Thermal Behavior of Solid Heated by Gaussian Moving Heat Source

In this paper, an analytical development is proposed to explicitly calculate the three-dimensional and transient temperature of a solid heated by a Gaussian moving heat source. The moving source dissipates heat in a thin layer near the irradiated surface of the solid and can be constant or pulsed or have any time evolution, depending on the application. The resulting solution requires only one convergent integral over time, which can be quickly computed numerically using, for example, a commercial formal calculation software. On the other hand, the derivative of the temperature with respect to time is fully explicit. We show that the results of the developed analytical solution are in excellent agreement with those of a numerical modeling that we performed under the same conditions. The temperature evolutions and the thermal maps are presented and commented.