Numerical analysis of conduction. Convection, and radiation in a gradually expanding channel

The problem with simultaneous conductive, connective, and radiative heat transfer is analyzed in a two-dimensional gradual expansion channel flow. The main objective is to generate a program to attack the radiation in a curvilinear coordinate system with momentum and energy equations involved. The governing equations are transformed into generalized coordinates. Whereas the SIMPLE algorithm developed in a body-fitted coordinate system is used to obtain the flow field solution, the finite volume method is applied to solve the radiative transfer equation. The accuracy and performance of the finite volume method for the radiation are validated in a well-known combined heat transfer problem by using a curvilinear grid system. Then detailed thermal characteristics are investigated in a gradually expanding channel through various parameters such as Prandtl number, conduction to radiation parameter, wall emissivity, and scattering albedo. Results show that radiation plays a significant role in the gradually expanding channel flow.