Effect of aspect ratio on the Double-diffusive convection of a fluid contained in a rectangular cavity with partially thermally active side walls

A numerical study is performed to investigate the effect of height-to-width aspect ratio, Grashof number, and Schmidt number on the Double-diffusive convection of a fluid contained in a rectangular cavity with partially thermally active side walls. The active part of the left side wall is at a higher temperature and concentration than that of the right side wall. The length of the thermally active part is equal to half of the height. The top and bottom of the cavity and inactive part of the side walls are considered to be adiabatic and impermeable to mass transfer. Nine different relative positions of the active zones are considered. The species diffusivity of the fluid is assumed to be constant but the density of fluid is assumed to vary linearly with temperature and concentration. The non-dimensional forms of governing transport equations that describe double-diffusive convection for laminar two-dimensional incompressible flow are functions of vorticity, temperature or energy, concentration and stream-function. The coupled differential equations are discretized by the Finite Difference Method. The SuccessiveOver-Relaxation (SOR) method is used in the solution of the stream function equation. The results are obtained for Grashof numbers between 10 and 10