Numerical Study of Double Diffusion Natural Convection of a Binary Fluid in a Square Enclosure with a Partially Active Vertical Wall

Abstract

In this work, we consider a two-dimensional numerical study of double diffusion natural convection in a square enclosure with horizontal temperature and concentration gradients. The flow is driven by thermal and solutal buoyancies. Half of the left vertical wall is maintained at a uniform temperature and concentration. This half is either in the bottom, in the middle or at the top of the wall. These configurations are henceforth labeled B (Bottom), M (Middle) and T (Top). The right vertical wall is maintained at a uniform temperature and concentration that are different from those of the left wall. The remaining boundaries are impermeable and thermally insulated. The convection is modeled by the two-dimensional partial differential equations of continuity, momentum and energy, with appropriate initial and boundary conditions. A finite volume method is used to solve the dimensionless governing equations. The problem solution depends on five parameters: the thermal Rayleigh number, the Prandtl number, the Schmidt number, the buoyancy forces ratio (N = 1) and the aspect ratio of the enclosure. The main focus of the study is on examining the effect of the thermal Rayleigh number (Rat) on the thermosolutal natural convection flow. The results are illustrated by the patterns of the flow field, the thermal field and the concentration field. The heat and mass transfer are quantified by the Nusselt and Sherwood numbers, for different values of the thermal Rayleigh number. The obtained results show that the heat and mass transfer increase when Rat increases. The flow is steady when Rat < 7 × 104 for (T) and Rat < 6 × 105 for (M). For the T configuration, an unsteady periodic flow appears when Rat = 7 × 104. For the M configuration, an unsteady periodic flow appears when Rat = 6 × 105. However, for the B configuration, the flow is steady for thermal Rayleigh numbers up to Rat = 108.