Analysis of two temperature thermoelastic diffusion plate with variable thermal conductivity and diffusivity

Abstract

ABSTRACT The current study explores the transient response of a thermoelastic plate in the light of the two-temperature generalized thermoelastic diffusion model involving variable thermal conductivity and diffusivity. The boundary of the plate is designed as mechanical, thermal, and concentration loadings on one side and rigidly fixed, insulated and impermeable on the other side. The thermal conductivity and diffusivity are assumed to be the linear function of thermodynamic temperature and concentration, respectively. Hence, governing equations are non-linear and transformed into linear form by applying Kirchhoff's transform. Transformed governing equations are solved by using the Laplace–Fourier transform technique. In the transform region, the closed form of expressions for conductive and thermodynamic temperature, displacement and stress components, mass concentration, and chemical potential are obtained. Numerical results are obtained by mathematical inversion technique for various quantities obtained analytically in closed form in the transform domain and depicted graphically to illustrate the impacts of variable thermal conductivity, variable diffusivity, and two temperature.