Bi-Stability Analysis Of Double Diffusive Convection In A Tilted Square Porous Cavity Filled With A Non-Newtonian Power-Law Fluids

Abstract

This research presents a numerical study of double-diffusive natural convection in a tilted square cavity with a porous layer filled with a non-Newtonian fluid. The cavity's active walls are subjected to uniform Neumann-type thermal and solute boundary conditions, involving constant heat and concentration fluxes, or Dirichlet-type conditions, with imposed constant temperature and concentration, whereas the remaining walls of the cavity are assumed to be adiabatic and impermeable. To elucidate the behavior of non-Newtonian fluids, we employed the power-law model, known as the predominant rheological model for addressing flow phenomena within porous media. The fundamental governing equations are numerically solved through the finite difference method, while the convective flow within porous media is characterized by the utilization of the Darcy model and Boussinesq approximation. The governing parameters controlling the problem include the Rayleigh number, , the power-law index, , the buoyancy ratio, , the Lewis number, , and the inclination angle . The results indicate that both the power-law index, , and the inclination angle, , exert notable influence on the flow intensity and the heat and mass transfer occurring through natural convection within the enclosure. Among the most fascinating findings of this research is the recognition of a phenomenon termed bi-stability, which signifies the presence of two stable solutions.