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This article deals with the effects of thermophoresis on thermosolutal mixed convection in a vertical wavy porous cavity. Three distinct flow features are chosen by changing the directions of the moving horizontal borders. A nonuniform temperature, as well as concentration distributions, are introduced to the bottom wall while keeping cold temperature and low concentration for the other walls. The governing equations are modeled to describe thermosolutal phenomena. These equations are solved by reconstructing a recently developed compact scheme. Furthermore, the significance of well-defined parameters influencing the fluid rotation and thermosolutal transfer, namely Richardson number ( 0.01 ≤ Ri ≤ 100 ), Buoyancy ratio (N = 1), number of undulations ( 0 ≤ d ≤ 2 ) of the wavy walls, Lewis number ( 1 ≤ Le ≤ 10 ), thermophoretic coefficient ( 0.0 ≤ K T ≤ 1.0 ), Darcy number ( 0.001 ≤ Da ≤ 0.1 ), and porosity of the porous medium ( 0.1 ≤ ε ≤ 1.0 ) are performed generously. Results are displayed in terms of streamlines, isotherms, iso-concentrations, Nusselt, and Sherwood numbers to evoke the thermosolutal phenomena for various physical parameters. It is observed that thermophoresis is effective in certain circumstances. In addition, heat and mass transfer enhancement is noted with decreasing Richardson number while heat and mass transfer reduction is noted with increasing undulation number of the wavy walls. We have noticed that for the change in Le from 1 to 10, heat transfer is diminished up to 2.91% in Case-1, 3.03% in Case-2, and 2.20% in Case-3 while mass transfer is enhanced by 162.85% in Case-1, 164.05% in Case-2, and 87.03% in Case-3. [ABSTRACT FROM AUTHOR]

The two-temperature model of local thermal nonequilibrium (LTNE) is utilized to investigate a weakly nonlinear stability of thermosolutal convection in an Oldroyd-B fluid-saturated anisotropic porous layer. The anisotropies in permeability, thermal conductivities of the porous medium, and solutal diffusivity are accounted for by second-order tensors with their principal directions coinciding with the horizontal and vertical coordinate axes. A modified Darcy-Oldroyd model is employed to describe the flow in a porous medium bounded by impermeable plane walls with uniform and unequal temperatures as well as solute concentrations. The cubic-Landau equations are derived in the neighborhood of stationary and oscillatory onset using a modified perturbation approach and the stability of bifurcating equilibrium solutions is discussed. The advantage is taken to present some additional results on the linear instability aspects as well. It is manifested that the solutal anisotropy parameter also plays a decisive role on the instability characteristics of the system. It is found that the stationary bifurcating solution transforms from supercritical to subcritical while the oscillatory bifurcating solution transforms from supercritical to subcritical and revert to supercritical. The Nusselt and Sherwood numbers are used to examine the influence of LTNE and viscoelastic parameters on heat and mass transfer, respectively. The results of Maxwell fluid are outlined as a particular case from this study. [ABSTRACT FROM AUTHOR]

• Heat and mass transfer in a SGSP are investigated experimentally and numerically. • 2D numerical model developed can accurately predict and describe the transfers. • Solar flux influence significantly on the SGSP temperature. • Solar flux influence is insignificant on the SGSP saline concentration. In this paper, experimental and numerical investigations of heat and mass transfer in a Salt Gradient Solar Pond (SGSP) are presented for the first time in the SGSP studies. The experimental approach consists of a thermally insulated parallelipedic tank filled with saline water and exposed under a solar simulator. The numerical model is developed in Fortran 95 basing on 2D Navier-Stokes, thermal energy and diffusion equations with an appropriate treatment of the SGSP boundary conditions. These equations are solved using the implicit Finite Volume Method and the SIMPLE algorithm. The study covers a 10-day period and involves two different values of the sun-like average radiation: 150 W/m2 (case 1) and 500 W/m2 (case 2). Comparisons between experimental and numerical results, for case 1, show that the numerical model developed can accurately predict and describe the heat and mass transfer with the development of the thermosolutal convection in the SGSP. Moreover, the time required to form the linear variation of the SGSP temperature is shorter for case 2 than for case 1 with a difference of 89 h, during which the LCZ temperature increases from 20 °C to 28.82 °C for case 1 and to 48.03 °C for case 2. Therefore, the energy storage takes place after a few days of the SGSP operation. In addition, the salt concentration of the LCZ decreases by about 0.83 kg/m3 and increases in the UCZ by about 1 kg/m3 for both cases. Thus, the sun-like average radiation does not have a significant influence on the mass transfer in the SGSP unlike on the heat transfer. [ABSTRACT FROM AUTHOR]

