M.T. Attia

Stochastic radiative transfer in a finite plane-parallel medium with general boundary conditions

Abstract The time-independent radiative transfer problem in a scattering and absorbing planar random medium with general boundary conditions and internal energy source 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 problem is solved in terms of the solution of the corresponding free-source problem with simple boundary conditions which is solved using Pomraning–Eddington approximation in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. The average partial heat fluxes are calculated in terms of the albedoes of the source-free problem. Results are obtained for isotropic and anisotropic scattering for specular and diffused reflecting boundaries.

Radiative transfer in an inhomogeneous sphere

Abstract We connect the problem of radiation transfer in a diffusely-reflecting sphere containing an energy source and source-free radiation transfer with isotropic boundary conditions. An equation for the radiation heat flux is obtained for a polynomial source. In the special case of a uniform source, the radiation heat flux and the angular flux are obtained in terms of the albedo of the second problem. Numerical results are presented for inhomogeneous and homogeneous spheres, and the results for the homogeneous sphere are compared with those of Mordant.

On the exact solution of a generalized equation of radiative transfer in a two-region inhomogeneous slab

Abstract The problem of radiative transfer in a two-region inhomogeneous slab of equal or unequal thickness has been solved with general boundary conditions. A Galerkin-iterative technique is used to solve the coupled integral equations for the two-regions. Numerical results are obtained for the reflection and the transmission coefficients for the homogeneous and inhomogeneous cases. The results obtained for homogeneous medium are compared well with the exact results.

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.

Radiative transfer in a spherical inhomogeneous medium with anisotropic scattering

Abstract The radiative heat flux at the boundary of a sphere containing an internal energy source and subject to general boundary conditions is obtained in terms of the albedo of the corresponding source-free problem with isotropic boundary condition. The relations obtained apply to the general case of anisotropic scattering in an inhomogeneous medium. The advantage of these relations is the result of the fact that there is no need to obtain a particular solution for specified internal sources. Therefore, calculations can be done easily for a non-uniform source distribution. The phase function is approximated by using a linear anisotropic relation. The linear coefficient is taken to be the sum of the coefficients of the Legendre expansion of the phase function. The resulting relations are used to calculate the partial heat flux and emissivity for a given internal energy source and inhomogeneous medium.

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.

Radiative transfer in inhomogeneous solid cylinder with anisotropic scattering using Galerkin method

Abstract The integral form of the radiative transfer equation in an inhomogeneous cylindrical medium with anisotropic scattering is solved using the Galerkin technique. The medium is considered to have an internal space-dependent energy source and diffuse reflecting boundary illuminated by diffuse external incidence. The partial flux at the surface and the irradiance and the net flux through the medium are calculated for different media. The calculations for homogeneous, isotropic scattering and transparent boundary media are compared with the published results and show agreement. The calculations are carried out for homogeneous and inhomogeneous media of transparent and diffuse reflecting boundaries with isotropic and forward and backward anisotropic scattering.

On Galerkin Technique for Transient Radiative Heat Transfer in Finite Thin Media

The transient radiative heat transfer problem in an absorbing and isotropically scattering plane-parallel medium is proposed. The medium is considered to be nonemitting and the boundaries are nonreflecting and nonrefracting, exposed to an external incident flux. The transient problem is transformed into a stationary-like one. Then, Galerkin technique is extended to obtain the analytical solution for the transient radiative heat transfer problem. The transient reflectivity and transmissivity of the medium are calculated for various values of optical thickness and scattering albedo at different times. The results are in fair agreement with those available in the literature using Pomraning-Eddington approximation.

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.

Radiative transfer in an inhomogeneous medium with reflecting boundary conditions

Abstract The bivariational principle is used to compute partial heat fluxes, as well as the total radiative heat flux, in an inhomogeneous, scattering, plane-parallel medium with specularly and diffusely reflecting boundaries.