Semianalytical Polynomial Interpolation Method For The Efficient Solution Of The Radiative Heat-Transfer Equation

This article presents a semianalytical solution method for solving a Fredholm equation of the second kind, which arises in the study of radiative heat transfer in a participating gray, isotropically scattering medium contained between two plane-parallel plates. Traditional solution methods that employ quadratures approximate both the unknown and known functions appearing in the integrand and have numerical difficulties in addressing singularities. The proposed method considers exactly the mutual interactions between the source function and the exponential integral kernel function in the entire domain. The method provides highly accurate solutions, and the method is computationally efficient. The method correctly predicts a constant heat flux for radiative equilibrium. It also readily handles Be singularity for the exponential integral function of the first order at zero. The technique is valid for a wide range of values of the scattering albedo and optical thickness. The proposed technique could be applied to a wide range of problems similar in form to the radiative heat transfer equation