Vorticity transport equation ∂ Φ ∂ + ∂ ∂ + ∂ Ω ∂ + ∂

Introduction Convective heat and mass transfer by combined thermal and solutal buoyancy forces, called double-diffusive natural convection assumes importance in many applications such as oceanography, food processing, nuclear waste disposal, solar ponds and metal solidification processes etc. In natural convection problems, the fluid momentum transport and convective heat and mass transfer take place solely due to the combined thermal and solutal buoyancy forces. Depending upon the type of application either the thermal buoyancy force or the solutal buoyancy force or the combination of these two will contribute to the resultant convective phenomenon. Buoyancy ratio defined as the ratio of solutal buoyancy force to thermal buoyancy force, is used to indicate the relative importance of these two buoyancy forces. The effect of variation in thermo physical properties of a fluid on the convective heat and mass transfer can be understood by varying the Lewis number. When heat diffusion effect is dominant compared to mass diffusion effect, as observed in problems related to solar ponds, crystal growth and metal solidification, the Lewis number becomes greater than unity. Since double-diffusive convection in a cavity resembles many engineering applications, the study of circulatory flow movement in cavity is considered to be a classical problem to understand the importance of buoyancy ratio and Lewis number on convective heat and mass transfer. Beghein et al. [1] studied aiding and opposing steady-state double diffusive natural convection flows in a square cavity using primitive variable form of Navier-Stokes equations. They obtained Nusselt and Sherwood number correlations for the variation of solutal Rayleigh number and Lewis number. Experimental and numerical investigations in horizontal and vertical rectangular cavities have been carried out by Wee et al. [2] using ω ψ − formulation. The rate of heat and moisture transfer in vertical and horizontal cavities with thermal and solutal gradients acting in the negative vertical coordinate direction was found to be five to nine times that of the horizontal cavity with both the gradients acting in the positive vertical coordinate direction. Lee et al. [3] studied experimentally the various flow patterns in natural convection of a salt-water solution due to the combined horizontal temperature and concentration gradients in rectangular enclosures with aspect ratio of 0.2 and 2.0. They observed smooth variation of temperature at the fluid layer interface contrary to the rapid variation of solutal concentration. Chen and Liu [4] studied numerically double diffusive natural convection due to heated cylinder submerged in a stratified salt solution in a rectangular cavity. Due to the interaction between the upward temperature and downward salinity gradients flow instability was created. Buoyancy ratio and thermal Rayleigh number had great influence on the variations in flow and temperature fields. Bennacer and Gobin [5,6] analyzed flow and heat transfer characteristics in a binary fluid contained in a two-dimensional enclosure with horizontal temperature and concentration gradients and proposed correlations in terms of the influence parameters using scaling law approach. It was observed that at high Lewis numbers, the heat transfer decreases with increasing buoyancy ratios. Weaver and Viskanta [7, 8] examined the effect of thermo-physical properties variation on heat and mass transfer in a cavity due to natural convection driven by combined thermal and solutal buoyancy forces with and without species inter-diffusion Soret and Dufour effects. The thermophysical properties and species inter-diffusion influence the velocity, heat and mass transfer rate but Soret and Dufour effects influence is not appreciable in these fields. Chamkha and Naser [9, 10] used ω ψ − form to predict the flow characteristics of