On the temperature distribution in a flat plate induced by an external thermal radiant source

Resumo

In this work, we investigate the effect of a small, high-temperature radiant source on a thin rectangular plate located at a significant distance. Starting from a partial differential equation with Neumann boundary conditions, we develop a nonlinear mathematical model for the heat transfer, aiming to determine the temperature distribution on the plate. The solution is obtained through a sequence of linear problems, solved numerically.The radiant view factor from the disk to the plate is calculated, enabling the modeling of heat conduction within the plate, which is assumed to be gray, without internal heat generation, and under steady-state conditions. A priori bounds for the solution are established, ensuring the avoidance of inconsistent numerical approximations.The proposed equation accounts for radiative heat transfer incident on the upper surface of the plate from the source, as well as radiation emitted from both the upper and lower surfaces of the plate.In our simulation we used the finite elements method and finite difference method. Convergence of the numerical solution is demonstrated, and results are validated by upper-bound estimates.The results show good agreement with those obtained through analytical approaches. This study provides insights into how small, high-temperature radiant bodies influence the temperature distribution in distant surfaces. Moreover, the mathematical approach adopted here lays the groundwork for applications to other geometries and sophisticated nonlinear heat transfer problems.