## Comparison Between Free and Rigid Boundaries Effects on Soret Driven Thermosolutal Convection in a Shallow Porous Enclosure
## AbstractHydrodynamic boundary conditions effects on Soret driven thermosolutal convection in a shallow porous enclosure subject to constant fluxes of heat, is conducted for the cases where both horizontal boundaries are stress-free (FFB) or rigid (RRB). The problem formulation is based on the Brinkman-Hazen-Darcy model with the Boussinesq approximation and the governing equations are solved numerically using a finite-difference method. The analytical solution is derived on the basis of the parallel flow approximation, and validated numerically using a finite difference method by solving the full governing equations. The critical Rayleigh numbers for the onset of subcritical, oscillatory and stationary convection are determined explicitly as functions of the governing parameters for infinite and finite layers. At the onset of instabilities, the wavenumber is equal to zero and the oscillation frequency vanishes at the onset of Hopf bifurcation. For a finite aspect ratio enclosure, the frequency is finite and decreases as the aspect ratio increases. The codimension-2 point exists and different flow regimes are delineated. As expected, both free and rigid boundaries yield results that are identical to those predicted by the Darcy model when the Darcy number is small enough. For sufficiently large values of the separation parameter, φ, the Nusselt and Sherwood numbers corresponding to free and rigid boundaries exhibit asymptotic behaviors. It is also found that, the flow intensity and heat and mass transfer rates are more affected by thermal diffusion effects in the case of free boundaries in comparison with rigid ones. |

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