Time-Fractional Hygrothermoelastic Problem for a Sphere Subjected to Heat and Moisture Flux

Abstract

In this paper, a non-Fourier model of heat conduction and moisture diffusion coupling is proposed. We study a hygrothermal elastic problem within the framework of time-fractional calculus theory for a centrally symmetric sphere subjected to physical heat and moisture flux at its surface. Analytic expressions for transient response of temperature change, moisture distribution, displacement, and stress components in the sphere are obtained for heat/moisture flux pulse and constant heat/moisture flux at the sphere's surface, respectively, by using the integral transform method. Numerical results are calculated and the effects of fractional order on temperature field, moisture distribution, and hygrothermal stress components are illustrated graphically. Subdiffusive and super-diffusive transport coupling behavior as well as wave-like behavior are shown. When fractional-order derivative reduces to first-order derivative, the usual heat and moisture coupling is recovered, which obeys Fourier heat conduction and Fick's moisture diffusion.