A variational multiscale stabilized finite element method for double diffusive incompressible flow with application to mixed convection in a heated staggered cavity under magnetic field

Abstract

In this work, a novel stabilized finite element scheme in a subgrid multiscale variational framework is proposed to efficiently solve double-diffusive incompressible Newtonian fluid flow in a complex geometry occurring in several real-life applications. Here, the fine scale effects are transferred to the course scale problem following algebraic subgrid analysis, and then, the course scale equations are computed and the key stabilization parameters are derived following the Fourier analysis. The influence of flow, heat, and mass transfer parameters such as Reynold’s Number, Hartmann Number, Richardson Number, and Lewis Number are analyzed under a magnetic field, through the streamlines, isotherms, and the local heat fluxes to understand the double-diffusive mixed convective process in a complex staggered cavity, which is relevant to engineering applications such as ventilation and contamination assessment systems. The study finds that maximum species contamination together with the maximum Sherwood Number (12.54) occurs when the Richardson number is 10, and the minimum contamination together with the minimum Sherwood Number (0.71) occurs when the Lewis number is 0.1 when other parameters are varied within the operational range. The results are validated with previously existing literature for simple cases.