Analysis of microchannel heat sinks for electronics cooling

Abstract

This paper presents an analytical and numerical study on the heat transfer characteristics of forced convection across a microchannel heat sink. Two analytical approaches are used: the porous medium model and the fin approach. In the porous medium approach, the modified Darcy equation for the fluid and the two-equation model for heat transfer between the solid and fluid phases are employed. Firstly, the effects of channel aspect ratio ( α s) and effective thermal conductivity ratio (k̃) on the overall Nusselt number of the heat sink are studied in detail. The predictions from the two approaches both show that the overall Nusselt number ( Nu) increases as α s is increased and decreases with increasing k̃. However, the results also reveal that there exists significant difference between the two approaches for both the temperature distributions and overall Nusselt numbers, and the discrepancy becomes larger as either α s or k̃ is increased. It is suggested that this discrepancy can be attributed to the indispensable assumption of uniform fluid temperature in the direction normal to the coolant flow invoked in the fin approach. The effect of porosity ( ε) on the thermal performance of the microchannel is subsequently examined. It is found that whereas the porous medium model predicts the existence of an optimal porosity for the microchannel heat sink, the fin approach predicts that the heat transfer capability of the heat sink increases monotonically with the porosity. The effect of turbulent heat transfer within the microchannel is next studied, and it is found that turbulent heat transfer results in a decreased optimal porosity in comparison with that for the laminar flow. A new concept of microchannel cooling in combination with microheat pipes is proposed, and the enhancement in heat transfer due to the heat pipes is estimated. Finally, two-dimensional numerical calculations are conducted for both constant heat flux and constant wall temperature conditions to check the accuracy of analytical solutions and to examine the effect of different boundary conditions on the overall heat transfer.