Abstract
An approximate method is developed for the study of radiative transfer in one-dimensional, non-planar systems. While this method can be regarded as an extension of some existing approximation techniques formulated for the one-dimensional planar problem, it does yield closed-form expressions for the radiant heat flux and the temperature profile for various non-planar problems, which have not been established before. Comparisons with the available numerical results show that the heat-flux expressions are accurate throughout the entire range of the optical thickness. Results for the temperature profile. however, have the same limitation as the various closed-form approximate solutions for the planar problem. They are not very accurate at regions near the boundary, except in the optically thick limit. Based on the closed-form expressions obtained for the non-planar radiative transfer problem, the present work establishes readily the effect of the various parameters, such as the optical thickness, the surface emissivity, the radius ratio and the heat-generation rate on the heat-transfer and the temperature profile. Differences between radiative heat-transfer characteristics of the two basic non-planar systems (concentric cylinders and concentric spheres) are discussed.
Published Version
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