investigation of the effects of the dimension of a localized heat … · 2014-05-13 · fringes...

Investigation of the effects of the dimension of a localized heat source on the natural convection in square cavities

B. Calcagni, F. Marsili & M. Paroncini Dipartimento di Energetica, Università Politecnica delle Marche

Abstract

The objective of the present study is to gain some insight into fluid motion and heat transfer phenomena in the case of a square enclosure heated from below and symmetrically cooled from the sides; the effects of different dimensions of the heat source are experimentally investigated. In this paper we analysed the effect of the variation in the heat source length on the natural convection inside the square cavity; the length of the heat sources studied are 1/5, 2/5, 3/5 and 4/5 of the wall. The temperature distribution is experimentally measured by real-time and double-exposure holographic interferometry. Different convection forms were obtained depending on Ra and on the heat source length. Graphs with relations between average Nu, Ra and the heat source length are finally presented. The Nusselt number was evaluated on the heat source surface and it showed a symmetrical form raising near the heat source borders. Keyword: natural convection, square enclosure, localized heat source, real-time and double exposure holographic interferometry.

1 Introduction

Thermal management is a critical task in the design of electronic systems especially the natural convection driven system which encompass the majority of the consumer products. In fact since proper cooling of electronic components by natural or mixed convection is a reliable operation, the study of heat transfer in these configurations must be examined in detail in order to provide adequate

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Computational Methods and Experimental Measurements XII 727

cooling and to prevent failure of the components. So the knowledge of natural convection in various geometry becomes fundamental in several engineering and environmental applications. The rectangular cavity is the most extensively studied enclosure because many engineering applications can be simplified to this geometry; these include solar collector cavities, air flow in rooms and other building structures such as cavity walls and double pane windows, cooling of electronic equipment and others. Although natural convection in a square cavity is a very good model and vehicle for both experimental and theoretical studies few recent papers deal with free natural convection in enclosures with a localised heat source; moreover the attention is focused essentially on numerical investigation as for Ntibarufata et al. [12] that analysed the natural convection in partitioned enclosures with localized heating from below. Ganzorolli and Milanez [8] numerically studied the natural convection in rectangular enclosures heated from below and symmetrically cooled from the sides; the paper investigated the influence of the Rayleigh and Prandtl numbers and of the aspect ratio on the motion and on the energy transport. Ramos and Milanez [14] treated numerically and experimentally the natural convection in cavities heated from below by a thermal source which dissipated energy at a constant rate; November and Nansteel [11] analytically and numerically studied the natural convection of water in a rectangular enclosure heated from below and cooled along one side. Aydin and Yang [1] treated numerically the convection of air in a rectangular enclosure that was locally heated from below and symmetrically cooled from the two vertical sides. The paper deals with an experimental investigation of free convection of air in square enclosures with a localized heat source located on the bottom wall of the cavity, and symmetrically cooled from the sides. The optical set-up allows the use of double-exposure or real-time holographic interferometry techniques, for steady-state and temporal evolution measurements of heat transfer processes respectively [4]. The real time technique has been used also to check the presence of plume oscillations. The holographic interferometry guarantees high precision and sensitivity, very low noise level and, moreover, the possibility of displaying the temperature distribution across the whole investigated region. The objective of the heat transfer analysis is the investigation of the Nusselt number distribution on the heat source at various Rayleigh numbers.

2 Enclosure geometry and experimental arrangement

The configuration of the test cell is seen in fig. 1 and 2; it consists of a square enclosure of dimensions HxHxL, with H=0.05m and L=0.405m; L was much greater than H to let the motion to develop in the L direction, parallelly to the laser beam, with a two-dimensional shape. The lateral vertical walls are made of aluminium and a thermostatic bath provided the circulation of the cooling fluid through a metal jacket attached to the back surface. The top and bottom surface of the enclosure are made of Plexiglas and, except for the heated section, are


728 Computational Methods and Experimental Measurements XII

considered to be adiabatic while the end vertical walls are made of glass that guarantees the optical access to the cavity. The heat source, centrally located on the lower wall, is in brass and it is maintained to a temperature Tc by a circulating fluid passing through it. The heat source dimensions investigated are 1/5, 2/5, 3/5 and 4/5 of the wall.