Through our paper, thermosolutal convection of viscoplastic materials 'so called Bingham plastics' which occurs into a porous matrix with an inner pollutant source has been treated numerically, in the aim to light out the impact of some relevant parameters; such Lewis and porous Rayleigh numbers; as well as the buoyancy ratio and the source dimension one; on a such conjugate phenomenon. To do so, the physical model for the momentum conservation equations is made using the Brinkman extension of the classical Darcy equation. The set of coupled equations is solved using the finite volume method and the SIMPLER algorithm. The heat and solute source within the porous space has taken a circular shape. Simply said, our pollutant source is a transport pipe which presented in 2D. To handle the latter in Cartesian Coordinates; the Cartesian Cut-Cell approach was adopted. After a careful treatment of such double-diffusive convection within the Bingham-porous space; powerful expressions that expect the mean transfer rates in such industrial geometry are set forth as a function of the governing parameters. These correlations, which predicted with '3% the numerical results, may count as a complement to previous Newtonian-fluid researches. It is to note that the validity of the computing code was ascertained by comparing our results with experimental data and numerical ones, already available in the literature. [ABSTRACT FROM AUTHOR]

In this study, we investigated numerically two- and three-dimensional convective heat and mass transfer in a horizontal rectangular enclosure filled with heterogeneous porous media. The main goal is to underline the limitation of the widely used classical parallel flow assumption. The considered configuration is Cartesian. The horizontal and vertical walls are submitted to different mass and heat transfer. The Darcy model and the Boussinesq approximation are considered. The governing parameters which control the problem are the Darcy-Rayleigh number, Rt, the buoyancy ratio, N, the enclosure aspect ratio, A, the local permeability ratio, Kr and the Lewis number (fixed to ten in the present study). The obtained results with two-dimensional (2D) and three-dimensional (3D) approaches are compared to underline similarities and differences. We demonstrate the limit validity of 2D solution and the transition to 3D solutions when the convective forces or the domain permeable heterogeneity increases. The flow intensity, heat and mass transfer increases with the domain permeable heterogeneity. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the results of a numerical study of double-diffusive convection in an inclined rectangular collector filled with two parallel porous layers. Each porous layer is considered homogeneous, isotropic and saturated with the same fluid. The vertical walls of porous cavity are subjected to uniform temperature and concentration whereas the other surfaces are assumed to be adiabatic and impermeable. The set of equations governing the heat and mass coupled problem within the enclosure are solved numerically. The numerical results are presented and analyzed in terms of streamlines, isotherms, isoconcentrations lines and average Nusselt and Sherwood numbers. A scale analysis is used to characterize the effect of the permeability ratio on the heat and mass transfer. It is found that the numerical solutions of the full governing equations are in good agreement with the scaling results for some specific conditions. Optimum operating tilted angle are deduced. [Copyright &y& Elsevier]

Thermosolutal convection in a square cavity filled with a binary perfect gas mixture and submitted to an oriented magnetic field taking into account the effect of radiation heat transfer is numerically investigated. The cavity is heated and cooled along the active walls whereas the two other walls are adiabatic and insulated. Entropy generation due to heat and mass transfer, fluid friction and magnetic effect has been determined for laminar flow by solving numerically: The continuity, momentum energy and mass balance equations, using a Control Volume Finite-Element Method. The structure of the studied flows depends on five dimensionless parameters which are: The Grashof number, the buoyancy ratio, the Hartman number, the inclination angle of the magnetic field and the radiation parameter. [ABSTRACT FROM AUTHOR]

