International Journal of Modern Trends in Engineering and Research e-issn No.: , Date: April, 2016

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1 International Journal of Modern Trends in Engineering and Research e-issn No.: , Date: April, 2016 An Experimental and Numerical Study of Thermal Performance of a Radial Heat Sink Under Natural convection Mangesh D. Shende 1, Dr. Ashish Mahalle 2 1 Department of Mechanical Engineering, Shreeyash COE & T, Aurangabad, Maharashtra, India shendemd@rediffmail.com 2 Department of General Engineering,LIT, Nagpur, ashishmahalle@rediffmail.com Abstract In this paper, the effects of various parameters have been experimentally and numerically investigated for air side thermal performance under natural convection of a radial heat sink and the optimum values are found out. The overall heat transfer coefficient is measured experimentally and numerically. The general flow pattern is that of a chimney; i.e., cooler air entering from outside is heated as it passes between the fins, and then rises from the inner region of the heat sink. The thermal performance characteristics are obtained for various parameters such as number of fins, height of the fins, length of fins and the heat supplied to the heat sink. Based on the experimental data in the given range of number of fins, length & height of fins a generalised correlation is developed. Keywords- Natural convection, Heat sink, Circular base, Computation Fluid Dynamics I INTRODUCTION In many electronic components, the dissipation of generated heat into the surrounding fluid is important since it can reduce the performance of device or even sometimes may destroy the components or system. Heat sinks are the heat exchanging devices that are employed extensively to increase heat transfer rate from electronic components to the surrounding fluid. Application of heat sinks is not restricted to just electronic components. They are used in various systems such as highpower semi-conductor devices, high-power lasers, light emitting diodes (LEDs), computer cooling, and many other sensitive devices [1]. The thermal design of the system is influenced by the key drivers like chip size, power dissipation, junction temperature and ambient air temperature. The semiconductor industries are taking great amount of effort over the years to reduce the size of the devices. With the increase in power dissipation and reduction in the size, the growth in power density is expected to increase further over the next decade as shown in Figures. 1 and 2 [2]. The increasing power density indicates the thermal management solutions play an important role in determining the future semiconductor device technology. Figure. 1. High performance chip power trend Figure. 2. High performance chip heat flux All rights Reserved 975

2 Numerous experimental [4 7] and numerical [6] studies of rectangular fin or pin fin heat sinks have been carried out. Starner and McManus [4] experimentally investigated natural convection heat transfer from four heat sinks of differing dimensions, with the heat sinks oriented vertically, at a 45 0 angle, and horizontal. Welling and Woolbridge [5] conducted an experimental study of vertically oriented rectangular fins of constant length attached to a vertical base. They found that there exists an optimal fin height, corresponding to a maximum rate of natural convection heat transfer, for any given fin spacing. Harahap and Mcmanus [6] performed experiments to calculate the average heat transfer coefficients for two different fin lengths, and established a correlation with non-dimensional parameters and relevant fin dimensions. Passive cooling is a widely preferred method for electronic, power electronic and telecommunication devices since it is a cost effective, quiet and reliable solution. Air-cooling is recognized as an important technique in the thermal design of electronic packages [7]. Mehran Ahmadi et.al. investigated numerically and experimentally steady-state external natural convection heat transfer from vertically-mounted rectangular interrupted fins. A new compact correlation is proposed for calculating the optimum interruption length [7]. However, most of these studies are concerned with heat sinks with rectangular bases, which might be inefficient for cooling circular LED lights or the electronics components having circular base. The present study focuses upon the passive cooling i.e. natural or free convective heat transfer from a heat sink with a circular base and rectangular fins. So in this study, the heat transfer of a radial heat sink was experimentally & numerically analyzed and the thermo-flow pattern was observed. The convective heat transfer depends on number of complex parameters such that fin geometry, fin spacing buoyancy forces and fluid properties. So to study the performance of radial heat sink the effects of the number of fins, fin length, fin height, and heat flux on the thermal resistance and the average heat transfer coefficient were investigated. II DESIGN OF EXPERIMENT The minimum number of experimental combinations (MNE) for conducting simulations are given by MNE = kn in this research nine experimental models were generated with different parameters. For this Taguchi L9 orthogonal array was used, in which nine rows corresponding to the number of tests, with three columns at three levels were selected. Table No. 1. Parameter & level Parameter Code Level Length of fin (m) L 35 mm 45 mm 55 mm Height of fin (m) H 15 mm 25 mm 35 mm Number of fin n Figure. 3. Radial heat sink with a circular base and rectangular fins The experiment set up consists of different aluminum radial fin structures heated with the All rights Reserved 976

