A leapfrog algorithm for coupled conductive and radiative transient heat transfer in participating media

This paper describes the first applications of a leapfrog algorithm applicable to coupled conductive and radiative transient heat transfer problems within participating media. The algorithm separates the effects of conduction and radiation within the media into two separate energy balance equations. Both of these new equations are initially considered individually. The solutions of the two separate energy equations are iterated in time through a leapfrog algorithm to obtain the transient temperature response of the media being modelled. For simple geometries and in certain cases, these equations can also be solved analytically. For cases in which analytic solutions can be employed, the algorithm is particularly accurate and stable, and especially for large time-steps. In this paper, the leapfrog algorithm is employed to solve the coupled conductive and radiative transient heat transfer problem in a planar layer for both one-dimensional and two-dimensional cases, for the purposes of validating the algorithm.