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

TL;DR

This study analytically investigates the heat transfer behavior in a 2D plate with a moving heat source along elliptical paths using the dual-phase-lag model, revealing distinctive thermal responses compared to linear motion.

Contribution

It provides an analytical solution for the dual-phase-lag heat conduction model with a moving elliptical heat source, highlighting the effects of phase lags and source velocity on temperature distribution.

Findings

Distinct thermal behaviors for elliptical vs. linear source movement

Influence of phase lags on temperature peaks and distribution

Analytical expressions for temperature in complex source trajectories

Abstract

In this paper, 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. At first, Green's function approach is applied to derive the analytical solution of temperature for the given model. Based on the series representation of this analytical solution, the 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 velocity 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.