Radiant heating of an absorbing and scattering slab

An analytical solution for the transient temperature distribution in a semi-transparent slab, which absorbs and scatters radiant energy, is presented for the case where re-radiation is negligible. The equation of transfer, whose solution appears as a radiant source term in the conduction equation, is approximated by a polynomial. A generalized solution is developed for a slab exposed on one side to a convective environment and diffuse radiant heating. The opposite side abuts an insulator, whose radiative properties are accounted for in the solution. The results show that the effect of scattering within the slab and the radiative properties of the insulator are important since they affect predicted temperature profiles greatly.