On the use of a spatial Chebyshev polynomials together with the collocation method in solving radiative transfer problem in a slab

Abstract EN

In this study, the integral form of the radiative transfer equation in planar slab with isotropic scattering has been studied by using the Chebyshev polynomial approximation which is called TN method.

The scalar flux is expanded in terms of Chebyshev polynomials in the space variable.

The expansion coefficients are solutions to a system of linear algebraic equations.

Analytical expressions are given for the scalar and angular flux everywhere in the slab.

Numerical calculations are done for the transmissivity and reflectivity of slabs with various values of the single scattering albedo.

Calculations are also carried out for the transmitted and reflected angular intensity at the slab boundaries.

Our numerical results are in a very good agreement with other results, as shown in the tables.