Mathematical Model of Heat Exchange and Approximate Methods of Solution of Radiation Transfer Equation in the Melting Furnace Tank

Mathematical model of heat exchange in melting furnace tank is considered. Equations of impulse balance for infinitesimal volume as well and continuity equation are simplified. Dimensionless parameters for compilation of discrete analogue are introduced. The system of equations of melt movement is made, solution of which issupposed to be performed using finite-difference methods. The approximate methods of solution of radiation transfer equation for optically thin and optically thick layers are considered. For optical thin layer expressions of spectral function of the source in the assumption of isotropic radiation and axial symmetry, intensity of radiation on the boundary areas and density of the monochromatic flux for the resulting radiation are simplified. Expression for the density of the monochromatic flux in the approximation of the optically dense layer is developed. Keywords: melting furnace, approximate methods, heat exchange by radiation, radiation transfer equation, mathematical model