Parallel computation of radiative heat transfer in an axisymmetric closed chamber: an application to crystal growth

Abstract

Parallel computation of view factors for gray diffuse surfaces is studied using a combination of methods developed by the authors and other researchers, exploiting the strengths and advantages of the respective methods. Kobayashi and Miyahara (Numer. Heat Transfer Part B 28 (1995) 437) introduced the use of a path integral to calculate the view factor and this method is accurate and robust, especially near the corners which are typically problematic. Dupret et al. (Int. J. Heat Mass Transfer 33 (1990) 1849) have a less preferred means of calculating the view factor integral but their visibility or blocking algorithm allows analysis of completely arbitrary axisymmetric closed geometries. In this paper, we introduce optimizations to the Dupret blocking algorithm. The computation of view factors and blocking requires more computer time than solving for the flux, and the parallel code developed exhibits excellent scalability. The code was applied to the design of a heat shield with a controlled temerature. The growth velocity and temperature gradients are measured and studied in terms of the constraint imposed by the equation for the formation of an oxidation induced stacking fault ring, V g/ G s> C crit.