Abstract: Two- and three-dimensional numerical studies of double-diffusive natural convection in homogeneous and isotropic porous media, saturated with a binary fluid are analyzed. Top and bottom faces of the enclosures are subject respectively to different but uniform temperatures and concentrations, while its vertical boundaries are considered adiabatic and impermeable to mass transfer. The flow through the medium is governed by the Darcy model. The existence of multiple steady-state solutions is proved for both 2D and 3D models and all the solutions obtained are presented and described. Conjugate effects of the thermal Rayleigh number and the buoyancy ratio on heat transfer, mass transfer and existence range of each flow structure are discussed. Important differences in terms of heat and mass transfer are observed between different solutions. Depending on the governing parameters and the type of solution, the flow structure could be 2D or 3D. It is also found that all the 2D solutions are obtained with the 3D model but the latter has more degrees of freedom allowing a reorganization of the flow not possible in the case of 2D model. For Ra=200 and opposing thermal and species buoyancy forces, there exists a critical value of N (N =−0.6) below which the concentration stabilizes the flow by settling a bulk stratification. In such a case, the corresponding heat and mass transfer processes are ruled by pure diffusion solely (Nu=Sh=1). [Copyright &y& Elsevier]

Abstract: Heat and mass transfer by natural convection coupled to wall surface condensation or evaporation in a two-dimensional cavity subjected to uniform, but time-dependent wall temperatures is investigated numerically. At initial state, the cavity is filled with quiescent humid air at uniform temperature and density. By decreasing the wall temperature, condensation occurs at the four wall surfaces until an equilibrium thermodynamic state is reached. The walls are then heated and evaporation of the liquid water film is considered. Various time variations of the wall temperature were investigated. Since the mass of humid air and average pressure experience large changes during transient regimes, a weakly compressible formulation has been used. The model considers only condensation/evaporation under the thin film approximation. The computations were carried out for temperatures of humid air varying between 300 K and 350 K, and pressure variations around atmospheric pressure. The typical width of the cavities is L = 0.1 m. The results show that very different transient flow structures occur during condensation and evaporation processes. The thickness distributions of the water films condensed at the walls are discussed, and it is shown that the thicknesses reflect the flow structures. The effect of the cavity aspect ratio reveals more complicated results than for convection without phase change at the wall surfaces. [Copyright &y& Elsevier]

Abstract: An extension of a slightly compressible flow model to double-diffusive convection of a binary mixture of ideal gases enclosed in a cavity is presented. The problem formulation is based on a low Mach number approximation and the impermeable surface assumption is not invoked. The main objectives of this paper are the statement of a new problem formulation, and the analysis of some significant results showing the influence of density variations on transient solutions for pure thermal or pure solutal convection. At steady-state, it is shown that the heat and mass transfer analogy may be applied for non-dilute mixtures at parameter ranges larger than those usually considered. To cite this article: H. Sun, G. Lauriat, C. R. Mecanique 337 (2009). [Copyright &y& Elsevier]

Abstract: In the present paper, a thorough analytical and numerical investigation is carried out to examine the double-diffusive convective instability within a horizontal porous layer heated and salted from below. A situation is considered where a lateral perturbing heat flux applied to the system is balanced by the horizontally induced Soret mass flux. The parameters governing this problem are the thermal Rayleigh number, R T; the Lewis Number, Le; the buoyancy ratio, N; the Soret parameter, M; the ratio of the horizontal to vertical heat flux, a; and the aspect ratio, A r; of the porous layer. The present investigation is focused on the situation where , which describes an equilibrium state between the induced Soret mass flux and the imposed heat flux. For this situation, a rest state solution is possible. The analytical solution, derived on the basis of the parallel flow approximation, is validated numerically using a finite difference method by solving the full governing equations. In the M ∗–Le plane , five distinct regions, describing different flow behaviors, are delineated and their location depends on the lateral heat flux parameter a. It is also demonstrated that supercritical and/or subcritical bifurcations are possible for specific ranges of M ∗ and Le. The effect of the lateral heating and the Soret parameter on the critical Rayleigh number, corresponding to the onset of parallel flow convection, is examined. The parameter a affects the flow and the heat transfer considerably, but its effect on the mass transfer is negligible. [Copyright &y& Elsevier]

