The Two-Flux Model Applied to Interaction of Radiation and Natural Convection in the Laminar Boundary Layer

Abstract

The effects of thermal radiation upon the laminar free convection boundary layer of a vertical flat plate was studied for an absorbing, emitting and scattering gray fluid. The two-flux model was used to represent the radiation term in the energy equation. This method allows to obtain a simpler formulation than required for exact representation of radiation in the boundary layer. The two-flux model reduces the governing equations: continuity, momentum, energy and irradiation, to a set of a coupled partial differential equations. A finite difference scheme is used to transform the resulting equations into an ordinary differential equation system which simplifies the numerical solution. Results for the velocity and temperature profiles and heat fluxes present close agreement with the optical thin and thick limits. Comparison of two-flux results with data obtained using an exact representation of radiation show very small deviations. The method proposed proves to be useful to investigate the effect of the different radiation parameters on natural convection boundary layer, and to obtain numerical results for engineering applications.