Integral Transform Solution of Porous Medium Models for Heat Sinks Subject to Periodic Heat Loads

Abstract

Analysis of the energy transport in thermal microdevices modeled as a porous medium under periodic heat loads is conducted using integral transforms. Coupled eigenvalue problems are employed and a single set of coupled ordinary differential equations conveying all information on the temperature fields in both the solid and fluid phases are reached, allowing for a relatively straightforward treatment of the local thermal nonequilibrium (LTNE) formulation. This characteristic proved instrumental in finding out that the local thermal equilibrium (LTE) hypothesis is inadequate for unsteady problems. The solid phase is shown to have a significant role on inducing thermal lag in the fluid, which may be severe, depending on the dimensions and operational conditions. In general, devices comprised of larger fractions of solid material and with poorer heat transfer characteristics are more prone to having larger thermal lag along them. These conclusions may be relevant to a wide range of applications such as electronics cooling, battery thermal management, solar energy harvesting, among others.