A novel approach to model moving heat sources

The solution of quasistationary heat-conduction problems with moving heat sources on the surface of a body is a demanding task and still a topic of ongoing research. The authors have shown in several contributions that an exact analytical solution exists for a constant velocity of the heat source and constant thermal properties of the body. Since also convection at the surface can be treated properly, cooling and quenching problems can be solved, accordingly. The main characteristic of the governing equation is that the partial derivative of the temperature with respect to time must be replaced by the convective term being the velocity of the heat source times the gradient of the temperature. In this contribution it is shown that the quasistationary problem can be transformed into a stationary one, if a modified heat-conduction coefficient is introduced. The application of this concept and its limits are demonstrated in comparison with existing analytical solutions. For this purpose a model is set up which consists of two parts. In the first part the concept of transforming to a stationary problem is employed, whereas in the second part fictitious heat sources are defined. The methodology is shown to be very efficient as it avoids difficulties arising from the necessity to use very dense meshes and proper time integration routines necessary when applying standard fine element codes for a spatially fixed configuration of a body with moving heat sources on its surface.