M.A. Madkour

Radiative transfer in a participating slab with anisotropic scattering and general boundary conditions

Abstract Radiative transfer has been considered within a participating plane slab bounded by two emitting and reflecting plates. The slab is assumed in radiative equilibrium and scatter radiation anisotropically. The scattering function is expanded into Legendre polynomials and a rigorous solution is developed based on the projection method. The resulting formulae for the partial and total heat fluxes have been numerically processed, for both linearly anisotropic and Rayleigh modes of scattering. For the isotropically scattering case, the computed values completely reproduce those available in the literature. As regards to the anisotropic results it has the same accuracy like that for isotropic.

Anisotropic radiation transfer in a plane medium with specularly-reflecting boundary conditions

Abstract Anisotropic scattering in radiation transfer through an inhomogeneous planar medium with internal energy sources and diffusely- and specularly-reflecting boundary conditions is considered (problem 1). The partial heat fluxes for this problem are given in terms of the albedos of the source-free problem with specularly-reflecting boundaries (problem 2). The Galerkin technique is used to calculate first the albedos for problem 2and then to calculate the partial heat fluxes for problem 1. Results are obtained for isotropic and anisotropic scattering for uniform and nonuniform internal sources.

ON THE MAXIMUM-ENTROPY METHOD FOR KINETIC EQUATION OF RADIATION, PARTICLE AND GAS

The maximum-entropy approach is used to calculate some problems in radiative transfer and reactor physics such as the escape probability, the emergent and transmitted intensities for a finite slab as well as the emergent intensity for a semi-infinite medium. Also, it is employed to solve problems involving spherical geometry, such as luminosity (the total energy emitted by a sphere), neutron capture probability and the albedo problem. The technique is also employed in the kinetic theory of gases to calculate the Poiseuille flow and thermal creep of a rarefied gas between two plates. Numerical calculations are achieved and compared with the published data. The comparisons demonstrate that the maximum-entropy results are good in agreement with the exact ones.

Radiation transfer in a spherical inhomogeneous medium by the projection method

Abstract The radiative heat flux at the boundary of an inhomogeneous sphere containing an internal energy source and subject to general boundary conditions (problem 1) is obtained in terms of the albedo of the corresponding source free problem with isotropic boundary condition (problem 2). The solution of problem 2 is obtained by the projection method. Numerical results for the partial heat flux and emissivity for a given internal energy source are obtained.

Radiative transfer in spherical and cylindrical media containing aerosols

Abstract Radiative transfer in media containing aerosols has been considered. The media may have spherical or cylindrical geometries. The boundary condition on the surface is taken to be the sum of the isotropic and diffuse-reflecting boundary conditions. Parameters such as extinction, absorption and scattering efficiencies are calculated by using the Mie theory for spherical particles. Averaged coefficients over different size distributions have been calculated. The radiation heat fluxes for different media with complex refractive indices are calculated.

Polarized radiative transfer in an aerosol medium

Abstract Polarized radiative transfer in a medium containing aerosols has been considered. The problem of determining the intensity and the degree of polarization of radiation emerging from a finite, plane medium, for the case of Rayleigh scattering with internal energy sources, is considered. A system of integral equations is obtained and solved by the Galerkin method. Parameters such as extinction, absorption and scattering coefficients are calculated using the Mie scattering theory for spherical particles. Average coefficients over different size distributions have been calculated. The degrees of polarization of the emerging radiation from homogeneous media with complex refractive indices are calculated for uniform and non-uniform internal sources.

Radiative transfer in an aerosol medium

Radiative transfer through a parallel-plane aerosol medium has been studied. The Mie theory is used to calculate the radiation transfer scattering parameters in the form of the extinction, absorption and scattering efficiencies. Averaged efficiencies over different size distributions for spherical particles of complex refractive index are calculated. The radiative heat fluxes through a plane medium of sodium and polydispersion aerosol are calculated.

Chandrasekhar's X- and Y-functions

Abstract Galerkins method is used to calculate Chandrasekhars X - and Y -functions and their moments. Numerical results are obtained and compared.

Radiative transfer in finite volcanic eruption clouds

Radiation transfer through a volcanic aerosol medium has been studied. The radiation transfer properties of the medium as scattering, absorption and extinction coefficients are calculated using the Mie scattering theory. Average coefficients over the size parameter and the radiation wavelength are calculated. The radiation heat fluxes for volcanic eruption ash medium are calculated using the Variational Pomraning–Eddington approximation and compared with those obtained from the Galerkin method. The comparison showed very good agreement.

Maximum-entropy for the laser fusion problem

The problem of heat flux at the critical surfaces and the surfaces of a pellet of deuterium and tritium (conduction zone) heated by laser have been considered. Ion-electron collisions are only allowed for: i.e. the linear transport equation is used to describe the problem with boundary conditions. The maximum-entropy approach is used to calculate the electron density and temperature across the conduction zone as well as the heat flux. Numerical results are given and compared with those of Rouse and Williams and El-Wakil et al.