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The present paper reports on an analytical and numerical study of combined Soret and Dufour effects on thermosolutal convection in a horizontal porous cavity saturated with an electrically conducting binary fluid under a magnetic field. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The main governing parameters of the problem are the Rayleigh, the Hartmann, the Soret, the Dufour and the Lewis numbers, the buoyancy ratio, the enclosure aspect ratio, and the normalized porosity of the porous medium. An asymptotic parallel flow approximation is applied to determine the onset of subcritical nonlinear convection. In addition, a linear stability analysis is performed to predict explicitly the thresholds for the onset of stationary, overstable and oscillatory convection, and the Hopf bifurcation as functions of the governing parameters. The combined effect of a magnetic field, Soret and Dufour parameters have a noticeable influence on the intensity of the convective flow, the heat and mass transfer rates, and the thresholds of linear convection. It is found that the imposition of a magnetic field delays the onset of convection and its intensification can lead to the total suppression of the convective currents. The heat transfer rate increases with the Dufour number and decreases with the Soret number and vice versa for the mass transfer rate.

The thermosolutal stability of a layer of the Rivlin-Ericksen fluid in a porous medium is considered under varying gravity conditions. It is found that for stationary convection, medium permeability and suspended particles have a destabilizing/stabilizing effect when gravity increases/decreases. The stable solute gradient has a stabilizing effect on the system.

Species separation in heterogeneous porous media is a field of interest of many industrial activities. In our investigation, the effect of a single discrete fracture on the thermosolutal convection coupled with the Soret effect have been analyzed. The main results show that the fracture can greatly affect the behavior of the thermogravitational flow and might play a positive role to the separation caused by the Soret effect. Furthermore, the fracture tilted to the cold wall causes a large separation compared to the one tilted to the hot wall with the same angle. Therefore, the separation process could be greatly improved.

We present a model for convection in a Navier–Stokes–Voigt fluid when the layer is heated from below and simultaneously salted from below, the thermosolutal convection problem. Instability thresholds are calculated for thermal convection with a dissolved salt field in a complex viscoelastic fluid of Navier–Stokes–Voigt type. The Kelvin–Voigt parameter is seen to play a very important role in acting as a stabilizing agent when the convection is of oscillatory type. The quantitative size of this effect is displayed. Nonlinear stability is also discussed, and it is briefly indicated how the global nonlinear stability limit may be increased, although there still remains a region of potential sub-critical instability, especially when the Kelvin–Voigt parameter increases.

International audience; Experiments of directional solidification of TiAl cylindrical samples were conducted within the frame of the ESA GRADECET project. The experiments were performed in the ESA "Large Diameter Centrifuge" using a furnace with a well defined thermal protocol. The furnace was mounted in the centrifuge and free to tilt in such a way that the total apparent gravity (sum of terrestrial gravity and centrifugal acceleration) was aligned to the cylinder centerline. Several centrifugation levels were investigated besides to one reference case out of the centrifuge. In this work, we present 3D numerical simulations of these experiments paying special attention in the liquid thermosolutal buoyancy convection and aluminum macrosegregation. The numerical model accounts for the non-inertial accelerations that appear in the rotating reference frame (centrifugal and Coriolis), motionless solid, the-mosolutal Boussinesq approximation and an infinitely fast microscopic diffusion model between the phases to depict the solid growth. The results showed that the Coriolis acceleration entirely modifies the liquid flow regime during solidification leading to a 3D aluminum segregation pattern with respect to the case solidified under normal terrestrial gravity conditions. Additionally the magnitude of aluminum segregation increases with the level of centrifu-* Corresponding author

In the present paper, a numerical investigation was performed to assess the effect of the rheological behavior of non-Newtonian fluids on Rayleigh–Benard thermosolutal convection instabilities within shallow and finite aspect ratio enclosures. Neumann and Dirichlet thermal and solutal boundary condition types were applied on the horizontal walls of the enclosure. Using the Boussinesq approximation, the momentum, energy, and species transport equations were numerically solved using a finite difference method. Performing a nonlinear asymptotic analysis, a bistability convective phenomenon was discovered, which was induced by the combined fluid shear-thinning and aiding thermosolutal convection effects. Therefore, bistability convection was the main focus in the current study using the more practical constitutive Carreau–Yasuda viscosity model, which is valid from zero to infinite shear rates. Also, the combined effects of the rheology parameters and double diffusive bistability convection were studied. For aiding flow, the shear-thinning and the slower diffusing solute effects were counteracting and, as a result, two steady-state finite amplitude solutions were found to exist for the same values of the governing parameters, which indicated and demonstrated evidence for the existence of bistability convective flows. For opposing flows, the shear-thinning effect strengthened subcritical flows, which sustained well below the threshold of Newtonian thermosolutal convection. Thus, bistability convection did not exist for opposing flows, as both the shear-thinning and the slower diffusing component effects favored subcritical convection.

