Transient response in an elasto-thermo-diffusive medium in the context of memory-dependent heat transfer

Abstract

In the present study, in order to provide some flexible and more appropriate tools which can better describe cases of the dynamics with memory effects or of nonlocal phenomena, a novel mathematical model of elasto-thermodiffusion introduced in the context of Taylor's series expansion involving memory-dependent derivative of the function for the dual-phase-lag heat conduction law is proposed. The governing equations of this new model are applied to a one-dimensional half-space, which is taken to be traction free and is subjected to different time-dependent thermal loadings (thermal shock, periodically varying thermal loading and ramp-type heating) and chemical shocks. Laplace transform technique is employed to find out the analytical solutions and the inversion of Laplace transform is carried out using a method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed due to thermodiffusion. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative also.

Keywords:

• Memory-dependent derivative
• generalized thermoelastic diffusion
• dual-phase lag thermoelastic model
• laplace transform
• time delay

Disclosure statement

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