Heat transfer enhancement for porous microchannel heat sinks by optimizing wall heat flux distribution

The porous microchannel heat sink can be used to meet the increasing demand for electronic device cooling. In this paper, heat transfer is enhanced by optimizing heat flux distribution for porous microchannel heat sinks subject to an exponential heat flux. The Nusselt number, dimensionless wall temperature and thermal resistance are obtained using the semi-analytical method. The Nusselt number is found to be dependent on the product of dimensionless exponent, Reynold number, and Prandtl number. The optimal heat flux distribution is dependent on the length of the channel and it is that under constant wall temperature boundary condition in most cases. The thermal performance is assessed using the thermal resistance ratio between constant wall temperature and constant heat flux boundary conditions. An optimal length exists when the constant wall temperature condition is used to reduce the maximum wall temperature. The effects of Biot number and the ratio between effective thermal conductivities of solid and fluid phases on the minimum value of the thermal resistance ratio and the optimal length are also studied. The result shows that the thermal resistance can be reduced by about 28% by optimizing the heat flux distribution, compared with the commonly used constant heat flux boundary condition.