3 heater and the eight thermocouples are used to measure the temperature of the heat sink and one thermocouple is used to measure the atmospheric temperature. By using taguchi optimization technique, nine different models were manufactured by varying length of fin, height of fin and number of fin by using L9 arrays. Copper and aluminum are among the most-frequently used materials for this purpose within electronic devices. Copper is significantly more expensive than aluminum but is also roughly twice as efficient as a thermal conductor. Aluminum has the significant advantage that it can be easily formed by extrusion, thus making complex cross-sections possible. Aluminum is also much lighter than copper, offering less mechanical stress on delicate electronic components. Some heat sinks made from aluminum have a copper core as a trade off. The heat sink is made of aluminum (Al2014), with no additional surface treatment. In order to measure the performance of the radial heat sink experimentally it is essential that the rate of heat transfer between the heat sink and the ambient air be accurately measured. Also it should be served for indirect measurement of convective heat transfer coefficient between the fins and ambient air The experimental analysis of natural convection around radial heat sink is carried out by using following specification as listed below:- Outer radius of base of fin (ro) = 80 mm, Inner radius of base of fin (ri) = 10 mm Thickness for all configureuration of fin (t) = 2 mm, Total number of thermocouple = 09 Temperature indicator: Type K type 2.1 Heating System The base of the heat sink was heated by a heater with 1000W electrical resistance strip heater. The assembly was firmly bolted together to the bottom surface of the base. The lower surface and side of heater was insulated thermally by Sindanyo H9. The power was varied by rheostat and it was measured by calibrated inline voltmeter and ammeter. The temperature at the base of heat sink at steady state was measured by equally distributed set of 8 thermocouples. The thermocouples were screwed in their positions so as to ensure thermal contact. The average values obtained from these thermocouples are regarded as the average base temperature of heat sink. At 10 min interval observations were recorded when consecutive values were identical it was assumed that steady state condition was attained. Experimentation was carried out in room temperature According to Newton s law of cooling, Q = ha( T) (1) Therefore heat transfer coefficient, h = = ( ) Δ Δ Therefore the effective thermal resistance of heat sinks, R =1/ h A (3) (2) III COMPUTATIONAL PROCEDURE The numerical simulation is conducted using ANSYS 13 (Workbench) Fluent toolbox commercially available CFD code based on the finite volume method. 3.1 Assumptions For the numerical analysis, the following assumptions were imposed. 1. The flow was steady, laminar, and All rights Reserved 977

4 Material Cp (J/kg 0 C) μ (N/m 2 s) k (W/m 0 C) ρ (kg/m3 ) Air x x 10-5 Eqn. (10) Heat sink (Aluminum) Air density was calculated by treating air as an ideal gas. 3. Aside from density, the properties of the fluid were independent of temperature. 4. Radiation heat transfer was negligible. 3.2 Governing equations The governing equations are as follows [10] Air side Continuity equation (ρ) Momentum equations (ρ ) + (ρ) + (ρ) + (ρ) +(ρ) Table 2. Air and heat sink properties = 0 (4) = - + µ + + (5) (ρ) + (ρ ) + (ρ) = - + µ g ρ ρ (6) (ρ) + (ρ) Energy equation (ρ) + (ρ) + (ρ ) + (ρ) = - + µ + = (7) (8) Solid side Energy equation + + = 0 (9) The density of air will be calculated from the ideal gas law, ρ= ( ) (10) where Mw of air is kg/kmol. 3.3 Grid Independency Study In the present work, grid independency test was done for a randomly selected simulated case for the grid sensitivity. Multiple grids were generated starting from 1.0E+04 cells to 1.0E+05 cells. The numerical analysis over this complete range was studied and the results were compared. The temperature values showed that there was negligible difference in the results after 7.0 E+04 cells. So finally it was decided to use cell count of nearly 7.0 E+04, where fairly constant values of temperature were obtained as shown in Figure. All rights Reserved 978

