Correlations for the double-diffusive natural convection in square enclosures induced by opposite temperature and concentration gradients

Double-diffusive natural convection in vertical square enclosures induced by opposite horizontal temperature and concentration gradients is studied numerically. A computational code based on the SIMPLE-C algorithm for pressure–velocity coupling is used to solve the system of the conservation equations of mass, momentum, energy and species. Simulations are performed using the thermal Rayleigh number, the buoyancy ratio, the Prandtl number, and the Lewis number, as independent variables. It is found that both heat and mass transfer increase as the thermal Rayleigh number and the Prandtl number are increased, while exhibit a minimum at a value of the buoyancy ratio which increases with increasing the thermal Rayleigh number and the Lewis number. Finally, the mass transfer rate increases with the Lewis number. Conversely, the heat transfer rate is practically independent of the Lewis number as long as the buoyancy ratio is lower than the value at which the minimum heat transfer occurs, whereas it decreases significantly with the Lewis number for higher values of the buoyancy ratio. Based on the results obtained, suitable correlations are developed for the Nusselt and Sherwood numbers of the enclosure.