NUMERICAL CALCULATIONS FOR COMBINED CONDUCTION AND RADIATION TRANSIENT HEAT TRANSFER IN A SEMITRANSPARENT MEDIUM

A numerical computer code was developed for calculating the combined conduction and radiation transient heat transfer in cylindrical, semitransparent materials that have temperature-dependent thermal properties. The radiative component is combined with the equation of conduction heat transfer by adding it as a heat source. The finite element method (FEM) was used for calculating the radiative component and for solving the temperature field in the medium. Very good agreement was observed between results obtained by using our code and those that exist in the literature for several steady-state cases. The advantage of the code is due to the fact that it incorporates temperature-dependent properties; thus it leads to more realistic and accurate results. The code was applied to calculate the cooling path of a large cylindrical sapphire boule while using varying, transient, temperature-dependent, combined heat transfer coefficients.