5 Temperature Differnce (K) Cell Count (million) Figure. 4. Confirmation of grid independency The velocity vectors give the results that are chimney effect so our assumption is correct. Also the values of velocity vector are shown in the Figure. 5. Figure. 5. Velocity vectors for heat sink Figure. 6.Temperature profile at centre of fin To reduce the number of experiments we have used Taguchi L9 orthogonal array, which has given the data corresponding to the number of tests. So the experimental and numerical data is analyzed by using statistical analysis software JMP 10. This software analyzes data by using analysis of variance (ANNOVA). Figureure 7 shows the comparison of temperature difference between the experimental and numerical results. The numerical results are very much comparable with the experimental result, so the validity of numerical results is done and at the same time the bench marking of both the experimental and numerical procedure is carried out. 250 Teperature Difference (Tavg-Ta) (K) Numerical Experimental Heat Input (W) Figure. 7. Comparison of temperature difference for numerical & experimental All rights Reserved 979

6 IV EXPERIMENTAL UNCERTAINTIES The uncertainties in the experimental measurement have been determined using root sum square method described by Holman (1984). In any experimental method a set of measurements is made, and these measurements are then used to calculate the desired results of the experiments. The uncertainties in the calculated results are estimates on the basis of the uncertainties in the primary measurements and are given in Table 3. [8] Uncertainty variable Table 3. Uncertainty of variables. Error Fin Length ± x 10-2 % Fin Height ± 4.00 x 10-2 % Outer diameter ± % Inner diameter ± 0.05 % Thickness ± 0.5% Base surface area A b ± % One fin surface area ± % L/H of the heat sink % Temperature ± % Heat transfer rate % Heat transfer coefficient ± % Thermal resistance ± % Nusselt number ± % Grashoff number ± % V RESULTS & DISCUSSION The thermal characteristics obtained in this study are applicable to this particular heat sink with natural convection. As expected average Nusselt number increases with increasing Rayleigh number. From Figureure 8 it is also observed that the numerical results are very much comparative with the experimental results. As result of high thermal conductivity and the thickness of the aluminum heat sink the sink approximate in uniform wall temperature boundary condition during experiments. The surface temperature has been observed under steady state All rights Reserved 980

7 Nu Ra Figure. 8. Nusselt number vs Rayleigh number 5.1 Influence of different parameters on the performance of heat sink. Figureure 9 shows the effect of number of fins on the heat transfer coefficient. It is observed from the Figureure that as the number of fins increases the average heat transfer coefficient decreases. This is because the spaces between the fins is decreased therefore flow rate of the cooler air entering decreases and the air is heated more quickly due to the reduced space between fins. The thermal resistance (R) of the heat sink decreased with increasing the number of fins (n) up to the number of fins is less than 28 as the increased heat transfer surface area is larger than the decreased heat transfer coefficient. As the number of fins increases and are greater than 28, the thermal resistance of the heat sink increases with increase in number of fins, since the heat transfer coefficient is very small. Therefore there is optimum number of fins that gives the minimum thermal resistance Thermal Resisitance R (K/W) Heat Transfer coefficient h (W/m 2 K) Number of fins n Number of fins n Figure. 9. Effect of number of fins on thermal resistance and heat transfer coefficient The effect of the fin height on the performance of heat sink is shown in Figure. 10. For the incremented fin height there is lower thermal resistance resulted from the increased heat transfer surface area. The change in the heat transfer coefficient is relatively small, since the velocity of the air entering from outside increased very little with increasing fin height All rights Reserved 981

8 Thermal Resisitance R (K/W) Height H (mm) Heat transfer coefficient h (W/m 2 K) Height H (mm) Figure. 10. Effect of fin height on thermal resistance and heat transfer coefficient From Figure. 11. which shows the effect of the fin length on the heat transfer coefficient & thermal resistance it is observed that the thermal resistance and average heat transfer coefficient decreases with increase in the fin length. For the fin with the length longer than 55 mm the thermal resistance leveled off and reached a steady value. This is because the air temperature in the inner region is almost the same as the heat sink temperature, and hence any additional fin length beyond 55 mm does not contribute to an increase in the heat transfer rate. Thermal performance of the heat sink is shown in Figure. 12. The Nusselt number is decreasing with the number of fins this is due to increase in number of fins the gap between the fins decreases and the boundary layer formed is restricting the flow of air and heat. Similarly for the L/H ratio as the length is increasing the air at the centre of heat sink is already heated as it is moving towards the centre of heat sink so the temperature difference is low so the Nusselt number decreases with L/H ratio. Thermal Resistance R (K/W) Length L (mm) Heat transfer coefficient h (W/m 2 K) Figure. 11. Effect of fin length on thermal resistance and heat transfer coefficient Lenght of Fin (mm) Nu n L/H 3 4 Figure. 12. Thermal performance of heat sink Nu All rights Reserved 982

