S. A. El Wakil

Bivariational calculations for radiation transfer in an inhomogeneous participating medium

Equations for radiation transfer are obtained for dispersive media with space-dependent albedo. Bivariational bound principle is used to calculate the reflection and transmission coefficients for such media. Numerical results are given and compared.

Stochastic radiative transfer in a finite plane with anisotropic scattering in a binary Markovian mixture

Abstract The time-independent linear transport problem in a stochastic finite-plane medium with linear anisotropic scattering is considered. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two-state homogeneous Markov process. The Pomraning–Eddington approach is used to obtain an explicit solution to the problem in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution for the problem under consideration. In the case of isotropic scattering, explicit analytic results for reflectivity and transmissivity, which show a good agreement with Monte Carlo benchmark results, are given. Results for reflectivity and transmissivity in the case of linear anisotropic scattering are also given.

Radiation transfer through coagulating media

Exact relations for radiation heat flux at the boundaries of a slab with reflecting boundary conditions and internal source are obtained in terms of the reflection and the transmission coefficients (albedos) of a source-free slab with isotropic boundary conditions. Available exact values of the albedos give exact values of radiation heat flux. Configuration factors are calculated for comparison.

Padé approximant in radiative transfer

Abstract A functional relation is obtained between radiative transfer in an inhomogeneous medium with internal sources and diffuse reflection. The intensity of the emerging radiation for a linear source is obtained by using the Pade approximation. The single scattering albedo is assumed to decrease exponentially with optical depth. Numerical results are given.

Anisotropic radiation transfer in dispersive media

Equations for radiation, scattered anisotropically from dispersive media are obtained for general boundary conditions. The Padé approximant technique is used to calculate the reflection coefficients for these media. Numerical results are given for diffuse reflected boundary condition.

Diffuse reflection and transmission of radiation for Rayleigh phase function

Diffuse reflection and transmission coefficients in a plane parallel medium are calculated for a Rayleigh phase-function averaged over polarization and Rayleigh polarized phase-function. This is calculated by imbedding the finite medium into a semi-infinite scattering and absorbing medium. Numerical calculations for semi-infinite albedo are compared with Pomraning results. The albedos for finite medium are calculated via the imbedding equations which converge for large τ to the value of semi-infinite medium.

Angular distribution of radiation in an isotropically scattering slab

The equation of radiative transfer in an isotropically scattering slab subject to general boundary conditions is solved. The Padé approximation technique is used to calculate the reflected and transmitted angular distributions. Numerical results for angular distributions through and at the boundaries of a finite slab are calculated by the Padé approximation technique. The results for a Padé approximation of [0/1] are compared with results obtained by the Galerkin method.

Radiation transfer in dispersive media

Equations for the reflection coefficients associated with radiation scattered by dispersive media are obtained. The Pade approximant technique is used to calculate the reflection coefficients. The results for the (0/1) Pade approximant lead to computationally useful results that compare well with the exact results.

Neutron transfer with anisotropic scattering

The finite slab problem is reduced to a semi-infinite one by adding an infinitesimally thick layer such that both the added layer and the total layer are semi-infinite. The relation between the reflection and transmission functions for a finite slab and those for an infinite one are obtained in terms of an operator which satisfies a semigroup equation. The method is applied to anisotropic scattering with azimuthal dependence. Numerical calculations are made and the results compared with those of Kavenoky (1971).

Bivariational calculation for the angular distribution of radiation in an inhomogeneous finite medium

Abstract A bivariational technique is used to solve the equation of radiative transfer in an isotropically scattering, inhomogeneous slab subject to general boundary conditions. Numerical results are calculated and compared with results obtained by the Galerkin and F N methods.