Nonlocal General Generalized Thermoelastic Interaction in a Rod with Memory Response

Abstract

In order to address the non-Fourier heat conduction phenomena for thermomass gas flow, the aim of the present contribution is to construct a new theory of generalized thermoelasticity for thermomass gas flow assimilating low velocity and linear resistance based on the generalized non-Fourier theory of heat conduction with memory responses. The effect of resistance has been included in the general heat conduction equation, which is based on the total derivative of the thermomass gas velocity. The constitutive equation has been formulated using the nonlocal theory proposed by Eringen. The governing equations have been solved for a thermoelastic rod, where both the boundary is free of traction and the left boundary is subjected to a thermal shock, while on the right boundary, there is no temperature. The problem is solved by means of the Laplace transform mechanism. In order to achieve the solutions in real space-time domain, a viable simulation has been carried out for the numerical inversion of the Laplace transform using the method of Zakian. The latest findings illustrate the contrasts between different kernel function of the heat transport process. The stability of the proposed model has been validated. The numerical results validate the superiority of the present revolutionary thermoelastic model over the existing one. The superiority of non-local behavior is also reported to accommodate the effect of thermomass within the medium. Finally, it may be said that it is beneficial to formulate the heat transport law involving various kernel as per the necessity of the physical situation.