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A finite element approach to combined conductive and radiative heat transfer in a planar medium
A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate integrodifferential governing equations for a grey and nonscattering medium with grey and diffuse walls are developed and solved for several model problems. We consider axisymmetric, cylindrical geometries with top and bottom boundaries of arbitrary convex shape. The method is accurate for media of any optical thickness and is capable of handling a wide array of axisymmetric geometries and boundary conditions. Several techniques are presented to reduce computational overhead, such as employing a SwartzWendroff approximation and cutoff criteria for evaluating radiation integrals. The method is successfully tested against several cases from the literature and is applied to some additional example problems to demonstrate its versatility. Solution of a freeboundary, combinedmode heat transfer problem representing the solidification of a semitransparent material, the Bridgman growth of an yttrium aluminium garnet YAG crystal, demonstrates the utility of this method for analysis of a complex materials processing system. The method is suitable for application to other research areas, such as the study of glass processing and the design of combustion furnace systems.
International Journal of Numerical Methods for Heat and Fluid Flow – Emerald Publishing
Published: Apr 1, 1992
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