A general integration method for radiative transfer in 3-D non-homogeneous cylindrical media with anisotropic scattering

Abstract

A general set of integral equations is presented to solve 3-D radiative heat transfer problems in emitting, absorbing and linear anisotropic scattering finite hollow or solid cylinders with non-homogeneous media. By tracing a ray to compute the intensity,it is much easier to handle the spatial change properties including extinction coefficient. Both the continuous change property and step-change property are dealt with without difficulties. The solid angle integration in getting the incident radiation and heat fluxes is represented by the bounding surface integration. In order to avoid the singularity problem near the bounding surface, the surface integrations are transformed to new modified integral equations by mathematical methods. By doing so, we get more flexible general integral equations applicable to all cases (3-D solid cylinders, 3-D hollow cylinders, finite cylinders or infinite cylinders). This scheme has been verified by comparing the results with published data in the literature. It is believed that this method will be useful in combined radiation and convection heat transfer problems.