Analytical results for a class of view factors occurring in the Vertical Bridgman method

The treatment of radiation heat transfer in the computer modelling of crystal growth from the melt requires the net heat flux q_i for the boundary conditions of the temperature field, and the view factors f_i_j for the radiative exchange between surfaces A_i, A_j of an enclosure, i, j=1 to N. Different methods can be used to determine q_i: The radiosity method, a direct and Gebhart's method. A new proof of the equivalence of Gebhart's method with the other two is given. The concept of view factors for gray-diffuse surfaces is briefly surveyed. For a simplified enclosure describing the interior part of a Vertical Bridgman furnace the f_i_j are determined within an analytical approximation. The convergence of this method is investigated for two singular cases: (i) A_i and A_j have a common edge, (ii) A_i is self-viewing. As the main result we present, for a coaxial enclosure partitioned into rings, the f_i_j in closed form by means of the Sparrow-Moon area-contour integral. It is further shown, that Sparrow's double contour integral is not generally applicable, if shadowing effects are present. (orig.)Available from TIB Hannover: RA 831(2870) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman