Radiant heating of an absorbing, isotropically scattering and emitting slab

We obtain a numerical solution for the transient temperature distribution in a semi-transparent slab which absorbs, scatters and emits radiant energy. A slab exposed on one side to a convective environment and diffuse radiant heating is considered. The opposite side abuts an insulator whose radiative properties are accounted for in the solution. The equation of radiative transfer is solved by using a polynomial approximation in order to determine the effective source term in the conduction equation for a broad range of typical values of the important parameters. The results are compared to a solution which neglects re-radiation from the slab showing its importance at elevated temperatures. The results show that in general the effect of re-radiation is to reduce the temperature and gradients in the slab.