Abstract

Multiscale oscillatory heat transfer and fluid flow of a gas in permeable media subjected to acoustic wave excitation is investigated in this paper. The two-scale asymptotic method of homogenisation is used to establish the macroscopic description of acoustic wave propagation in such media With the aid of this method, an effective complex-valued frequency-dependent volumetric heat capacity that describes the thermal response of the gas in a permeable medium, accounting for the finite heat capacity of its solid frame, to an acoustic wave is introduced Analytical models for materials with simple geometry and scaling functions for those with complex geometry are provided. These predict the behaviour in frequency of the dynamic volumetric heat capacity and effective compressibility of a fluid equivalent to the permeable material. The latter effective parameter is shown to be affected by the finite heat capacity of the materials' solid frame as well. The predictions of both types of models are successfully compared with the results of direct pore-scale numerical simulations. Extensions of the developed theory to account for rarefied heat transfer and fluid flow as well as multiple scales of porosity (e.g., double porosity materials and porous composites) are also presented. This study provides insight into the fundamental understanding of heat transfer phenomena in permeable media subjected to acoustic excitation and paves the way for further studies on the use of acoustic waves to measure the volumetric heat capacity of the solid-frame substrate material of simple and multiscale permeable media.