Heat Transfer by Combined Conduction and Radiation Between Concentric Spheres Separated by Radiating Medium

Steady-state heat transfer by simultaneous conduction and radiation through a spherical shell of absorbing, emitting, and scattering medium has been investigated analytically. The medium is confined between two gray, diffuse, isothermal spheres kept at different but uniform temperatures and is capable of generating heat. The problem is formulated rigorously using exact radiative transfer methods. The governing equations were solved numerically using an iterative scheme. The results reported illustrate the interaction of conduction with radiation heat transfer as well as reveal the effects of the parameters on the heat transfer characteristics. A simple approximation is suggested for predicting total heat transfer through a spherical shell from the results through a plane layer. The results are compared with available solutions and super position approximations.