Analysis of heat capacity ratio on porous media in oscillating flow

Abstract

The paper analyzes heat transfer between an oscillating compressible fluid and solid to evaluate the influence of finite thermal capacity on the heat exchanged between these media. This type of problem is often studied in porous media applications by assuming the solid to have its surface at a constant temperature. When this hypothesis fails, in the frequency domain, the analytical solutions of the thermal field involve a complex dimensionless parameter known in the literature as εs. It was introduced in thermo-acoustic applications to model the solid properties of the porous core. In this work, the parameter is revisited by deriving an analytical formulation valid for arbitrarily shaped channels of porous materials, and a physical interpretation of the parameter is proposed in terms of fluid and solid entropy oscillation. CFD-based simulations of the thermal coupling between solid and fluid on three different simplified geometries of porous material have been conducted to confirm this physical interpretation, by comparing numerical and analytical data. Furthermore, from a numerical point of view, the parameter εs has been written as the inverse of a dimensionless Robin boundary condition. In this work, it is verified that the latter can be adopted at the fluid-solid interfaces to reproduce the thermal effects of the solid material, without numerically simulating it, both in frequency and time domain.