Multiplicity of solution for natural convective heat transfer and entropy generation in a semi-elliptical enclosure

Abstract

The problem of steady natural convection in a bottom-heated semi-elliptical enclosure has been investigated numerically for a wide range of geometric and flow configurations using the finite volume method. The results are presented for varying Rayleigh numbers, Ra, in the range 1 × 102 ≤ Ra ≤ 5 × 104 and different values of aspect ratio, A = 1, 0.75, 0.5, and 0.25, where the aspect ratio, A, is defined as the ratio of lengths of the semi-minor axis to the semi-major axis of the semi-elliptical enclosure. It has been found that the steady-state solution appears in the form of single or multiple pairs of counter-rotating convection cells depending on the values of physical parameters. For A = 1, 0.75, and 0.5, as the value of Rayleigh number exceeds a critical value, natural convective flow inside the semi-elliptical enclosure exhibits multiple steady solutions with varying pairs of counter-rotating convection cells; however, such multiplicity of steady solutions could not be found for the cases of A = 0.25. The parametric variations of heat transfer and entropy generation rates are studied in detail. It is observed that the average Nusselt number associated with the natural convection in the semi-elliptical cavity is governed by several parameters: aspect ratio, Rayleigh number, number of convection cells, and intensity of convective motion inside the convection cells. The entropy generation due to viscous dissipation is found to be negligible as compared to the entropy generation due to conduction.