HaeOk Skarda Lee

Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular enclosures

Abstract Radiative heat transfer in two-dimensional rectangular enclosures is studied using the S - N discrete ordinates method. The medium in the enclosure is gray and absorbs, emits, and anisotropically scatters radiative energy. General Mie-anisotropic phase functions are treated by Legendre polynomial expansions. The average incident radiations and the radiative heat fluxes are presented in graphical and tabular forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is nonsymmetric, but it is not important for symmetric environments. Side wall heat losses are significant for back scattering phase functions, moderate optical thicknesses, large scattering albedos, and small reflectivities.

Nongray Radiative Gas Analyses Using the S-N Discrete Ordinates Method

The S-N discrete ordinates method is applied to analyze radiative heat transfer in nongray gases. Spectral correlation between the terms in the equation of transfer is considered for black or nearly nonreflecting walls. Formulations to apply the S-N method using a narrow-band or the exponential wide-band model are presented. The net radiative wall heat fluxes and the radiative source distributions are obtained for uniform, parabolic, and boundary layer type temperature profiles, as well as for a parabolic concentration profile. The narrow- and wide-band nongray solutions are compared with gray-band approximations using the same band models. The computational speed of the gray-band approximation is obtained at the expense of accuracy in the internal fluxes and radiative source distributions. The wall radiative flux predictions by the gray-band approximation are satisfactory.

Radiative transfer in two-dimensional anisotropic scattering media with collimated incidence

Abstract An accurate analysis is performed by using the S-N discrete ordinates method for radiative transfer in two-dimensional rectangular enclosures exposed to an arbitrarily inclined, collimated incident beam. The enclosed gray medium absorbs and anisotropically scatters radiative energy. General anisotropic Mie-scattering phase functions are treated by Legendre polynomial expansions. A highly accurate S-14 approximation is used for the analysis. Benchmark results for the average incident radiations, the radiative fluxes and the source functions, obtained from the radiative intensity fields, are presented for purely scattering and absorbing-scattering media. Normal incidence and oblique incidence problems are analyzed. Anisotropy of the phase functions is found to have a strong effect on the radiative transfer. The reflected energy may differ by an order of magnitude when the phase function is changed from highly forward-scattering (phase function F1) to backward-scattering (phase function B2). The transmitted energy changes by a factor of two for the two phase functions F1 and B2. The effect of phase-function anisotropy on radiative transfer is found to be more significant for collimated incidence than for diffuse incidence.

Discrete ordinates solutions for radiatively participating media in a cylindrical enclosure

The radiative transfer equation is solved by the S-N discrete ordinates method in the two-dimensional r-z coordinates system. The walls of the enclosure are diffuse, and the participating medium absorbs, emits, and anisotropically scatters the radiative energy. Diffuse wall incidence, isothermal medium emission, and collimated incidence problems are considered. Effects of the scattering phase functions on average incident radiation and net radiative heat fluxes are studied. In addition, the effects of scattering albedo, optical thickness, and the wall emissivity are briefly discussed.

Discrete Ordinates Solutions of Nongray Radiative Transfer With Diffusely Reflecting Walls

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Scaled isotropic results for two-dimensional anisotropic scattering media

The full anisotropic scattering solutions of the radiative equation of transfer are compared with the scaled isotropic scattering solutions. Square enclosures with a collimated incidence, a diffuse incidence, or an isothermal emission are considered for comparison. The isotropic scaling approximation is found to predict accurately the radiative flux and the average incident radiation for the isothermal emission problem and for most diffuse incidence problems. For the collimated incidence problem, the isotropic scaling solutions are acceptable only for weakly scattering media. For large scattering albedo the error in the isotropic scaling is appreciable for the diffuse incidence problem and unacceptably large for the collimated incidence problem. The largest error in the y-direction net flux is found at the side wall regions when the medium is purely scattering. The isothermal emission problem or problems with symmetric boundary conditions can be accurately modeled by a scaled isotropic phase function, since the effect of the phase function anisotropy is negligible in such problems.

Two-dimensional anisotropic scattering radiation in a thermally developing Poiseuille flow

Combined heat transfer by laminar convection and two-dimensional radiation in a thermally developing Poiseuille flow between two infinite plane parallel plates is studied. The gray fluid participates radiatively by absorbing, emitting, and anisotropically scattering radiative energy. Effects of the conduction-radiation parameter, scattering albedo, optical height of the channel, diffuse wall reflectivity, and scattering phase function are studied. Results obtained from one-dimensional treatment of the radiative transfer are shown to be quite different from those obtained from two-dimensional radiation analysis, which show significant preheating of the entering fluid. The two-dimensional effects are more pronounced as the channel optical height increases and as the conduction-radiation parameter and the scattering albedo decrease. The scattering phase functions also significantly influence the preheating as the channel optical height increases.

Modified δ-M Scaling Results for Mie-Anisotropic Scattering Media

A modified δ-M scaling method, which adjusts the δ-M scaled phase functions to be always positive, is applied to radiative transfer problems in two-dimensional square enclosures. The scaled anisotropic results are compared with the results obtained from an accurate model of the full anisotropic scattering problems using the S-N discrete ordinates method

Heat transfer—a review of 1984 literature

Synthese bibliographique et bibliographie des publications mondiales sur le transfert de chaleur en 1984

Determination of refractive indices of dyed polymer monospheres

The complex refractive indices of commercial composite spherical particles (black dyed [Dp = 1.041 μm] and red dyed [D p = 0.999 μm]) were determined by two different methods. The first method measured angular scattered-energy distributions to determine experimental phase functions that were compared with Mie phase functions. The second method examined several mixture rules to obtain the effective refractive indices of dyed polymer monospheres. The refractive indices of black and red dyes were measured independently for the mixture rule study. The effect of different refractive indices on the particle sizing accuracy was investigated using an optical liquid-borne particle counter and a wafer surface scanner.