Averaging approach for microchannel heat sinks subjected to the uniform wall temperature condition

The present paper is devoted to the modeling method based on an averaging approach for thermal analysis of microchannel heat sinks subjected to the uniform wall temperature condition. Solutions for velocity and temperature distributions are presented using the averaging approach. When the aspect ratio of the microchannel is higher than 1, these solutions accurately evaluate thermal resistances of heat sinks. Asymptotic solutions for velocity and temperature distributions at the high-aspect-ratio limit are also presented by using the scale analysis. Asymptotic solutions are simple, but shown to predict thermal resistances accurately when the aspect ratio is higher than 10. The effects of the aspect ratio and the porosity on the friction factor and the Nusselt number are presented. Characteristics of the thermal resistance of microchannel heat sinks are also discussed.