The present work introduces numerical simulations based on an incompressible scheme of smoothed particle hydrodynamics (ISPH) method for the thermosolutal convection from an inner I-shaped inside an infinite-shaped cavity embedded by nano-encapsulated phase change materials (NEPCMs). An infinite-shaped enclosure is occupied by a nanofluid and a porous medium. In this work, the heat capacity of a core and shell is used for the overall heat capacity of encapsulated nanoparticles. An inner I-shaped is embedded inside a center of an enclosure and it carries T h and C h . The simulations are performed for different values of a length of an inner I-shaped L 2 ( 0.4 ≤ L 2 ≤ 1.5 ) , a Stefan parameter S t e ( 0.2 ≤ S t e ≤ 0.9 ) , a fusion temperature θ f ( 0.05 ≤ θ f ≤ 0.95 ) , Darcy parameter D a ( 10 − 2 ≤ D a ≤ 10 − 5 ) , an inclination angle γ ( 0 ≤ γ ≤ π / 2 ) and Rayleigh number R a ( 10 3 ≤ R a ≤ 10 6 ) . The numerical simulations showed that a fusion temperature θ f adjust the situations of a melting solidification zone. Further, the intensity of a melting solidification zone is adjusted by a Stefan parameter. Augmentations of an inner I-shaped length and Rayleigh number are powering buoyancy forces and thus the flow speed, and heat & mass transport are enhanced inside an infinite-shaped cavity. Mean Nusselt and Sherwood numbers are enhanced as I-shaped length and Rayleigh number are powered.

The results of a study of convection of moist air in conditions close to atmospheric are presented. Numerical estimates of dimensionless gas-dynamic parameters characteristic of the problem of convection of dry and moist air are presented and analyzed. Distinctive features of convection caused by a change in the concentration of water vapor as a result of its evaporation (condensation) are described. The effect of water vapor concentration on the convective stability of moist air is considered from the point of view of concentration convection, characterized by the concentration Rayleigh number. The technical characteristics of an experimental setup using the principle of holographic interferometry to study the thermoconcentration convection of moist air in the temperature range from 5 to 45 C are shown. The ability to distinguish convective heat and mass transfer in humid air under laboratory conditions is demonstrated.

In this paper, three-dimensional thermosolutal natural convection and entropy generation in a cubic cavity filled with a non-Newtonian Carreau-Yasuda fluid has been simulated by Lattice Boltzmann Method (LBM). This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 104 and 105), the Buoyancy ratio (N = -1, 0.1, 1), the Lewis number (Le = 0.5, 2.5, 10, 100, and 1000), power-law indexes (n = 0.5, 1, and 1.5), Carreau number (Cu = 0.01, 0.1, 1, 10 and 100), and Carreau-Yasuda parameter (m = 0.1, 0.5, and 1). Results indicate that the rise of Rayleigh number enhances heat and mass transfer for various studied parameters. The increase in power-law index provokes heat and mass transfer to drop gradually. However, the effect of power-law index on heat and mass transfer rises steadily as Rayleigh number rises. The enhancement of Carreau number decreases heat and mass transfer, but; the increases in the Carreau-Yasuda parameter augments heat and mass transfer significantly. The augmentation of the buoyancy ratio number enhances heat and mass transfer. It was found that mass transfer increases as Lewis number augments. The augmentation of Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the power-law index provokes various irreversibilities to drop significantly. The enhancement of the buoyancy ratio causes the summation entropy generations to increase considerably. The rise of Carreau number and Carreau-Yasuda parameter decreases and increases the total irreversibilities; respectively.

