Thermal analysis of dual-phase-lag model in a two-dimensional plate subjected to a heat source moving along elliptical trajectories

We focus on the study of heat transfer behavior for the dual-phase-lag heat conduction model, which describes the evolution of temperature in a two-dimensional rectangular plate caused by the activity of a point heat source moving along elliptical trajectories. The Green's function approach is applied to derive the analytical solution of the model into a series. Benefiting from the periodic motion of the heat source, all coefficients of the series would be efficiently calculated by numerical integration. Using this representation of the solution, thermal responses for the underlying heat transfer problem, including the relations between the moving heat source and the concomitant temperature peak, the influences of the pair of phase lags and the angular speed of heat source on temperature, are then investigated, analyzed and discussed in detail for three different movement trajectories. Compared with the results revealed for the common situation that the heat source moves in a straight line with a constant speed, the present results show quite distinctive thermal behaviors for all cases, which subsequently can help us to better understand the internal mechanism of the dual-phase-lag heat transfer subjected to a moving heat source with curved trajectory.