NEW APPROACH TO SIMULATION OF RADIATIVE-CONDUCTIVE HEAT-TRANSFER IN SEMITRANSPARENT CRYSTALS BEING PULLED FROM A MELT

A method is suggested for the solution of multi-dimensional radiative heat transfer problems arising in growing crystals. The basic idea of the approach lies in the construction of a special division of the uni t sphere into a set of solid angles (cells) and in the approximation o f the radiation intensity in each solid angle by the P-1 approximation . The radiant transport equation is satisfied in the mean over each el ementary cell and the system bf partial differential equations of the second order relative to the local zeroth-moments of radiation intensi ty are obtained. It is shown that the solid angle subdivision can be c arried out in different ways with respect to specific features of the heat transfer problem under consideration. As a result even a very rou gh partition permits satisfactory accuracy of the numerical solutions. One of the main advantages of the method consists in using solid angl e subdivisions which can be varied from point to point of the spatial domain. The latter gave possibility to simulate the radiative heat tra nsfer in a circular cylinder of finite length with specular side surfa ce. On this basis the calculation of the temperature field in a cylind rical sapphire crystal being pulled from the melt has been carried out without any restriction on the size of the crystal.