Numerical computation of double-diffusive natural convective flow within an elliptic-shape enclosure

This paper deals with numerical investigation of double-diffusive natural convective flow in an annular space between confocal elliptic cylinders filled with a Newtonian fluid. Uniform temperatures and concentrations are imposed along walls of the enclosure so as to induce aiding thermal and mass buoyancy forces within the fluid. Equations of concentration, energy and momentum are formulated using the dimensionless form of transport equations in elliptic coordinates for laminar two-dimensional incompressible flow which is expressed in terms of stream function, vorticity, temperature and concentration. Laminar regime is considered under steady state condition. The coupled differential equations are discretized by the finite volume method (FVM) and are solved via an in house-built computer code. Beforehand, this last has been validated through reliable results available elsewhere. The present study considered the effects of pertinent parameters on fluid flow, heat and mass transfer: the Rayleigh number up to 5.105. Throughout the study, the Prandtl number has been varied from 0.3 to 1. The relevant results are presented in terms of isotherms, streamlines and iso-concentrations. In addition, the heat and mass transfer rate in the annulus is translated in terms of the average Nusselt and Sherwood numbers along the enclosure's sides. Based on the obtained results, it is concluded that, in the context of double diffusive natural convective flows in elliptic-shape annuli, the potential of the proposed approach is demonstrated.