Optimization of the Thermal Performance of Microchannel Heat Sinks Using Thermally Developing Nusselt Number Correlation

One-dimensional (1-D) thermal resistance model has been shown in various works to be a computationally economical alternative to the full three-dimensional (3-D) conjugate heat transfer analysis achievable by computational fluid dynamics (CFD) codes for evaluating the thermal performance of microchannel heat sinks. This simplified 1-D approach is often exploited to obtain the optimum microchannel geometry that would give rise to the best thermal performance under certain constraint such as constant flow rate, pressure drop or pumping power. The thermal resistance model essentially consists of the following three thermal resistive components: conductive, convective and caloric. In evaluating the convective thermal resistance, fully developed Nusselt number correlations were often used. However, the small length scale of microchannels and the fact that liquid coolant with high Prandtl number is often used as the working fluid means that the flow encountered in microchannel heat sinks is typically thermally developing rather than fully developed. The present work utilizes a recently proposed Nusselt number correlation that was specifically developed for rectangular channels of various aspect ratios to evaluate the convective thermal resistance. Comparison shows that the optimized microchannel geometry obtained using the more appropriate thermally developing Nusselt number correlation is different from that obtained using a fully developed Nusselt number correlation. In fact, the discrepancy in the channel width can be as large as 30% for the range of constant pressure drop constraint examined.