H. M. Machali

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.

Radiative transfer in a spherical medium

Abstract The problem of radiative transfer in a spherical medium is solved by inspection once the slab solution is known. In this work we try to solve the Pseudo-slab problem using a set of trial functions that depend on Cases eigenvalues plus a linear combination of exponential integral functions. The proposed trial functions are used in the integral equation which transforms it to a system of algebraic equations in the expansion coefficients. These expansion coefficients are used to calculate the albedo and the partial heat flux for isotropic scattering in a homogeneous spherical 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.

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.

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.

The solution of radiation transfer problem for a slab with space-dependent albedo and anisotropic scattering

The transport of thermal radiation has been considered within a finite slab which absorb and scatter anisotropically. The problem involves the space-dependent single-scattering albedow(x). Two approximations are taken forw(x). In the first it is represented in exponential form asw(x)=w0 exp(−x/s), wherew0 ands are given constants andx is the optical variable. The second approximation assumes the formw(x) = ∑r=0Rdr*pr(x/a), wheredr* are known expansion coefficients anda is the half optical thickness of the slab. Analytic expressions for the forward, backward radiation intensities and fluxes are given in each approximation. The solution of the linear transport equation is performed on the basis of integral Fourier transforms.

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.

Pade approximants for linear Boltzmann equation. V. Albedo for finite slab and radiative heat flux constant

For pt.IV see ibid., vol.15, p.365 (1982). The Pade approximant is used to estimate the transmission and reflection coefficients for a finite slab as well as the radiative heat flux constant. A functional relation between both problems is obtained and this gives the possibility of calculating the radiative heat flux constant as a function of the albedo for a single scatter c. The Pade approximants for both problems are compared with the exact results; it is found that higher-order Pade approximants are required to give convergence to the exact results as c approaches 1.

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.