Analytical modeling of moving heat sources in memory-dependent heat transfer using Green’s functions

Abstract

The present paper deals with the thermal-wave propagation in a bounded elastic medium. In this context, hyperbolic type heat conduction model is considered subjected to a moving heat source. The analysis incorporates memory-dependent derivatives (MDD) within the framework of generalized thermoelasticity to account for thermal memory effects in the hyperbolic heat conduction model. Including a sequence of delayed temperature gradient, the concept of a memory-dependent adjoint operator is introduced. Finally, the Green’s function method is applied to derive analytical solutions, and the salient features of the temperature profile are analyzed in detail.