Memory effect on the thermoelastic responses of a porous half-space with a novel fractional heat conduction model

Abstract

Studies have shown that the existence of the anomalous diffusion of porous media leads to the abnormal heat conduction, which can be well described by fractional derivatives. In the present work, memory dependent derivative is introduced into the existing linear thermoelastic theory to analyze the transient thermoelastic responses of a porous half-space subjected to a thermal loading at the boundary. By using the method of Laplace transform and its numerical inversion, the closed form solutions of temperature, volume fraction, displacement, and stress are obtained. The effects of time delay, kernel function and a memory-dependent parameter on the physical fields are discussed. The results show that the memory dependent derivative plays an essential role in controlling the heat transfer process of porous materials.