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Solutions for One-Dimensional Radiative Transfer Problems

Leonid A. Dombrovsky

Following from: P1 approximation of the spherical harmonics method, The simplest approximations of double spherical harmonics

Leading to: Radiation of an isothermal plane-parallel layer, Radiative equilibrium in a plane-parallel layer, Hemispherical transmittance and reflectance at normal incidence, An estimate of P1 approximation error for optically inhomogeneous media, Radiation of a nonisothermal layer of scattering medium, Diffusion approximation in multi-dimensional radiative transfer problems

The majority of practical radiative transfer problems are not one-dimensional. The known exception is radiative transfer in thin coatings and in samples used for identification of material radiative properties. Nevertheless, some aspects of one-dimensional problems are of interest. First of all, one can obtain exact solutions, and there is the possibility of estimating the accuracy of different approximate methods. It is also important that comparably simple solutions for model problems can be used as an effective instrument in studying the physical features of the processes. These solutions also can have widespread adaptation in asymptotic evaluations in combined heat transfer analysis and in numerous engineering applications.

The present article is a brief introduction to the above-specified articles on two well-known one-dimensional problems: self-thermal radiation of an isothermal plane-parallel layer of scattering medium and heat transfer at radiative equilibrium in a layer between walls having different temperatures. Thermal radiation of a medium with a known temperature field and the radiative equilibrium of the medium can be considered as two of the limiting conditions of combined heat transfer. In the first case, the thermal radiation has no influence on the temperature field, which is formed by the predominant effect of heat conduction and/or convective heat transfer. At the radiative equilibrium, thermal radiation is, in contrast to the first problem, the only energy transfer mode determining the medium temperature.

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