaces channel using latticeBoltzmann method. International Journal of Heat and Mass Transfer, 117,1291–1303.

Murshed, S. S., De Castro, C. N., Lourenço, M., Lopes, M., & Santos, F. (2011). Areview of boiling and convective heat transfer with nanofluids. Renewableand Sustainable Energy Reviews, 15, 2342–2354.

Nazari, M., Kayhani, M., & Mohebbi, R. (2013). Heat transfer enhancement in achannel partially filled with a porous block: lattice Boltzmann method.International Journal of Modern Physics C, 24, 1350060.

Nazari, M., Mohebbi, R., & Kayhani, M. (2014). Power-law fluid flow and heattransfer in a channel with a built-in porous square cylinder: lattice Boltzmannsimulation. Journal of Non-Newtonian Fluid Mechanics, 204, 38–49.

Nie, J., & Armaly, B. F. (2002). Three-dimensional convective flow adjacent tobackward-facing step-effects of step height. International Journal of Heat andMass Transfer, 45, 2431–2438.

Nikkhah, Z., Karimipour, A., Safaei, M. R., Forghani-Tehrani, P., Goodarzi, M., Dahari,M., et al. (2015). Forced convective heat transfer of water/functionalizedmulti-walled carbon nanotube nanofluids in a microchannel with oscillatingheat flux and slip boundary condition. International Communications in Heatand Mass Transfer, 68, 69–77.

Öztop, H. F. (2006). Turbulence forced convection heat transfer over doubleforward facing step flow. International Communications in Heat and MassTransfer, 33, 508–517.

Park, T. S., & Sung, H. J. (1995). A nonlinear low-Reynolds-number κ-ε model forturbulent separated and reattaching flows—I. Flow field computations.International Journal of Heat and Mass Transfer, 38, 2657–2666.

Patanker, S. (1980). Numerical heat transfer and fluid flow. New York: HemispherePublishing Corporation.

Ranjbar, P., Mohebbi, R., & Heidari, H. (2018). Numerical investigation ofnanofluids heat transfer in a channel consisting of rectangular cavities bylattice Boltzmann method. International Journal of Modern Physics C (IJMPC),29, 1–23.

Rhee, G. H., & Sung, H. J. (1996). A nonlinear low-Reynolds-number k-ε model forturbulent separated and reattaching flows—II. Thermal field computations.International Journal of Heat and Mass Transfer, 39, 3465–3474.

Richardson, H. W. (2002). Copper compounds in Ullmann’s encyclopedia ofindustrial chemistry. Weinheim: Wiley-VCH.

Safaei, M., Togun, H., Vafai, K., Kazi, S., & Badarudin, A. (2014). Investigation of heattransfer enhancement in a forward-facing contracting channel using FMWCNTnanofluids. Numerical Heat Transfer, Part A: Applications, 66, 1321–1340.

Saidur, R., Leong, K., & Mohammad, H. (2011). A review on applications andchallenges of nanofluids. Renewable and Sustainable Energy Reviews, 15,1646–1668.

Selimefendigil, F., & Öztop, H. F. (2015). Numerical investigation and reducedorder model of mixed convection at a backward facing step with a rotatingcylinder subjected to nanofluid. Computers & Fluids, 109, 27–37.

Sheikholeslami, M., & Chamkha, A. J. (2016). Flow and convective heat transfer ofa ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in thepresence of a variable magnetic field. Numerical Heat Transfer, Part A:Applications, 69, 1186–1200.

Sheikholeslami, M., & Ganji, D. (2016). Nanofluid convective heat transfer usingsemi analytical and numerical approaches: a review. Journal of the TaiwanInstitute of Chemical Engineers, 65, 43–77.

Trisaksri, V., & Wongwises, S. (2007). Critical review of heat transfer characteristicsof nanofluids. Renewable and Sustainable Energy Reviews, 11, 512–523.

Tylli, N., Kaiktsis, L., & Ineichen, B. (2002). Sidewall effects in flow over a backward-facing step: experiments and numerical simulations. Physics of Fluids, 14,3835–3845.

Vajjha, R. S., & Das, D. K. (2009). Experimental determination of thermalconductivity of three nanofluids and development of new correlations.International Journal of Heat and Mass Transfer, 52, 4675–4682.

Wang, X.-Q., & Mujumdar, A. S. (2007). Heat transfer characteristics of nanofluids:a review. International Journal of Thermal Sciences, 46, 1–19.

Williams, P., & Baker, A. (1997). Numerical simulations of laminar flow over a 3Dbackward-facing step. International Journal for Numerical Methods in Fluids,24, 1159–1183.

Xu, D., Pan, L., & Yao, Q. (2007). Heat transfer cost-effectiveness of nanofluids. InCleantech 2007: the Cleantech Conference, Venture Forum and Trade Show,May 23–24, 2007, Santa Clara, California, USA (p. 79).

Yu, W., & Xie, H. (2012). A review on nanofluids: preparation, stability mechanisms,and applications. Journal of Nanomaterials, 2012, 1.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.


characterization the effects of nanofluids and heating on

Documents