Analytical study of transient thermo-mechanical responses in a fractional order generalized thermoelastic diffusion spherical shell with variable thermal conductivity and diffusivity

Abstract

ABSTRACT With the great development of micro-electromechanical devices and wide application of subpicosecond/femtosecond ultrafast laser technology in micro-machining of micro-electromechanical devices, the investigations of interactions between thermodiffusion and deformation become significantly important. To accurate modeling the thermo-elasto-diffusive coupling, a new time fractional-order (i.e. memory-dependent derivative) based model of generalized thermoelastic diffusion for a perfect thermally and isotropic conducting medium which is assumed to have variable thermal conductivity and diffusivity is given in this work. This model is applied to investigate transient responses of a spherical shell subjected to instantaneous thermal and chemical shock loadings at external surface, whilst it is assumed that a permeating substance is in contact with the rigid surface at its internal surface. The solutions in the Laplace transform domain are obtained by using Kirchhoff and Laplace transform techniques and then the numerical inversion process based on fast Fourier transformation is carried out to derive the transient solutions in the time domain. Numerical computations for all the physical quantities considered are implemented and represented graphically. The results show that the variable thermal conductivity and diffusivity as well as memory-dependent parameters have the varying degrees of influences on the structural transient thermo-elasto-diffusive responses.