Thermal Shock Formation in a Three-Dimensional Solid Around a Rapidly Moving Heat Source

Abstract

The thermal shock studied in this work results from the accumulation of thermal energy in a preferential direction around a rapidly moving heat source in the solid. It is a physical phenomenon pertinent to the thermal wave model and cannot be depicted by the classical diffusion theory. The present work further extends the thermal shock theory to a three-dimensional solid. The energy equation with temperature representation will be considered in the analysis. Because the effect of the finite wave speed intrinsically varies the mathematical type of the energy equation, the temperature distributions will be obtained individually in the subsonic, transonic, and supersonic ranges (Tzou, 1989a). In a similar manner to the two-dimensional problem, the hypo-variable transformations will applied to reduce the three-dimensional energy equation to a one-dimensional equation. The Green's functions for the one-dimensional equations in the hypo-space are then sought to yield analytical expressions for temperature, which facilities an exact description on the thermal shock formation around a rapidly moving heat source.