The effects of magnetic field dependent (MFD) thermosolutal convection and MFD viscosity of the fluid dynamics are investigated between squeezing discs rotating with different velocities. The unsteady constitutive expressions of mass conservation, modified Navier-Stokes, Maxwell and MFD thermosolutal convection are coupled as a system of ordinary differential equations. The corresponding solutions for the transformed radial and azimuthal momentum as well as solutions for the azimuthal and axial induced magnetic field equations are determined, also the MHD pressure and torque which the fluid exerts on the upper disc is derived and discussed in details. In the case of smooth discs the self-similar equations are solved using Homotopy Analysis Method (HAM) with appropriate initial guesses and auxiliary parameters to produce an algorithm with an accelerated and assured convergence. The validity and accuracy of HAM results is proved by comparison of the HAM solutions with numerical solver package BVP4c. It has been shown that magnetic Reynolds number causes to decrease magnetic field distributions, fluid temperature, axial and tangential velocity. Also azimuthal and axial components of magnetic field have opposite behavior with increase in MFD viscosity. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems, heating up or cooling processes, biological sensor systems and biological prosthetic etc. Keywords: MFD viscosity, Thermosolutal convection, Magnetic field, Reynolds numbers, HAM

This study is a contribution to the numerical study of the thermosolutal convection in a 3-D porous cavity filled with a binary fluid submitted to cross gradients of temperature and concentration. The Navier-Stokes equations, mass and energy governing the physical problem are discretized by the finite volume method. The equations of conservation of momentum coupled with the continuity equation are solved using the SIMPLEC algorithm, then the obtained system is solved using the implicit alternating directions method. The numerical simulations, presented here, correspond to a wide range of thermal Rayleigh number (103< Ra < 106) and buoyancy ratio (1 < N < 12). The Lewis and Prandtl numbers were fixed respectively at 5 and 0.71 and the sections dimension ? = D / H = 0.4. The temperature distribution, the flow pattern and the average heat and mass transfer are examined. The obtained results show significant changes in terms of heat and mass transfer, by proper choice of the governing parameters.

We propose a new phase-field model formulated within the system of lattice Boltzmann (LB) equation for simulating solidification and dendritic growth with fully coupled melt flow and thermosolutal convection–diffusion. With the evolution of the phase field and the transport phenomena all modeled and integrated within the same LB framework, this method preserves and combines the intrinsic advantages of the phase-field method (PFM) and the lattice Boltzmann method (LBM). Particularly, the present PFM/LBM model has several improved features compared to the existing phase-field models including: (1) a novel multiple-relaxation-time (MRT) LB scheme for the phase-field evolution is proposed to effectively model solidification coupled with melt flow and thermosolutal convection–diffusion with improved numerical stability and accuracy, (2) convenient diffuse interface treatments are implemented for the melt flow and thermosolutal transport which can be applied to the entire domain without tracking the interface, and (3) the evolution of the phase field, flow, concentration, and temperature fields on the level of microscopic distribution functions in the LB schemes is decoupled with a multiple-time-scaling strategy (despite their full physical coupling), thus solidification at high Lewis numbers (ratios of the liquid thermal to solutal diffusivities) can be conveniently modeled. The applicability and accuracy of the present PFM/LBM model are verified with four numerical tests including isothermal , iso-solutal and thermosolutal convection–diffusion problems, where excellent agreement in terms of phase-field and thermosolutal distributions and dendritic tip growth velocity and radius with those reported in the literature is demonstrated. The proposed PFM/LBM model can be an attractive and powerful tool for large-scale dendritic growth simulations given the high scalability of the LBM.

The main purpose of our investigation is to show the impact of pertinent parameters; such Lewis and porous thermal Rayleigh numbers as well as the buoyancy and the aspect ratios; on the double-diffusive convection phenomena which occur within a porous annulus; found between a cold (and less concentric) outer circular cylinder and a hot (and concentric) inner one, to come out with global correlations which predict the mean transfer rates in such annulus. To do so, the physical model for the momentum conservation equation 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. Summarizing the numerical predictions, global correlations of overall transfer within the porous annulus as a function of the governing studied parameters are set forth which predict within ±2% the numerical results. These correlations may count as a complement to previous researches done in the case a Newtonian-fluid annulus. It is to note that the validity of the computing code used was ascertained by comparing our results with the experimental data and numerical ones already available in the literature.

International Conference on Materials and Energy (ICOME), La Rochelle, FRANCE, MAY 17-20, 2016; International audience; An hybrid Lattice-Boltzman finite-difference method is proposed to assess the impact of the inclination angle of the cavity on thermosolutal natural convection of a binary fluid confined in a square cavity differentially heated and salted from two opposite walls with constant temperatures and concentrations. This method seems more flexible in implementing additional effects and apparently more efficient than the classical CFD methods. The study is conducted in the case of aiding buoyancy forces and many other controlling parameters. Results obtained showed important qualitative and quantitative effects of the governing parameters on fluid flow and heat and mass transfer characteristics. The heatlines and masslines concepts are also implemented to obtain additional details on heat and mass transfer processes. (C) 2017 The Authors. Published by Elsevier Ltd.

