Evaluation of the Radiative Heat Flux in Absorbing, Emitting and Linear-Anisotropically Scattering Cylindrical Media

The contribution of thermal radiation to heat transfer in an emitting, absorbing and linear-anisotropically scattering medium of one-dimensional cylindrical geometry is investigated. It is assumed that the radial temperature distribution in the medium is known or is found in conjunction with overall conservation of energy. The exact solution results in a first-order integral equation in the radial coordinate which is a substantial improvement over previous formulations developed for nonscattering media. Also, two approximate methods are established and tested for their accuracy. The first method is the differential approximation modified to accommodate linear-anisotropic scattering. The second method consists of an exponential kernel approximation in which the geometric integrand functions are replaced by simple exponential functions. The results presented indicate that in engineering applications either approximate method may be used to accurately model the radiative contribution to overall heat transfer rates, reducing the nonlinear integrodifferential energy conservation equation to a nonlinear differential equation.