Analytical heat diffusion models for different micro-channel heat sink cross-sectional geometries

This study explores heat diffusion effects in micro-channel heat sinks intended for electronic cooling applications. Detailed analytical models are constructed for heat sinks having micro-channels with rectangular, inverse trapezoidal, triangular, trapezoidal, and diamond-shaped cross sections. Solutions are presented for both monolithic heat sinks and heat sinks with perfectly insulating cover plates. The analytical results are compared to detailed two-dimensional numerical models of the same cross-sections over a broad range of cover plate thermal conductivities for different micro-channel aspect ratios, fin spacings and Biot numbers. These comparisons show the analytical models provide accurate predictions for Biot numbers of practical interest. This study proves the analytical models are very effective tools for the design and thermal resistance prediction of micro-channel heat sinks found in electronic cooling applications.