Modeling of microchannel heat sinks for electronic cooling applications using volume averaging approach

In this paper, thermal and hydrodynamic characteristics in microchannel heat sinks are studied to determine the parameters required in modeling heat sinks as fluid saturated porous medium. A three-dimensional conjugate heat transfer model is developed for characterizing fluid flow and heat transfer in microchannel heat sinks. This numerical model is first validated with the results reported in literature. For effective modeling of heat sinks, two different porous medium models are studied, namely Darcy and Forchheimer flow models. Darcy flow model is used for characterizing hydrodynamically and thermally developed flow and Forchheimer model is considered for the developing flow. The regime of applicability of these models is specified in terms of non-dimensional parameter, Forchheimer number. It is found that for Forchheimer number greater than 0.008, the Forchhiemer flow model is more appropriate as compared to Darcy flow model. A generalized expression for permeability with aspect ratio of the channel is obtained. The average Nusselt number defined based on modified heat flux and modified length scale is found to remain constant for different aspect ratios and porosities of microchannel heat sink. The velocity and temperature profiles obtained from the present porous medium model, porous model reported in literature and three-dimensional microchannel heat sink are compared and a good agreement is achieved between present and three-dimensional model. The present model can be used as a reduced order model for analyzing microchannel heat sinks with entrance effects.