Combined natural convection and radiation in a vertical annulus

Abstract

This paper presents a numerical study of the effects of thermal radiation on the heat transfer of steady natural convection in a participating fluid contained inside a cylindrical annulus. The fluid absorbs and emits radiation energy. Uniform temperature difference is imposed across the inner and outer cylinder walls. The radiation part of the problem is treated by using the two-dimensional P-l approximation. The numerical calculations were executed using the PROJECTION algorithm with a power law scheme. The analysis are performed for Rayleigh number ranging from 10(4) to 10(6), aspect ratio varying between 2 and 10, and the radius ratio ranging from 1.25 to 10 for N=0.1, 1, and infinity where N is the conduction-to-radiation parameter. The thermal radiation greatly influences the flow field and temperature distribution inside the enclosure for different aspect ratio and radius ratios. Those results are presented vividly by the streamlines and isotherms. Based on the results, the average Nusselt number is correlated by a relation of the form <(Nu)over bar = a+blnA> and <(Nu)over bar = c+d> exp(-eta/e). The coefficients for various N are tabulated.