Numerical study of the interaction of natural convection with radiation in nongray gases in a narrow vertical cavity

A differential approximation method was employed to study the interaction of natural convection with radiation in nongray gases enclosed in narrow vertical cavities. The flow in the cavity was assumed laminar, two-dimensional, and incompressible, with the cavity walls being gray diffuse emitters and reflectors. The nondimensionalized equations were defined in a stream function-vorticity formulation and thermal boundary conditions were configured for isothermal walls. Both a P-1 and an exponential wide band approximation were used to describe the radiation source term. Calculations were performed for the effects of the nongrayness factor at various Rayleigh numbers, moderate values of the radiation parameters, and a mean temperature of 600 K. The P-1 model overestimated values for local Nusselt number, while the wide band model produced the general gray trends.