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.

目前的文献调查研究了由于存在时间相关的激光热源而导致的移动有限介质的双相滞后 (DPL) 热传递的热相互作用。由于幂律分布存在各种缺点，因此本问题的热传输方程已通过结合记忆相关导数以滑动区间上的公共导数的积分形式定义。以拉普拉斯变换为工具，在拉普拉斯变换域求解控制方程，并采用合适的数值格式求解，并采用Zakian方法对拉普拉斯变换进行了相应的数值反演。根据数值结果对应的图形表示，构建了关于新理论的结论。由于存在与记忆相关的导数、移动速度的影响、相位滞后参数的影响以及延迟时间，因此证明了出色的预测能力。此外，还证明了相位滞后参数的一些限制情况。