H

HTc

Th

Tc1 1

2

23

l

Figure 1: Configuration of the test cell: (1) walls at temperature Tc; (2) Plexiglas layers; (3) heat source at temperature Th.

Figure 2: Photo of the test cell.

The temperatures of fluids are measured by copper-constantan thermocouples; three of them are located 1 mm under the surface of the brass of the heat source, and other five of them are inside the aluminium of each vertical walls; the difference between the three temperature measured on the heat source is about 0.1K so that it is possible to consider the heat source isotherm.

X

Y

ε = l/H



The experimental set-up includes, besides the test-cell filled with air at atmospheric pressure, the pneumatic auto levelling table, the holographic interferometer, the optical instruments, two thermostatic baths and the data acquisition system (fig. 3) The light source is an Argon-ion laser with a nominal power rating of 4W, with etalon for the 514.5 nm wavelength; the object and the reference beam have a maximum diameter of 0.15 m. The holograms have been obtained with the interferometer infinite fringe position field, so that the fringe pattern shows directly the distribution of the isothermal lines. The temperatures of the heat source and of the walls measured by the thermocouples cannot be considered as reference in the evaluation of the interferograms because their position on them is uncertain due to diffraction effects so another thermocouple is located in the core of the test volume to provide a reference temperature. The interferograms are evaluated by using a travelling microscope to obtain the intensity distribution. According to Hauf and Grigull [10], the expected accuracy for small fringe numbers (less than 30) can be of about 10%.

Figure 3: Experimental set-up.

The local (Nu) and the average Nusselt ( Nu ) number on the heat source are given respectively by

TH

yTNu

0 ∆⋅

∂∂

−==y

(1)

where H is the side of the square test volume and it is equal to 0.05 m, ∆T=Th-Tc, and y is the vertical direction, and by



∫ ⋅⋅=l

l 0

dxNu1Nu (2)

where l is the source length, which was equal to 0.04 m (ε=4/5), 0.03 m (ε=3/5), 0.02 m (ε=2/5) and 0.01 m (ε=1/5).

3 Results and discussion

The experimental analysis studies the development of the convective heat transfer with the real time technique; figures 4, 5 show three photograms of a real-time video recording for ε=1/5 and ε=3/5.

(a) the start (b) elapsed time 37 sec (c) elapsed time 1740 sec

Figure 4: Real time interf.; ε=1/5.

(a) the start (b) elapsed time 30 sec (c) elapsed time 1800 sec

Figure 5: Real time interf.; ε=3/5.

The first photogram corresponds to the start of the fluid circulation inside the lateral walls and in the heat source, after few seconds a modest curvature in the fringes denotes a weak convection while after several minutes the photograms reveal a well-developed convective motion. Figure 6 is a double exposure interferogram for ε = 2/5 and Ra=1.63•104; the image shows a persisting prevalent conductive heat transfer up to Ra≃104. The following figures (7-8) are the interferograms of the experimental test carried out on the cavity with a heat source of 0.002m (ε = 2/5) and of 0.004m (ε = 4/5).



Figure 7a: ε = 2/5; Ra = 6,1·104. Figure 8a: ε = 4/5;Ra = 5.9·104.

Figure 7 b: ε = 2/5; Ra = 1,63·105. Figure 8 b: ε = 4/5;Ra = 1,425·105.

Figure 7 c: ε = 2/5; Ra = 1,86·105. Figure 8 c: ε = 3/5; Ra = 1,881·105.

.

Figure 6: Double exp. interf.; ε = 2/5; Ra = 1.63•104.



