Comparison of four analytical and numerical models for a microchannel heat sink

The wide range of applications makes microchannel heat sinks an extremely interesting field of study. In this paper analytical and numerical tools are presented including the most important design parameters. A ID model is first developed under the lumped capacitance assumption and resorting to standard correlations for Nu under HI boundary conditions. This model is suitable for both design problem and performance calculations. Model extensions are then provided separately for highly and poorly conductive substrates: in the former case a two-dimensional model is developed, in which axial conduction is neglected in the latter case the two-dimensional model is modified to include axial conduction by exploiting the results from the one-dimensional model. This innovative approach provides a significant reduction in computational costs with respect to a conventional fully three-dimensional model, allowing either to enhance simulation detail or to perform parametric analysis to a larger extent. A three-dimensional model was therefore developed to validate the previous results and to evaluate the effects of thermal entrance. A detailed analysis was performed to determine the range of applicability of each model, suggesting that a proper choice should be guided by two non-dimensional parameters. The three-dimensional model was finally modified to account for the entrance length effects.