Cross‐diffusion effects on the onset of double‐diffusive convection in a rotating vertical heterogeneous porous cylinder with vertical throughflow

Abstract

AbstractThe effects of vertical throughflow, rotation, cross‐diffusion, and vertical heterogeneous permeability on the onset of double‐diffusive convection in a finite vertical porous cylinder have been studied. The fluid in the cylinder is warmed and salted from below with its top and lower walls considered to be isothermal, isosolutal, and permeable. In the model, the Brinkman model was adopted, coupled with the Oberbeck–Boussinesq approximation. The normal mode technique is used for linear stability analysis and a single‐term Galerkin method is used to solve the eigenvalue problem. Further, the influence of parameters such as the thermal and solute Rayleigh, Taylor, and the Soret and Dufour numbers on the fluid system instability have been investigated. Among other results, we found that vertical heterogeneity may either stabilize or destabilize a fluid system. The stabilization of the throughflow remains consistent irrespective of the orientation in the absence of a cross‐diffusion effect. The dual effect of throughflow is observed when there are cross‐diffusion effect. We found that increasing the Dufour parameter delays the onset of both stationary and oscillatory convection. The positive Soret number has a stabilizing effect on stationary convection and a destabilizing effect on the oscillatory convection case.