For Ra lower than about 104 the isotherms had the typical aspect of the conductive heat transfer and only for Ra>1.63·104 a change in the isotherms curvature show the development of a weak convection. As the Rayleigh number increases the intensity of the fluid circulation raises producing a distortion in the isotherms and the convective component is more evident. For Ra near 105 it is possible to observe in the interferograms the formation of a second curvature (figures 7b and 8b) of the isotherms; this is due to the downward movement of the cooled fluid. This implied an increase of circulation velocity and that the convection became the first mechanism for heat exchange. Figures 7-8 are the double exposure interferograms for ε=2/5 and ε=4/5 for the above mentioned ranges of Ra, with the isotherms which tended assume a mushroom form. Figures 9 and 10 show how the temperature gradients are concentrated near the middle of the cavity due to the dimension of the heat source; high local Nu number at the extremity of the heat source means intense recirculation of the fluid with high temperature gradients. As soon as the heat source dimension rises the temperature gradients tend to decrease on the source with a consequently reduction of the local Nu. The differences between the temperature gradients on the heat source, for example for an ε=4/5, are not very high, thus the trend of the local Nu tends to become flat (figure 10). Figure 11 show an inverse proportionality between Nu and ε, for a fixed Ra; the development of the heat exchange generates that inders the central hot layer of fluid to approach the cold fluid near the vertical walls. Increasing the dimension of the heat source, the central layer become more wide and the heat transfer is reduced. An increase in the dimension of the heat source produces, for a fixed Ra, a compression of the fluid near the vertical walls preventing the forming of a regular circular flow; the decrease of the average Nusselt number Nu confirms this phenomenon. For this reason, an enlargement of the heat source, that means an increase of ε, makes the central channel to grow, causing a higher thermal resistance.

Position on the heat source (ε=2/5)

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

Nu

0

5

10

15

20

25

30

Ra = 6,1 .104

Ra = 1,63 .105

Ra = 1,86 .105

Ra = 2,2 .105

Figure 9: Experimental local Nusselt for ε = 2/5.



Position on the heat source (ε=4/5)

0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5

Nu

0

5

10

15

20

25

30Ra=1.205 105

Ra=1.425*105

Ra=1.836*105

Ra=2.142*105

Figure 10: Experimental local Nusselt for ε = 4/5.

0

2

4

6

8

10

12

14

16

0 50000 100000 150000 200000 250000Ra

Nu

Nu_exp (1/5)

Nu_exp (2/5)

Nu_exp (3/5)

Nu_exp (4/5)

Figure 11: Experimental Nu for ε = 1/5, ε = 2/5 and ε = 3/5.

4 Conclusions

This paper presents an experimental investigation on natural convection of air (Pr = 0.71) inside a square cavity with a localized heat source localized on the bottom wall of the enclosure. The length (l) of the source analysed varied from 1/5 to 3/5 of the side (H). The two vertical walls provide the cooling of the cavity; all the others zones are adiabatic. The condition imposed on the exchanging surfaces is of constant temperature. The range of Ra numbers experimentally investigated are from 1.63•104 to 1.88•105 The local and average Nusselt numbers are evaluated on the heat source. The experimental investigation is realized with the holographic interferometry both in real time and in double exposure. The interferograms show a weak convective motion for Ra<1.63•104 and it increase for Ra near to 105 that represents the principal point of convection beginning.



Ra and Nu have a direct proportionality while Nu and ε (ε = l/H) are linked with an inverse proportionality; this means that a larger heat source can limit the development of an efficient convective heat transfer.

Nomenclature

Ra = Rayleigh number (Ra=gβH3(Th-Tc)/(να)) Nu = local Nusselt number (dimensionless) Nu = average Nusselt number (dimensionless) H =L = square cavity side (m) W = length of the cavity l = heat source length (m) T = temperature (K) ∆T = temperature difference between heat source and cold plates ε= dimensionless heat source length (ε =1/5; 2/5; 3/5;4/5) c = cold wall h = hot wall.

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investigation of the effects of the dimension of a localized heat … · 2014-05-13 · fringes...

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