The integral form of the equation of transfer in finite, two-dimensional, cylindrical media

The corresponding integral form of the equation of radiative transfer in absorbing, emitting, linear-anisotropic scattering media bounded by emitting, diffusely-reflecting walls is formulated. The formulation includes a development of expressions for the radiation intensity, the incident radiation and the forward and backward radiation heat fluxes in the axial and radial directions, respectively. The integral form is represented by a system of coupled Fredholm type integral equations, which can be solved accurately by numerical techniques. The two-dimensional formulation is subsequently used to develop the corresponding integral equations in one-dimensional, axi-symmetric media. In addition, it is also shown that the developed expressions for the net radiant fluxes in the r- and z-directions, respectively, are different from the equations presented recently in the literature.