Abstract: A layer of a ferromagnetic fluid permeated with dust particles heated and soluted from below saturating a porous medium is considered in the presence of a transverse uniform magnetic field. Using linearized stability theory and normal mode analysis, an exact solution is obtained for the case of two free boundaries. For the case of stationary convection, medium permeability, dust particles and non-buoyancy magnetization have a destabilizing effect whereas stable solute gradient has a stabilizing effect on the onset of instability. The critical wave number and critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of buoyancy magnetic parameter M 1 and results are depicted graphically. It is observed that the critical magnetic thermal Rayleigh number is reduced because of the specific heat of the dust particles. The principle of exchange of stabilities is found to hold true for a ferromagnetic fluid saturating a porous medium heated from below in the absence of dust particles and stable solute gradient. The oscillatory modes are introduced due to the presence of the dust particles and stable solute gradient, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The paper also reaffirms the qualitative findings of earlier investigations which are, in fact, limiting cases of the present study. [Copyright &y& Elsevier]

Abstract: The Soret effect on thermal natural convection within a horizontal porous enclosure heated uniformly from below by a constant heat flux is studied analytically and numerically using the Brinkman–extended Darcy model along with the Boussinesq approximation. The governing parameters of the problem are the Darcy–Rayleigh number, R T, the Lewis number, Le, the separation parameter, ϕ, the Darcy number, Da, and the aspect ratio of the enclosure, A r. In the limit of a shallow enclosure, an analytical closed form solution is obtained on the basis of a parallel flow approximation. A numerical study is also conducted to validate the results of the analytical predictions. The thresholds for the onset of stationary and finite amplitude convection are determined explicitly as function of Le, ϕ and Da. The obtained results show that in the ϕ–Le plane there exists three regions that correspond to different parallel flow regimes, namely the subcritical and supercritical flows. The separation parameter has a strong effect on the threshold of instabilities and on the characteristics of heat and mass transfer. The threshold for Hopf bifurcation is obtained on the basis of the linear stability analysis. The wavenumber and the oscillation frequency at the onset of instabilities are null for an infinite extent layer. [Copyright &y& Elsevier]

Abstract: The effect of magnetic field dependent (MFD) viscosity on thermosolutal convection in ferromagnetic fluid is considered for a ferromagnetic fluid layer heated and soluted from below in the presence of a uniform vertical magnetic field. Using the linearized stability theory and the normal mode analysis method, an exact solution is obtained for the case of two free boundaries. For the case of stationary convection, stable solute gradient and MFD viscosity have stabilizing effects on the onset of instability. The magnetization may have destabilizing or stabilizing effect in the presence of MFD viscosity, whereas magnetization has always destabilizing effect in the absence of MFD viscosity. The critical wave number and critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of magnetic parameter M1 and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in the absence of stable solute gradient. The oscillatory modes are introduced due to the presence of the stable solute gradient, which were non-existent in its absence. A sufficient condition for the non-existence of overstability is also obtained. [Copyright &y& Elsevier]

Abstract: This paper deals with natural convection driven by combined thermal and solutal buoyancy forces in a binary fluid. The configuration under study is a confined enclosure partially filled with a vertical porous layer. The mathematical description of the problem is based on a one-domain formulation of the conservation equations. The set of numerical results presented here quantitatively shows the influence of the porous layer on the flow structure and on heat and species transfer in the enclosure. The paper is focused on the analysis of the influence of the characteristic parameters governing double diffusive convection, namely the ratios of solutal and thermal parameters: the diffusivities and the buoyancy forces. Heat and mass transfer is analyzed as a function of the permeability of the porous layer. It is shown that the coupling of the flow penetration in the porous layer with the combined buoyancy forces induces a specific behavior of the flow structure and average heat transfer in the enclosure. [Copyright &y& Elsevier]

This paper reports numerical results of two-dimensional double-diffusive natural convection in a square porous cavity partially heated from below while its upper surface is cooled at a constant temperature. The vertical walls of the porous matrix are subjected to a horizontal concentration gradient. The parameters governing the problem are the thermal Rayleigh number (Ra=100 and 200), the Lewis number (Le=0.1, 1 and 10), the buoyancy ratio (-10N10) and the relative position of the heating element with respect to the vertical centerline of the cavity (δ=0 and 0.5). The effect of the governing parameters on fluid characteristics is analyzed. The multiplicity of solutions is explored and the existence of asymmetric bicellular flow is proved when the heated element is shifted towards a vertical boundary (δ=0.5). The solutal buoyancy forces induced by horizontal concentration gradient lead to the elimination of the multiplicity of solutions obtained in pure thermal convection when N reaches some threshold value which depends on Le and Ra. [Copyright &y& Elsevier]