Space-dependent Albedo Research Articles

Completely Spectral Collocation Solution of Radiative Heat Transfer in an Anisotropic Scattering Slab With a Graded Index Medium

A completely spectral collocation method (CSCM) is developed to solve radiative transfer equation in anisotropic scattering medium with graded index. Different from the Chebyshev collocation spectral method based on the discrete ordinates method (SP-DOM), the CSCM is used to discretize both the angular domain and the spatial domain of radiative transfer equation. In this approach, the angular derivative term and the integral term are approximated by the high order spectral collocation scheme instead of the low order finite difference approximations. Compared with those available data in literature, the CSCM has a good accuracy for a wide range of the extinction coefficient, the scattering albedo, the scattering phase function, the gradient of refractive index and the boundary emissivity. The CSCM can provide exponential convergence for the present problem. Meanwhile, the CSCM is much more economical than the SP-DOM. Moreover, for nonlinear anisotropic scattering and graded index medium with space-dependent albedo, the CSCM can provide smoother results and mitigate the ray effect.

On the Analytical Solution of the SN Radiative Transport Equation in a Slab for a Space-dependent Albedo Coefficient

In this work, we report a genuine general analytical solution for the linearized SN radiative-conductive transfer problem in a heterogeneous plane parallel atmosphere with the albedo coefficient depending continuously on the spatial variable. By general solution, we mean that the solution is valid for an arbitrary albedo coefficient continuous functions of the spatial variable having the property of fulfill the requirements of existence and uniqueness. The key feature of this novel approach embodies the steps: following the idea of the Decomposition method, we transform the original problem into a set of recursive problems with constant albedo coefficients, having the main feature that the sources terms takes the information of the spatial dependency of the albedo coefficient into account. This procedure allows us to solve, analytically, the resulting recursive system by the LTSN method developed for a constant albedo coefficient. Finally, we present the error control analysis of the solution and numerical comparisons against the literature results.

A collocation method for radiative transfer in a linearly anisotropically-scattering slab media with internal sources, space-dependent albedo and reflecting boundaries

A collocation method is used to obtain numerical values for the radiative transfer in absorbing, emitting, linearly anisotropically-scattering-inhomogeneous finite slab media. The results for the isotropic scattering are compared with those obtained by Thynell and Ozisik (1986) for the homogeneous slab and with those obtained by Garcia and Siewert (1981) for the inhomogeneous slab.

Exact integral formulation for radiative transfer in an inhomogeneous scattering medium

The exact integral formulation in terms of the moments of intensity is developed for radiative transfer in a three-dimensional, inhomogeneous medium with anisotropic scattering. Since the use of the present formulation in radiation computation requires the integration only over spatial variables, introduces the labor of computation. Examples, including isotropic scattering and anisotropic scattering in a slab, and isotropic scattering in a two-dimensional, rectangular medium exposed to collimated radiation, are presented to show the effectiveness of the present formulation. The examples are solved by the Nystrom method. Numerical results for the one-dimensional, isotropically scattering case show excellent agreement with available solutions reported in the literature. Graphic results of both one- and two-dimensional examples are presented to show the effects of the space-dependent albedo. 18 refs.

Radiation transfer due to a point source in an inhomogeneous finite sphere

A simple method for solving the radiation transfer due to a point source in an isotropically-scattering sphere with space-dependent albedo is presented. The results are compared with the only other available results obtained by Thynell and Ozisik (1986) for inhomogeneous sphere. The present method is applicable for a wider class of albedo functions.

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.

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.

Radiation transfer due to a point-source in an inhomogeneous finite sphere

A simple method for solving the radiation transfer due to a point source in an isotropically-scattering sphere with space-dependent albedo is presented. The results are compared with the only other available results obtained by Thynell and Ozisik (1986) for inhomogeneous sphere. The present method is applicable for a wider class of albedo functions.

A moment method for radiative transfer in an anisotropically-scattering slab medium with space-dependent albedo?(x)

The moment method is used to solve the radiative transfer problem in an anisotropic scattering plane medium with arbitrary space-dependent albedoω(x). The results are compared with those obtained recently by Cengel and Ozisik.

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.

Radiation transfer in an anisotropically scattering plane-parallel medium with space-dependent albedo ω(x)

A method of analysis is presented for solving radiation-transfer problems involving space-dependent albedo ω( x) for an absorbing, emitting and anisotropically scattering plane-parallel medium with reflecting boundaries. The albedo is represented in terms of Legendre polynomials in the form ω( x) = Σ R r=0 D r P r ( x/ L), where x is the optical variable, L is the half optical-thickness of the slab, P r ( x/L) are the Legendre polynomials and D r are known expansion coefficients. The effects of spatial variation of albedo on the reflectivity and transmissivity of a medium having a slab geometry are examined for the cases of both forward and backward anisotropic scattering over a wide range of system variables. The effects of ω( x) on the angular distribution of radiation are also shown for some representative cases.

Radiation Transfer in an Isotropically Scattering Solid Sphere With Space Dependent Albedo, ω(r)

Radiation Transfer in an Isotropically Scattering Solid Sphere With Space Dependent Albedo, ω(r)

Radiative transfer in a plane-parallel medium with space-dependent albedo, [formula omitted

Presentation d'une methode de calcul du transfert de chaleur radiatif entre deux plaques paralleles dans un milieu a albedo variable dans l'espace. Application numerique a une couche a limites transparentes