Three dimensional structures of the thermal shock waves around a rapidly moving heat source

Abstract

This paper investigates the thermal shock formation in a three-dimensional solid due to energy accumulation in preferential direction around a rapidly moving heat source. An analytical method is employed to yield closed form solutions for the temperature field which not only provides an exact means for studying the shock wave structures but also suitable forms readily extendable for the study of the resulting thermal stresses. The temperature field is characterized by a thermal Mach number ( M) defined as the ratio of the speed of the moving heat source (ν) to the finite speed of heat propagation ( C) in the solid. Mathematically, M = ν/ C. In the subsonic range with M < 1, a detailed comparison with the classical diffusion theory is made to reveal the importance of considering the wave nature when the response time is short. At the transonic and in the supersonic range with M ≥ 1, the emphasis is placed on the physical mechanism of the thermal shock formation. All the special features in the two-dimensional theory for the thermal shock formation are preserved in the present three-dimensional analysis. The temperature level, additionally, is found to increase with the distance away from the heat source in the direction perpendicular to the plane containing the moving heat source.