Approximate method for calculating the temperature field in a growing crystal with account of thermal radiation

An engineering method is described for solving the heat-conduction problem in a growing single crystal for the case in which heat is lost at the surface through radiation. An integral substitution is used to transfer the nonlinearity in the boundary condition into the basic equation for the process; the nonlinear complex in the transformed equation can be evaluated. The approximate solution is compared with the results of a computer numerical calculation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 2, pp. 89–95, February, 1971.