## THERMAL SCIENCE

International Scientific Journal

### FREE CONVECTION LIMIT TO HEAT TRANSFER FROM HEATSINKS WITH SQUARE FINS ON A HORIZONTAL BASE: COMPARISON WITH CYLINDRICAL FINS

**ABSTRACT**

Free convection about a single vertically orientated square fin on a horizontal plate has been investigated numerically. Fluid is drawn towards the fin from the far field which cools the fin and finally leaves through the top. For short fins, convection rather than the conduction is the controlling mechanism and this renders the fin thermal conductivity a parameter of little importance for such fins. Heat flux at the base of the fin decreases with increasing width of the fin confirming the benefits of large number of slender fins. A correlation has been developed to evaluate the heat flux at fin base which may be used to predict the upper bound of free convection heat transfer from any heat sink with square fins on a horizontal base. Rate of heat transfer so calculated has been compared with experimental data published recently. The study also reveals the advantage of the cylindrical fins over square fins.

**KEYWORDS**

PAPER SUBMITTED: 2012-10-04

PAPER REVISED: 2014-05-18

PAPER ACCEPTED: 2014-05-18

PUBLISHED ONLINE: 2014-12-14

**THERMAL SCIENCE** YEAR

**2015**, VOLUME

**19**, ISSUE

**Issue 5**, PAGES [1565 - 1574]

- Kim, D.K., Kim, S.J. and Bae, J.K., Comparison of Thermal Performances of Plate-fin and pin-fin Heat Sinks subject to an Impinging Flow, Int. J. Heat Mass Transfer, 52 (2009), pp. 3510-3517.
- Li, H.Y., Chiang, M.H. and Chen, K.Y., Performance Analysis of Pin-fin Heat Sinks with Confined Impingement Cooling, IEEE Trans. on Components and Packaging Tech., 30 (2007), pp. 383-389.
- Kim, D., Kim, S.J. and Ortega, A., Compact Modeling of Fluid Flow and Heat Transfer in Pin Fin Heat Sink, J. Electronic Packaging, Trans. ASME, 126 (2004), pp. 342-350.
- Yang, K.S., Chu, W.H., Chen, I.Y. and Wang, C.C., A Comparative Study of the Airside Performance of Heat Sinks having Pin Fin Configurations, Int. J. Heat Mass Transfer, 50 (2007), 23-24, pp. 4661-4667.
- Aihara, T., Maruyama, S. and Kobayakawa, S., Free Convective/Radiative Heat Transfer from Pin-fin Arrays with a Vertical Base Plate (general representation of heat transfer performance), Int. J. Heat Mass Transfer, 33 (1990), 6, pp. 1223-1232.
- Zografos, A.I. and Sunderland, J.E., Natural Convection from Pin fin Arrays, Experimental Thermal Fluid Sci., 3 (1990), 4, pp. 440-449.
- Sahray, D., Magril, R., Dubovsky, V., Ziskind, G. and Letan, R., Study of Horizontal-base Pin-Fin Heat Sinks in Natural Convection, Proceedings of IPACK2007 ASME InterPACK Vancouver British Columbia Canada, 2007.
- Kobus, C.J. and Oshio, T., Development of a Theoretical Model for Predicting the Thermal Performance Characteristics of a Vertical Pin-fin Array Heat Sink under Combined Forced and natural convection with Impinging Flow, Int. J. Heat Mass Transfer, 48 (2005), pp. 1053-1063. \
- Sahiti, N., Durst, F. and Dewan, A., Heat Transfer Enhancement by Pin Elements, Int. J. Heat Mass Transfer, 48 (2005), pp. 4738-4747.
- Huang, R.T., Sheu, W.J. and Wang, C.C., Orientation Effect on Natural Convective Performance of Square Pin Fin Heat Sinks, Int. J. Heat Mass Transfer, 51 (2008), 9-10, pp. 2368-2376.
- Sahray, D., Shmueli, H., Ziskind, G. and Letan, R., Study and Optimization of Horizontal-base Pin-fin Heat Sinks in Natural Convection and Radiation, J. Heat Transfer Trans. ASME, 132 (2010), pp. 012503-1-13.
- Leonard, B.P., Bounded Higher-order Upwind Multidimensional Finite-volume Convection-diffusion Algorithms, in: Adv. in Num. Heat Transfer, (Eds. W.J. Minkowycz, E.M. Sparrow) Vol.1, Taylor and Francis 2000.
- Sharma, A. and Eswaran, V., Conservative and Consistent Implementation and Systematic Comparison of SOU and QUICK Schemes for Recirculating Flow Computation on a Non-staggered Grid, Proc. 2nd Int. and 29th National FMEP conf., Roorkee, India, 2002, pp.351-358.
- Haldar, S.C., Natural Convection about a Cylindrical Pin Element on a Horizontal Plate, Int. J. Thermal Sc., 49 (2010), pp. 1977-83.
- Cebeci, T., Laminar Free Convection Heat Transfer from the Outer Surface of a Vertical Slender Circular Cylinder, Proc. Fifth Int. Heat Transfer Conf., Tokyo, 1974, pp.15-19.
- Raithby, G.D. and Hollands, K.G.T., Natural Convection, in: Handbook of Heat Transfer, (Eds. W.M. Rohsenow et. al.), 3rd Edition, McGrawHill, Ch.4, 1998.