A new differential formulation of radiative transfer and its application to the one-dimensional problem

Radiation intensity in an absorbing-emitting medium is reformulated in a new differential form. The energy conservation equation for radiative transfer becomes an infinite-order partial differential equation. Multi-moment boundary conditions are introduced. Successive approximation techniques from physical consideration are then developed. Application of the present approximate method to the one-dimensional problem yields results in excellent agreement with existing numerical solutions. The method is shown to be accurate with no restriction on the value of various physical parameters, such as the optical thickness, the radiation-conduction parameter, and the wall emissivity.