Plane Wave Propagation in Non-Local Generalized Thermoelastic Solid with Diffusion Using Eigen Value Approach

In this paper, we explore a fascinating thermoelastic boundary value problem within a two-dimensional, non-local, homogeneous, and isotropic thermoelastic medium that incorporates diffusion. Our focus centers on a boundary that is traction-free, insulated, and maintained at a constant temperature. To achieve this, we meticulously derive the governing equations. We use a vector matrix differential equation for representing the two-dimensional problem. Employing the elegant eigenvalue approach, we solve these equations and unveil the intricate relationships at play. We then present a compelling numerical analysis, vividly illustrating the effects of nonlocal and diffusion parameters on displacements and temperature stresses through engaging graphical representations. Moreover, we delve into particular cases of interest, drawing insightful comparisons with established results to enrich our understanding. This study not only highlights the complexities of thermoelastic behavior but also opens avenues for further exploration in this dynamic field.