The radiative heat transfer problem for an isotropically scattering slab with specularly reflecting boundaries is reduced to the solution of a set of algebraic equations by expanding the source function in Legendre polynomials in the space variable in the integral form of the equation of radiative transfer. The lowest order S-1 analysis requires very little computer time for calculations, is easy to apply and yields results which are sufficiently accurate. For an absorbing, emitting, isotropically scattering medium with small and intermediate optical thickness (i.e., τ = 2), which is of great interest in engineering applications, and for which the P-1 and P-3 solutions of the P-N method are not sufficiently accurate, the S-1 solution yields highly accurate results. In the case of a slab with diffusely reflecting boundaries, the problem is split up into a set of simpler problems each of which is solved with the source function expansion technique as a special case of the general problem considered.

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