An implicit‐iterative solution of the heat conduction equation with a radiation boundary condition

Abstract

Abstract In predicting temperatures with an implicit finite difference method there is a tendency for the surface temperature to oscillate if a non‐linear radiation boundary condition is imposed. An iterative method is described which eliminates these oscillations in temperature prediction. Several examples are given that allow a comparison with other implicit methods. These examples are for cases which are typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its ability to predict surface conditions without the debilitation of other methods in regard to step size control, along with the ease of incorporating it into the solution routine.