Shock wave formation around a moving heat source in a solid with finite speed of heat propagation

The thermal field around a moving heat source in a solid with finite speed of heat propagation is studied analytically in this work. A thermal Mach number M defined as the ratio between the speed of the moving heat source and that of the heat propagation in the solid is introduced in the analysis. The resulting energy equation is found to be elliptic, parabolic, and hyperbolic in the subsonic (M < 1), transonic (M = 1), and supersonic (M > 1) ranges, respectively. Thermal shock wave is shown to exist in the physical domain as the speed of the moving heat source is equal to or faster than that of the heat propagation, and the thermal shock angle is obtained analytically as sin‑1 (1M) for M ⩾ 1. In the numerical examples, the evolution of the temperature and the heat flux distributions in the heat affected zone is present as a function of the thermal Mach number and a swinging phenomenon for the thermal field in transition is discussed.