Double-diffusive convection in a rectangle with opposing horizontal temperature and concentration gradients

Abstract

A numerical study is made of double-diffusive convection in a rectangular cavity with combined horizontal temperature and concentration gradients. The boundary conditions at the vertical side walls are imposed in such a way that the thermal and solutal buoyancy effects are counteracting, resulting in an opposing gradient flow configuration. Numerical solutions to the governing full time-dependent Navier-Stokes equations at large thermal ( R t ) and solutal ( R s ) Rayleigh numbers are acquired. The essential details of flow, temperature and concentration fields are described for a large Lewis number. The time evolutions of these fields are portrayed. Distinct flow regimes in the steady-state are identified as the buoyancy ratio R p ( = R s R t ) varies over a wide range. The structures of the thermal, solutal and velocity boundary layers near the side wall are examined. When R p is moderate, the multi-layered flow structure in the interior is clearly depicted; the attendant S-shaped thermal field and the step-like concentration distribution are brought into focus. The existence of the layered flow structure in the core is strongly corroborative of the results of the prior experimental visualizations. Based on the numerical data, the steady-state mean Nusselt number Nu and Sherwood number Sh are tabulated for varying values of R p . As R p increases from a very small value, Nu decreases monotonically towards a value characteristic of conductive transfer; however, Sh reaches a minimum value when R p takes a moderate value. This behavior is qualitatively consistent with the previous experimental findings.