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.

Keywords:

• Memory dependent derivative
• memory effect
• porous material
• thermoelasticity

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study is supported by National Natural Science Foundation of China (12002391), Natural Science Foundation of Shandong Province of China (ZR201910290189), and Fundamental Research Funds for the Central Universities (20CX06021A).