Analytical Determination of the Dynamic Temperature Field of a Steel Sample Exposed to Intense Heating by Applying a Line-Heat-Source

Abstract

The paper presents an analytical closed-form solution to the problem of dynamic change in the temperature field of a steel sample model during a short-term heating up and thereafter intense heat removal. It is demonstrated how a relatively complex thermal problem can be solved analytically based on differential equation that describes the temperature field. Differential equation that describes the temperature field is formed via the power of several heat sources with limited action time, as shown mathematically by applying the Dirac and Heaviside functions. In the present paper the example provided includes two heat sources. In accordance with boundary conditions the differential equation is solved by applying the finite Fourier transforms and Laplace transform. Based on obtained analytical solution of the problem, a numerical model was created corresponding to the simulation of steel sample heating on a thermomechanical welding simulator. The welding thermal simulator is a device used to achieve controlled heating and cooling, similar to the one in welding. Analytically calculated temperature fields were utilized to obtain the strain distribution in the heat source environment by applying the finite element method.