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Published: 1960

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The problem of heat transfer from media that absorb and scatter thermal radiation was studied analytically, and the theory of thermal radiation is presented in a form useful for application to the radiant heat transfer problems. The basic equation of radiant heat transfer which governs the radiation field in a media that absorbs, emits, and scatters thermal radiation was derived. The mathematical analogy between thermal radiation and neutron transport is pointed out, and a few illustrations of the applicability of the solutions obtained for neutron transport problems to the radiative transfer problems are given. The derivation of the integral equations for radiant heat exchange in a geneal enclosure composed of a system of surfaces separated by an absorbing and scattering media are presented. The enclosure walls under consideration can reflect specularly and the scattering from the medium is not considered to be isotropic. The equation for the conservation of energy, including contributions due to thermal radiation, was derived by evaluating the energy transported into an imaginary closed surface fixed in space and then by applying Gauss's divergence theorem. The formulations developed are then used to gain insight into the problem by considering a few simple physical situations and obtaining numerical results for the grey case only. The Rosseland approximation for the radiant flux vector is employed in the study of Couette flow, and it is found that for large optical thicknesses the calculated temperature distributions agree well with those predicted by the exact formulation. Numerical solutions of the boundary layer equations for the flow of a radiating media along a wedge were obtained. The effect of radiation is to decrease the temperature gradient for both the hot and the cool walls; however, the heat transfer is affected only little. The validity of the diffusion approximation for radiation in boundary layer problems is limited, and should be used with caution only in situations where the mean free path of radiation is much smaller than the thermal bouadary layer thickness. The transport of radiant energy between two parallel plates separated by an absorbing and scattering media is studied. The temperature distributions were obtained by solving the nonhomogeneous Milne integral equation of the first kind. It was found that the polynomial approximation for the black body emissive power is satisfactory for all values of the optical thickness. The transport of energy by simultaneous conduction and radiation in a one-dimensional system was considered. A nonlinear integral equation governing the temperature distribution in an absorbing media was solved, and it is shown that the temperature distribution is strongly dependent on the optical thickness of the slab and on the dimensionless parameter, N, which determines the relative role of energy transfer by conduction to that by radiation. The presence of radintion generally increases the heat transfer by conduction. (auth).