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Solution differences of natural convection in a tall cavity filled with air in which the density of the body force term are approximated by using the Boussinesq approximation (BA) and by using the real air density equation (RE) are numerically investigated. The main parameters for the investigation are Nusselt numbers and numbers of cells in the multi-cellular flow. The investigation is carried out for the Rayleigh number of 10 4 , and the cavity aspect ratio equal to 60. The temperature differences of the vertical cavity walls are varied from 1 K to 200 K. These conditions are appropriate to form the multi-cellular flow in the tall cavity obviously, and close to the boundary of the laminar and turbulent flows. Consequently, the differences in both Nusselt numbers and numbers of the cells in the multi-cellular flow can be easily observed. The finite volume method with the Lagrange interpolating polynomial (LIP) scheme are selected to discretize the governing equations of the flow, and the Semi-implicit method for pressure linked equations (SIMPLE) algorithm is used to determine the pressure field of the flow. The maximum difference of the average Nusselt numbers of natural convection in the tall cavity simulated by using BA and RE is 0.436 % for the range of the investigation. This indicates that the difference of heat transfer solutions of natural convection in the tall cavity simulated by using BA and RE is insignificant for practical applications, but there is an obvious difference on the numbers of the cells in the multi-cellular flow, when the temperature difference of the vertical cavity walls is greater than or equal to 120 K.

iop conference series. materials science and engineering

Investigation of solution differences on natural convection in a tall cavity simulated by using the Boussinesq approximation and the real air density equation