THERMAL RADIATION HEAT TRANSFER EFFECTS ON SOLIDIFICATION OF FINITE CONCENTRIC CYLINDRICAL MEDIUM-ENTHALPY MODEL AND P-1 APPROXIMATION

Abstract

The effect of thermal radiation on solidification of an absorbing, emitting, isotropically scattering finite, semitransparent gray medium bounded between two concentric cylinders is investigated. The law of conservation energy which employs enthalpy and temperature as dependent variables is coupled with a set of moment equations which are derived from the radiative transfer equation and Marshak-type boundary conditions by applying P-l differential approximation.

The transient temperature distribution, interface location of a semitransparent phase-change medium, and the local radiative and axial heat fluxes have been obtained by using the Gauss-Seidel iterative numerical scheme for an optically thick medium. The numerical approximations of the finite cylindrical two-dimensional case are compared with those of the infinite axisymmetric one-dimensional case for some typical geometric dimensions and parameters. The use of enthalpy model coupled with a set of moment equations yielded a more general analysis of the multidimensional Stefan problem, where an internal thermal radiation heat transfer simultaneously occurs.