Thermo-Solutal Buoyancy Induced Mixed Convection in a Backward Facing Step Channel using Velocity-Vorticity Formulation

Abstract

Double diffusive mixed convection in a horizontal channel with backward facing step is analyzed using velocity-vorticity formulation with a focus on the effect of recirculatory flow pattern on convective heat and mass transfer. The governing equations consist of vorticity transport equation with thermal and solutal buoyancy force terms, velocity Poisson equations, energy equation, and solutal concentration equation. Galerkin's weighted residual finite-element method has been employed to solve the equations for vorticity, velocity, temperature, and concentration fields in the computational domain. Test results are obtained to study the effect of thermal Grashof number (Gr _T ), solutal Grashof number (Gr _S ), and expansion ratio on the average Nusselt and Sherwood numbers. Results indicate that the convective heat transfer increased with increase in Gr _T only when the Gr _S number is in the aiding mode. The maximum local Nusselt number is always observed to be located adjacent to the downstream of the fluid reattachment point. Using the matched method of asymptotic expansions, correlations have also been developed for average Nusselt and Sherwood numbers for both cases of aiding and opposing buoyancy forces.