This paper reports analytical solutions for both velocity and temperature profiles in Microchannel heat sinks by modeling the Microchannel heat sink as a fluid-saturated porous medium. The analytical solutions are obtained based on the modified Darcy model for fluid flow and the two-equation model for heat transfer. To validate the porous medium model and the analytical solutions based on that model, the closed-form solution for the velocity distribution in the fully-developed channel flow and the numerical solutions for the conjugate heat transfer problem, comprising the solid fin and the fluid, are also obtained. The analytical solutions based on the porous medium model are shown to predict the volume-averaged velocity and temperature distributions quite well. Using the analytical solutions, the aspect ratio and the effective thermal conductivity ratio are identified as variables of engineering importance and their effects on fluid flow and heat transfer are studied. As either one of these variables increases, the fluid temperature is shown to approach the solid temperature. Finally, the expression for the total thermal resistance, derived from the analytical solutions and the geometry of the microchannel heat sink for which the thermal resistance of the heat sink is minimal, is obtained.
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e-mail: sungkim@me.kaist.ac.kr
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Research Papers
Forced Convection in Microstructures for Electronic Equipment Cooling
S. J. Kim,
S. J. Kim
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
e-mail: sungkim@me.kaist.ac.kr
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D. Kim
D. Kim
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
Search for other works by this author on:
S. J. Kim
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
e-mail: sungkim@me.kaist.ac.kr
D. Kim
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea
J. Heat Transfer. Aug 1999, 121(3): 639-645 (7 pages)
Published Online: August 1, 1999
Article history
Received:
September 28, 1998
Revised:
March 8, 1999
Online:
December 5, 2007
Citation
Kim, S. J., and Kim, D. (August 1, 1999). "Forced Convection in Microstructures for Electronic Equipment Cooling." ASME. J. Heat Transfer. August 1999; 121(3): 639–645. https://doi.org/10.1115/1.2826027
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