Combined Natural Convection and Volumetric Radiation in a Horizontal Annulus: Spectral and Finite Volume Predictions

Combined natural convection and radiation in a two-dimensional horizontal annulus filled with a radiatively participating gray medium is studied numerically by using a control-volume-based finite difference method and a spectral collocation method coupled with an influence matrix technique. The mathematical model includes the continuity equation, the incompressible Navier-Stokes equations, the energy equation, and the radiative transfer equation (RTE), which is modeled using the P1 differential approximation. Computed results for two Rayleigh numbers, Ra = 104 and Ra = 105, for several combinations of the radiation-conduction parameter, NR, and the optical thickness, τ, are presented. The differences observed in the predicted flow structures and heat transfer characteristics are described. Furthermore, an unusual flow structure is studied in detail, and multiple solutions are found. Finally, the potential benefits of applying spectral methods to problems involving radiative heat transfer are demonstrated.