Interaction of conduction and radiation in anisotropically scattering, spherical media

Steady-state heat transfer by simultaneous conduction and radiation in absorbing, emitting, linear anisotropically scattering spherical media occupying the region 0 r R is analyzed. The medium, which contains continuous heat-generating sources, is confined within a gray, diffuse spherical boundary. To obtain a rigorous solution to the nonlinear heat-transfer problem, the integral form of the equation of transfer is utilized. This integral form is solved in a highly accurate manner by first expanding the unknown functions in power series and then employing the Galerkin method for generating a system of linear algebraic equations, which is then solved by standard methods. The energy equation for the temperature is discretized according to a standard finite-difference approach, and the resulting nonlinear system of equations is linearized utilizing the Newton-Raphson method and solved iteratively by standard routines. A comprehensive parametric study is performed in order to examine the interaction between the radiation and conduction.