Analysis of Multi-Layer Mini- and Micro- Channel Heat Sinks in Single Phase Flow Using One and Two Equation Porous Media Models

Research in liquid cooled mini- and micro-channel heat sinks is growing due to the potentially high heat fluxes that can be dissipated with such devices. Deterministic mini- or micro-channel heat sinks with rectilinear channels are derivatives of more generalized porous structures. The present paper is devoted to an examination of the application of one and two equation porous media theory for modeling the thermal-fluid behavior of stacked multi-layer micro- or mini-channel heat sinks. One surface of the heat sink is exposed to high heat flux, while the other is insulated. The objectives of the paper are to examine generalizations of the geometric scaling that is elucidated by adopting a porous media approach, and the unification of models for apparently dissimilar geometries. This paper examines the relative accuracy and computational efficiency of one and two equation approaches. The error between the two models and the experimental data are examined by an error map given as a function of conductivity ratios, Darcy number (Da) and Reynolds number (Re).