Prior analyses and experiments have demonstrated that varying or scaling the number of fluid channels in each layer of a stacked multi-layer heat sink yields distinct advantages over traditional single-layer designs which use channels with high aspect ratios. Specifically, a design which implements scaling in order to vary the porosity (or equivalently, the number of channels) from one layer to the next allows a given thermal performance to be realized at a lower pressure drop than the corresponding non-scaled design. In previous work, the authors have used volume-averaged non-equilibrium porous media heat transfer theory to analyze a range of heat sinks of this type, including those with discrete or step-wise porosity variation (in earlier efforts) and continuous porosity variation (in more recent efforts). The authors have used discrete variation to model stacked mini-channel multi-later heat exchangers, and continuous variation as a more general investigative tool for this class of heat sinks. The continuous variation approach can also be used as a design tool for heat sink envelopes that use scaled micro- or nano-channels or engineered porous media with spatially varying porosity or pore diameter.

This paper reports on the results of a parametric study of water-cooled copper heat sinks which employ 0.50 mm × 0.50 mm square channels in a range of porosity scaling profiles that yield and total integrated porosities of 0.10 to 0.95. The investigation identifies the highest and lowest performing designs based upon temperatures on the heated surface, and analyzes their performance characteristics in terms of the spatial distributions of solid and fluid temperature distributions, thermal resistance components and ratios, and conductive and convective heat flows. In general, the results imply the existence of an optimum level and distribution of porosity and confirm the potential benefits of spatial variation of porosity.

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