Elasto-Thermodiffusion in a Slim Strip Revisited with New Definition of Nonlocal Heat Conduction

The control of diffusion in solids plays a significant role in diverse fields due to a wide range of applications in surface hardening, nuclear waste disposal and doping of semiconductor devices and in many other fields. The present study explores a comprehensive novel analysis of thermoelastic diffusion in presence of thermal and diffusion processes. Governing equations for the elastic materials through thermodiffusion have been obtained for a homogeneous and isotropic finite thin slim strip which is exposed to a moving heat source, where both the ends of the strip are fixed. The Moore-Gibson-Thompson (MGT) theory of generalized thermoelasticity modifies and defines the new form of equations for thermal conduction and mass diffusion that occur in solids. The built model has been applied to examine the influence of the moving heat source for which, both ends of the strip are fixed and subjected to prescribed chemical shock. Laplace transform technique has been assimilated to determine the solution of the governing equations. In order to accomplish the solution in the real space-time domain, the inversion of the Laplace transform has been carried out numerically using the Riemann sum approximation technique. The graphical results show that the nonlocal length scale parameter and the nonlocal heat conduction parameter have significant effects on the transient thermoelastic responses, which is crucial to predict the thermoelastic response accurately for the design of the materials. The graphical illustration illuminates the effectiveness of various kernel function of the heat transport law and the effect of delay time is also reported.