Transient responses of two temperature, fractional thermo-diffusive-elastic half space with temperature dependent properties

Abstract

In scientific disciplines such as control engineering, astrophysics, geomechanics, nuclear physics, etc., thermoelastic diffusion plays a crucial role. When physical processes involve high temperature, considering two temperature theories and temperature-dependent material properties contribute to more rational results. The inclusion of fractional calculus in such studies provides results with significant accuracy. In this light, a model is formulated under two temperatures, fractional order Lord Shulman and Green Lindsay's theories of generalized thermo-diffusive-elasticity. The medium under consideration is a half space which is kept unstressed initially at a uniform temperature The material properties are considered to be a function of temperature. Governing equations and constitutive relations of the model are non-dimensionalized and simplified using potential functions. The field variables are determined analytically in the closed form in Laplace-Fourier transformed domain. Numerical computations are conducted with the assistance of MATLAB software. The study aims to observe the behavior of physical quantities for different values of two temperature, temperature-dependent, and fractional order parameters. Graphical representation is displayed with respect to space variables x and z. The results reveal that physical quantities express varying degrees of influence corresponding to different effects involved in the study.