Heat transfer by conduction and radiation in a one-dimensional planar medium using the differential approximation

The combined conduction and radiation heat transfer problem for a gray planar medium between two diffuse, isothermal infinite parallel plates is considered using the differential aproximation. e P-1 and P-3 spherical harmonics approximations for the intensity distribution are used. In addition, isotropic scattering and uniform volumetric generation terms are included. The governing energy equations developed using the P-1 and P-3 intensity expressions are fourth and sixth order nonlinear ordinary differential equations, respectively, and these equations have been solved numerically using a spline-collocation algorithm. Results are compared with the exact solutions and show that the differential methods are accurate for predicting both temperature profiles and heat transfer rates.