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.

The steady energy transfer equation for simultaneous conduction and radiation in an absorbing, emitting, and nonscattering gray planar medium is studied theoretically. For extremely high-temperature applications, where radiative transfer plays an important role, ceramic-matrix composites, considered as semitransparent materials, are being explored for potential use in turbine and compressor components, spacecraft structures, engine control systems, and nuclear reactors. Exact solution of the above-mentioned radiative problems is seldom possible and time-consuming numerical approximations are then used. A technique combining an accurate physical formulation, the two-flux model, coupled to a fast numerical procedure for the calculation of the temperature and heat fluxes is described.

A numerical study is made of the thermal characteristics of semitransparent materials exposed to simultaneous conduction and radiation between concentric cylinders. For extremely high-temperature applications, where radiative transfer plays an important role, ceramic-matrix composites, considered as semitransparent materials, are being explored for potential use in turbine and compressor components, spacecraft structures, engine control systems and nuclear reactors. Through the use of a gray model and the two-flux method, specialized equations are developed that generate a system of nonlinear ordinary differential equations. To facilitate the solution of this system, an iterative strategy is adopted. In order to demonstrate the versatility and accuracy of the proposed methodology, the results of several numerical experiments are presented and compared with benchmark solutions.

This study presents the analysis of the thermal boundary layer considering combined convection and radiation in an absorbing, emitting, and scattering medium flowing over a flat plate. At high temperatures the presence of thermal radiation alters the temperature distribution in the boundary layer, which in turn affects the heat transfer at the wall. In many industrial applications, such as in the cooling of turbine and compressors blades, radiative heat transfer plays an important role. The treatment of heat transfer by combined convection and radiation in the boundary layer leads to a set of partial differential and integrodifferential equations, which must be solved simultaneously. The exact solutions are seldom possible and the investigators resort to approximate methods. In the present analysis the two-flux model is used to describe the radiative heat flux in the energy equation. This model reduces the equations that govern the problem to a set of coupled partial differential equations. A finite difference scheme, called “method of columns,” is used to transform the resulting equations into an ordinary differential equation system which simplifies the solution. Results for the temperature profile and heat fluxes showed close agreement with the thin and thick limits. The method proposed proves to be useful to investigate the effect of the different radiation parameters on the thermal boundary layer, and also to be accurate enough for engineering applications.

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