Computational analysis of memory-dependent nonlocal response due to ramp-type heating under thermomass thermoelasticity theory
Abhik Sur, Sudip Mondal
Abstract
The present analysis proposes a novel theory of generalized thermoelasticity, taking into account the general heat conduction law, which depends on thermomass motion. This is defined as the equivalent mass of phonon gas in dielectrics, according to Einstein’s mass–energy relation, involving the inertia effect on the temporal and spatial variations of heat flux and temperature. The constitutive equation is formulated using nonlocal stress theory proposed by Eringen. The governing equations have been solved for a thermoelastic rod, where the boundaries are traction-free and the left boundary of the rod is subjected to ramp-type heating, while on the right boundary, there is no temperature. Invoking the Laplace integral transform, the solution of the present problem is achieved. In order to capture 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 findings illustrate the differences between various kernel functions in the heat transport process. Moreover, the impact of the present revolutionary thermoelastic model is also reported. How various effective parameters, such as the nonlocal parameter and the time delay parameters influence each of the physical fields, have also been analyzed.