Integral equation method for radiative transfer and its application in combined heat transfer enhancement analysis

The general SV- and S-type integral radiative transfer equations for absorbing, emitting, and linear-anisotropic scattering media in multidimensional enclosures with space-dependent properties are presented. The modeling techniques are subsequently applied to develop numerical schemes for solving the corresponding integral transfer equations in one- and two-dimensional, axisymmetric and nonhomogeneous cylindrical media as well as three dimensional cubic media subjected to externally incident radiation or bounded by emitting and diffusely-reflecting walls. It is shown that the product-integration method can produce accurate solutions for multidimensional radiation problems based on the SV-type integral radiative transfer equation. The result thus obtained is used as a basis for evaluating more efficient iterative schemes which are essential in solving the S-type integral radiative transfer equation. Finally, an application using the porous convection-radiation-converter (CRC) to enhance combined modes of heat transfer for laminar flows in a circular duct is proposed. The Navier-Stokes and Darcy-Brinkman equations are employed to predict flow field in the gas layer and porous core region, respectively. The radiation field is modeled by the S-type integral radiative transfer equation for its efficiency. The effects of heat transport augmentation due to the insertion of the porous CRC in the flow system are investigated numerically for various flow and thermal parameters.