Effect of the Aspect Ratio of a Heated Block on the Interaction Between Inertial and Thermosolutal Buoyancy Forces in a Lid-Driven Cavity

In this article thermosolutal buoyancy-induced fluid stratification in a lid-driven square cavity with a heated block at different aspect ratios is studied using velocity-vorticity form of Navier-Stokes equations. The governing equations consist of vorticity transport, velocity Poisson, energy and solutal concentration equations. Galerkin's weighted residual finite element method has been employed to solve the coupled and nonlinear governing equations. The effect of fluid stratification obtained as a result of interaction between inertial and thermosolutal buoyancy forces on convective heat and mass transfer has been analyzed in detail. Simulation results obtained for 0.5 ≤ Ri ≤ 10, −50 ≤ N ≤ 50, 50 ≤ Re ≤ 500, and 0.5 ≤ AR ≤ 2 indicate that Nusselt number variation is felt only at higher values of aspect ratio; whereas, there is a significant increase in Nusselt number at lower values of aspect ratios for the variation of Richardson number (Ri) and buoyancy ratio (N). A steep increase in Sherwood number is observed up to a transition Ri and this increase is found to be the same for all values of aspect ratio. Beyond this transition value no visible variation in Sherwood number is observed but the influence of aspect ratio is found to be appreciable on the magnitude of Sherwood number. The increase in Sherwood number with Re remains the same for all aspect ratios up to a transition Re, beyond which the rate of increase of the Sherwood number is determined by the magnitude of aspect ratio. Correlations for average Nusselt and Sherwood numbers have also been obtained using the asymptotic computational fluid dynamics method.