Parametric study of spatially-uniform mini-channel heat sinks using a porous media modeling approach

Abstract

Pumped-liquid single-pass heat sinks with channel dimensions on the order of 0.1mm to 1.0mm are commonly researched for cooling small-scale electronic devices that generate high heat fluxes. This paper presents a simulation-based parametric study that investigates the steady-state thermal and hydrodynamic performance of 1,014 unique designs that employ square channels of a uniform size that are evenly distributed throughout the heat sink. The volume-averaged two-equation porous media model is used to simulate thermal behavior and provides the 2D spatial distributions of solid and fluid phase temperatures. Hydrodynamic behavior of the coolant is modeled using Darcy's law. The model is implemented via a user-defined element in the commercial finite element analysis code Abaqus. Thermal response is found to fall into two regimes which are defined based on an effective Biot number. Response in the low-Biot regime is found to scale with an effective resistance that is composed of a fin-type resistance (which the authors have not encountered previously) and an advective resistance. Response in the high-Biot regime is found to scale with an effective resistance that is composed of the conductive, convective and advective resistances. Hydrodynamic performance is assessed briefly, and as expected, does not follow the same trends as thermal performance. A basic design methodology for this class of heat sink is also discussed.