On the local thermal equilibrium in microchannel heat sinks

In this paper, analytical solutions for temperature distributions in the microchannel heat sink are obtained by using both one-equation and two-equation models for heat transfer. From the analytical solutions, variables of engineering importance are identified as the Darcy number and the effective thermal conductivity ratio, and their effects are studied. To check the validity of the local thermal equilibrium assumption and the corresponding one-equation model, the relative temperature difference between the fluid and solid phases and the relative error for using the one-equation model are defined. The asymptotic behavior of the relative temperature difference between the phases is examined by using the order of magnitude analysis to confirm the applicability of the local thermal equilibrium assumption and the one-equation model. Finally, the relative error map is presented with respect to variables of engineering importance to identify the applicable region of the one-equation model in practical problems involving the microchannel heat sinks. (C) 2000 Elsevier Science Ltd. All rights reserved.