A modified effectiveness-NTU approach for analysis of low-aspect ratio mini-channel heat sinks using novel shape factor formulations

In the electronics cooling literature, the use of the overall thermal resistance to describe the thermal performance of cooling technologies, has hindered the adoption of more robust and powerful thermal performance metrics, most notably the heat exchanger effectiveness, epsiv , that arises in the theory of heat exchangers. This paper presents a theoretical treatment of the heat transfer in cold plates with low aspect ratio channels which leads to a modified form of the epsiv-NTU equation for single-sided heat exchangers. The heat transfer from the surface where heat is applied to the coolant channels is separated into the thermal impedance caused by conduction through the solid matrix, and that caused by the convection in the coolant channels. The heat conduction through the solid and into the surfaces of the channel is modeled using novel analytical shape factor formulations. This generalized conduction treatment leads to a modification of the traditional epsiv-NTU formulation that includes a generalized Biot number, defined in terms of the conduction shape factor. The new formulation robustly correlates recently reported experimental data from compact copper-water heat sinks used to cool small 1 cm times 1 cm heat sources.