Purpose This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting. Design/methodology/approach The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed. Findings The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained. Practical implications The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities. Originality/value The authors believe that the presented results are original and have not been published elsewhere.

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This work deals with the Soret separation of a binary liquid mixture (Water 60 wt %-Ethanol 40 wt %). The studied configuration is a tilted rectangular cavity of large aspect ratio A. It is assumed that the right wall is heated uniformly or non-uniformly, while the left wall is maintained at a constant cold temperature. The top and bottom walls are well insulated. A developed program (based on the finite-volume method and the semi-implicit method for pressure-linked equations algorithm) was utilized to numerically solve the governing Navier-Stokes equations, the energy and the species equations with the associated boundary conditions. The relevant parameters in this study are the tilting angle (), the aspect ratio (A), the mass Rayleigh number (Ram) and the Lewis number (Le). number, Ra, and the flux ratio, a, for given values of the Lewis number, Le, and the separation ratio, .

A numerical study is performed to analyze steady state forced convection fluid flow through a confined porous square cylinder. The Darcy-Brinkman-Forchheimer model is adopted for the porous region. The finite volume method and the iterative SIMPLE algorithm are used to solve the governing equations. The results obtained are presented for the streamlines, variation of Nusselt number and drag coefficient for the range of conditions as 5 ≤ Re ≤ 40 and 10−2 ≤ Da ≤ 10−6.