Two-Dimensional, Combined-Mode Heat Transfer by Conduction, Convection, and Radiation in Emitting, Absorbing, and Scattering Media-Solution by Finite Elements

This paper is concerned with a two-dimensional analysis of combined mode heat transfer using finite elements. Conduction, convection, and radiation are coupled in the emitting, absorbing, and scattering medium. The standard Galerkin finite elements can be used if the product of Reynolds number and Prandtl number is equal to or less than 1000. It is shown that the two-dimensional heat flux integration can be efficiently performed via Gaussian quadrature applied to isoparametric finite elements where no limitations to optical thicknesses are imposed. Numerical results are demonstrated for a diverging or converging channel. It is observed that the radiation effect on the temperature profile is more significant in the diverging than in the converging channel. Effects of Reynolds number, Prandtl number, albedo, and optical thickness upon temperature distributions are also investigated.