Interaction between natural convection and surface thermal radiation in tilted slender cavities

Abstract

In this paper a numerical investigation of the interaction between two modes of heat transfer, natural convection and surface thermal radiation, in a tilted slender cavity is studied. The bottom and top surfaces of the cavity are heated and cooled at constant temperatures, while its sidewalls remain thermally insulated. The studied parameters are: the Rayleigh number ( 10 4 ⩽ Ra ⩽ 10 6 ) , the aspect ratio ( 8 ⩽ A ⩽ 16 ) and the inclination angle ( 15 ° ⩽ λ ⩽ 35 ° ) . The steady state 2-D governing equations have been solved by the finite volume method. All the inner surfaces are assumed to be gray diffuse emitters and reflectors of radiation. The numerical model was reduced and compared to cases reported in the literature finding a good agreement. Streamlines, isotherms and total Nusselt numbers as a function of Rayleigh number for different inclinations are presented. The interaction between the two modes of heat transfer reveals that the decoupling of two mechanisms of heat transfer is not possible; the performance of the flow patterns, the isotherms and the radiative behavior on the walls was different for the uncoupled and coupled modes of heat transfer in the tilted slender cavity. The steady state results indicated that the radiative surface radiation coupled with natural convection modifies appreciably the flow patterns and the average heat transfer in the slender cavity. The total heat transfer increases when the inclination angle increases, except when the flow structure changes from the multi-cell to the unit-cell pattern. However, the total heat transfer decreases when the aspect ratio increases. A comprehensive correlation for the total Nusselt number has been proposed.