The memory effect on thermal wave propagation in a moving thin slab

Abstract

The present literature survey examines the thermal interaction due to dual-phase-lag (DPL) heat transfer for a moving finite medium due to the presence of a time-dependent laser heat source. Since, various kinds of shortcomings persist in the power-law distribution, the heat transport equation for the present problem has been defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent derivative. Incorporating the Laplace transform as a tool, the governing equation has been solved in the Laplace transform domain and a suitable numerical scheme is adopted to arrive at the solution and the corresponding numerical inversion of the Laplace transform has been carried out using Zakian method. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are constructed. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative, effect of moving velocity, effect of phase-lag parameters, delay time also. Moreover, few limiting cases of the phase-lag parameters have also been demonstrated.