Media Radiative Transfer Research Articles

Investigation and optimization of the covering power and coloristic properties of paint coatings of complex composition

A method for finding the optimum sizes of pigment particles, their volume concentration, and the paint coating thickness that provide the covering power and the required coloristic characteristics of reflected light for the minimum flow rate of pigments is based on using a four-flow approximation of the solution to the equation of radiation transfer in dispersion media and is extended to coatings of complex composition. The capabilities of the method are demonstrated by examples of coatings of mixtures of hematite and rutile particles in a binder with n=1.5 for variations of the modal size and the half-width of the size distribution of the pigment particles.

Radiation Transfer in Fibrous Media with Large Size Parameters.

Radiation transfer in fibrous media with large size parameters has been numerically investigatad using a pseudo-continuous model. In this study, first, we examine how the scattering from a single fiber can be approximated by the specular reflection on the fiber surface and the Fraunhofer diffraction of a rectangular aperture which is considered to be a single fiber. Considering the Fraunhofer diffraction and specular reflection, we derive approximate solutions for estimating the optical characteristics of fibers, such as extinction and scattering efficiencies, which are required in this model. By comparing the approximate solutions with the conventional exact solutions, it is shown that the approximate solutions are useful at size parameters of more than 50 and at absorption indexes of more than 0.1. Furthermore, with use of the optical characteristics obtained by the approximate solutions in combination with the conventional exact solutions, radiation transfer in two types of planar fibrous media with typical fiber orientations is estimated, and the effects of the optical constant of fibers, fiber diameter and the orientation on the radiation transfer in the media are presented.

A fourier transform solution of radiation transfer in a spherical-inhomogeneous medium

The radiative heat flux at the boundary of a 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 performed on the basis of the integral Fourier transforms method. Numerical results for the partial heat flux and emissivity for a given internal energy source and inhomogeneous medium, isotropic scattering are obtained.

Radiative transfer in media with cylindrical symmetry

The problem of radiation transfer in a cylinder with diffuse reflectivity and containing an energy source is connected with the source free radiation transfer problem with isotropic boundary condition. Equation for the radiation heat flux is obtained for a polynomial source in the special case of isotropic scattering, the radiation heat flux is given in terms of the albedo of the second problem. An expression is also given for the net radiation heat flux. Numerical results are given for a source within the medium of the form Q(r) = (1 - w)[1 - (r/R)2]. Calculations are also done for anisotropic scattering where we consider the scattering phase function in the form: X(γ) = n/4π + L δ(μ - μ') δ(φ - φ').

Radiative transfer in spherical and cylindrical media containing aerosols

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.

Radiation transfer in stochastic media

The present paper deals with certain problems of the radiation transfer in one-dimensional and three-dimensional infinite media with the assumption that the quantum survival probability is a homogeneous isotropic gaussian arbitrary field. The Dyson equation relative to the first moment of the source function is obtained, and the condition of its soluvability is studied. In the known Bourret approximation, the average number of the quantum scatterings and radiation intensities are calculated.

A fourier transform solution of radiation transfer in plane-parallel medium with space-dependent albedo

A method is presented for solving radiation transfer problems involving space-dependent single-scattering albedoc(x) for a grey plane non-emitting medium with isotropic scattering. Expressions for the exit distributions and the reflection and transmission coefficients, relevant to a medium having a slab geometry, are given. The solution of the linear transport equation is performed on the basis of integral Fourier transforms. Numerical results are obtained in the case of exponentially varying single-scattering albedo and compared with previous results.

Analytical and numerical algorithm for calculating the radiation intensity in a two-dimensional inhomogeneous medium

The authors consider the boundary-value problem of radiation transfer in a two-dimensional inhomogeneous medium with a given optical thickness and a spherical characteristic scattering curve. The simplicity of the computer realization of the algorithm presented, its theoretical validity, and comparison between this one and other algorithms suggest that this algorithm effectively supplements the existing algorithms for solving the equation of transfer in a two-dimensional inhomogeneous medium.

Radiation field in media with spherical symmetry

A study is made of the structure of the Green's functions of problems in the theory of radiative transfer in media with spherical symmetry. Linear integral equations are obtained for the coefficients of reflection of light from a sphere and from an infinite medium with a spherical, absolutely black cavity. The kernels and free terms of these equations are expressed in terms of the Green's function for infinite space. The angle of incidence of the radiation and the optical radius of the sphere occur in these equations as parameters. Half-range biorthogonality relations are obtained for the eigenfunctions of the homogeneous equation of radiative transfer. The adjoint functions used in these relations are expressed in terms of the coefficients of reflection. i. Introduction To solve problems in the theory of radiative transfer in plane media, Case's method is often used [i]. It is based on expansion of the radiation intensity (or the corresponding Green's function) with respect to a complete system of eigenfunctions of the homogeneous transfer equation. The coefficients in the expansions are determined by means of orthogonality conditions. In the case of infinite media, the orthogonality of the eigenfunctions in the complete range of the angular variable ~ (--i ~ ~ ~ I) with weight is used. But in the case of semi-infinite media and plane layers of finite optical thickness one uses the biorthogonality established in [2] of the system of eigenfunctions in the half-ranges (0 < ~ < 1 or --i < ~ < O) with respect to the system of adjoint functions with weight ~H(~), where H(~) is the H function introduced into the theory by Chandrasekhar [3]. The half-range biorthogonality condition was formulated in a dif

Simple Approximations for Calculations of Absorption in Clouds

Abstract Scaling principles can be used to transform problems of radiative transfer in media that scatter anisotropically to equivalent isotropic problems with exact solutions. By using such scaling principles together with geometric optics to relate the albedo for single scattering to drop radius and bulk absorption coefficient, very simple relationships can be obtained to calculate absorption of solar radiation by optically thick clouds. The results predict a dependence of absorption on the square root of cloud drop radius and thereby a dependence on air mass and pollution. Although these formulas are approximate, they are probably as good as the exact theory to within the limits of experimental accuracy, and they have the virtue of being exceedingly simple while retaining in their derivation the physics underlying the dependences that they indicate.

Equation for radiation transfer in a dispersive medium with space-time inhomogeneities

Equation for radiation transfer in a dispersive medium with space-time inhomogeneities

Radiative Transfer in Media Exhibiting Large Horizontal Variations

Radiative Transfer in Media Exhibiting Large Horizontal Variations