Transient conduction and radiation in a semi-transparent phase change medium in an annulus

Abstract

The effect of thermal radiation on the solidification of an absorbing, emitting, isotropically scattering infinite and finite, semi-transparent gray medium bounded between two concentric cylinders is investigated. The conservation of energy principle employing enthalpy and temperature as dependent variables is coupled with a set of moment equations which are derived from the radiative transfer equations and Marshak type boundary conditions by applying P-1 differential approximations.

The transient temperature distribution, interface location of a semi-transparent phase change medium, and the local radiative radial and axial heat flux has been obtained by using a Gauss-Seidel iterative numerical scheme for some typical geometric dimensions and parameters. The numerical results for the one-dimensional axisymmetric case of pure conduction are verified by comparison with an analytical approximation where the change in the internal energy in the solid phase is neglected.

The results for an optically thick cylindrical medium are obtained, analyzed, and displayed in graphs.