Natural convection and volumetric radiation interactions in a concentric square annulus

Abstract

This paper focuses on a numerical investigation of steady two-dimensional natural convection and volumetric radiation interactions in a concentric annulus between two square isothermal cylinders. The annulus is filled with a gray absorbing–emitting and non-scattering medium. All the walls are assumed to be gray, diffuse, and opaque. The dynamic and thermal interactions are studied through a finite volume method combined with an immersed boundary technique to handle the square-shaped cylinder, whereas the discrete ordinates method is used to solve the radiative transfer equation. The present study is performed to investigate the effect of volumetric radiation on the flow for a variety of Rayleigh numbers 103 –106, three different optical thicknesses τ 0.2–1–5, a variety of Planck numbers 0.01–1, and three different aspect ratios A 0.2–0.4–0.6. The analysis is based on the dynamic and thermal fields in addition to the heat transfer rate. Results show that radiation affects significantly the flow and temperature distributions for a higher Rayleigh number Ra > 104, depending on the Planck number. The optical thickness and the aspect ratio has an important impact on the Nusselt number and percentage of radiation in heat transfer