9 5.2 Development of convective heat transfer correlation function It was assumed that the steady state natural convective behavior of radial heat sink could be described in terms of Ra, H/L, n (no of fins) with the range 7000 Ra 13000, 1.5 H/L 3.35, 24 n 32 Nu = f (Ra, H/L, n). Where Nu is classical Nusselt number, Gr is Grashof number, Pr is Prandtl number and Ra is Rayleigh number. Nu = (11) Pr = (12) Gr = (13) All the above values are obtained at mean temperature T mean =T avg + T (14) The functional relationship between the dimensionless terms was determined by regression analysis for the range of experimental variables tested at steady state heat transfer and correlation was obtained by least square fit. Nu = Ra.. n. (15) CONCLUSION Natural convection heat transfer from a radial heat sink was experimentally and numerically investigated. Sensitivity measuring instruments were used to carry out accurate and repetitive experiments. CFD analysis was performed as numerical analysis for the determination of natural convection from a radial heat sink with different study parameters. The following results were obtained In this study Nusselt number increases with increasing Rayleigh numbers. The results obtained from experimental and numerical studies on the average nusselt number are found to be in good agreements. Comparison of average Nusselt number was done using the correlations of Ra, H/L and n. A new correlation was proposed on the determination of average Nusselt numbers for the range 7000 Ra 13000, 1.5 H/L 3.35, 24 n 32 for air. Temperature distribution over the radial heat sink was obtained by CFD analysis. Also the general flow pattern is that of a chimney; i.e., cooler air entering from outside is heated as it passes between the fins, and then rises from the inner region of the heat sink was observed. REFERENCES [1] Scott, W. A., Cooling of Electronic Equipment, John Wiley and Sons Interscience, NewYork, USA, 1974 [2] NEMI Technology Roadmaps, 2002 [3] Kristiansen, H., Thermal Management in Electronics, Chalmers University of Technology, Goteborg, Sweden, 2001, All rights Reserved 983

10 [4] K.E. Starner, H.N. McManus, An experimental investigation of free convection heat transfer from rectangular fin arrays, J. Heat Transfer 85 (2) (1963) [5] J.R. Welling, C.B. Wooldridge, Free convection heat transfer coefficients from rectangular vertical fins, Trans. ASME J. Heat Transfer 87 (3) (1965) [6] F. Harahap, H.N. McManus, Natural convection heat transfer from horizontal rectangular fin arrays, J. Heat Transfer 89 (1) (1967) [7] R.T. Huang, W.J. Sheu, C.C. Wang, Orientation effect on natural convective performance of square pin fin heat sinks, Int. J. Heat Mass Transfer 51 (9 10) (2008) [8] J.P. Holman, Experimental Methods for Engineers, McGraw Hill [9] S. Baskaya, M. Sivrioglu, M. Ozek, Parametric study of natural convection heat transfer from horizontal rectangular fin arrays, Int. J. Therm. Sci. 39 (8) (2000) [10] R.C. Sachdeva, Fundamentals of Engineering Heat and Mass Transfer, Wiley Eastern Ltd. India. [11] Abdullatif Ben-Nakhi, Ali J. Chamkha, Conjugate natural convection in a square enclosure with inclined thin fin of arbitrary length, International Journal of Thermal Sciences 46 (2007) [12] S.A. Nada, Natural convection heat transfer in horizontal and vertical closed narrow enclosures with heated rectangular finned base plate International Journal of Heat and Mass Transfer 50 (2007) [13] Dr. Ashish Mahalle, Mangesh D. Shende, Experimental & numerical analysis of natural convection heat transfer from a radial heat sink, Proceedings of the 23 rd National Heat and Mass Transfer Conference and 1 st International ISHMT-ASTFE Heat and Mass Transfer Conference All rights Reserved 984

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