Numerical study of fast transient non-diffusive heat conduction in a porous medium composed of solid-glass spheres and air using fractional Cattaneo subdiffusion model

Abstract

This research aims to carry out the fast-transient process of heat flow in a porous medium, proposing the Caputo-type fractional Cattaneo subdiffusion model to study the anomalous diffusion process in the temperature response of the two-phase system. It has been shown that during the short thermal disturbance of porous medium, the solid-fluid interactions in microscale, energy swap through the solid-glass spheres and air, the local non-equilibrium state, and also the fast transient process can be simulated by use of fractional calculus approach. The classical Fourier model fails to interpret such effects, because it is assumed that the thermal wave propagates with infinite speed, and also the thermal interactions between phases occur simultaneously. The energy equation has been developed upon the Caputo fractional derivative, then numerically solved and it has been observed that its results are comparable to the measured data, which reveals the accuracy of the time-fractional model proposed. The numerical results exactly follow the experimental data, which illustrates the applicability of fractional Cattaneo subdiffusion model for examining the transient process in a porous medium at the short temporal scales, and also its capability to interpret the solid-fluid interactions in microscale.