In this paper, thermo-diffusion (Soret effect) and diffusion-thermo (Dufour effect) effects on double-diffusive natural convection induced in a horizontal Brinkman porous layer with a stress-free upper boundary are investigated. The cavity is filled with a binary fluid and subjected to uniform fluxes of heat and mass on its long sides. An analytical solution based on the parallel flow approximation is developed for the problem considered in order to allow prompt determination of the thresholds of stationary and finite amplitude solutions and also heat and mass transfer characteristics. The analytical solution is validated numerically by using a finite difference method. The combined effects of the Soret and Dufour parameters, the thermal Rayleigh number, the buoyancy ratio, and the Darcy number on the flow intensity and heat and mass transfer are illustrated graphically, and some particular behaviors observed are discussed. The analytical solution proves the existence of different regions in the buoyancy ratio-Dufour parameter plane, corresponding to different parallel flow behaviors. The number, the location, and the extent of these regions, which are impossible to predict numerically, depend strongly on Soret and Dufour parameters. The effect of thermo-diffusion and diffusion-thermo on flow intensity and heat and mass transfer is found to be important.

A numerical investigation of Soret and Dufour effects on heat and mass transfer in a Salt Gradient Solar Pond (SGSP) and its storage efficiency under meteorological conditions of Tangier (Morocco) is presented. This SGSP consists of an open square cavity filled with a saline solution. Its vertical and bottom walls are adiabatic and impermeable. Transfers are described by the Navier-Stokes, thermal energy and diffusion equations which are solved with a finite volume scheme and the Gauss method. The link between the pressure and velocity fields is carried out by the SIMPLE algorithm. The numerical model, developed in Fortran 95 language, is satisfactorily validated by comparisons with previously published numerical and experimental studies. Results show that the Dufour effect on thermosolutal convection in a SGSP is more relevant than the Soret effect. Nevertheless, increasing the value of the Dufour coefficient from 0 to 0.8 improves heat and mass transfer in the SGSP. Therefore, the amount of the thermal energy accumulated in the storage zone is reduced by about 5.56 %. In addition, the heat losses through the SGSP free surface are improved by around 8.53 %.

In this study, the bifurcation phenomenon and the existence of dual asymmetry solutions of double-diffusive convection driven by an internal thermal and solutal source in a horizontal cavity have been investigated systematically. The problem is solved by the SIMPLE algorithm with the QUICK scheme in a non-uniform staggered grid system. The Rayleigh numbers, 200 ≤ Ra ≤ 106, buoyancy ratios, −20 ≤ Nc ≤ 20, Soret numbers, 0 ≤ Sr ≤ 0.8, and Dufour numbers, 0 ≤ Df ≤ 0.8, are considered in this study. Different streamlines for the onset and evolution of static bifurcation are tracked. The paper aims to determine the critical Rayleigh numbers and buoyancy ratios for the onset of symmetry-breaking through bifurcation diagrams based on the vortex length. The results indicate that increasing buoyancy can destabilize the symmetric system. The strong couple diffusion effect delays the onset of bifurcation flow. A pair of asymmetric modes can be obtained under different initial conditions.

The effect of cooperating and opposite buoyancy forces on the flow structure and the heat and mass transfer rates is numerically investigated in a horizontal annular space of radius ratio R = 2, filled with a porous medium saturated by a binary fluid. Uniform and constant temperatures and concentrations are imposed along the active walls. The steady-state solutions have been obtained using the discretization of the governing equations with the Centered Finite Difference method based on the ADI scheme. The influence of the dimensionless thermosolutal parameters, namely Darcy-Rayleigh numbe, Ra, Lewis number, Le, and buoyancy ratio, N , is investigated. The study is focused on the effect of Ra and Le on the steady-state solution under the cooperating (N = 2) and opposite (N = -2) buoyancy forces cases. The increase in Rayleigh number in the opposite case results in a full development of the convection and gives rise to multicellular flow structures. The critical Rayleigh number values corresponding to the onset of this flow pattern are determined for a large range of Lewis number values by using two initial conditions types. On the other hand, the unicellular flow dominates the cooperating case whatever the Darcy-Rayleigh and Lewis numbers values. The heat and solutal transfer behaviors are also considered.

Thermosolutal convection inevitably occurs during the solidification of alloys owing to the nonuniform distribution of temperature and/or solute concentration, and this can drastically alter the resulting solidification microstructures. In this study, we present a large-scale simulation scheme for the phase-field lattice Boltzmann model, which can express dendrite growth upon considering the solute, heat transport, and liquid flow. A multiple mesh and time step method was employed to reduce computational costs, where different mesh sizes and time steps are used to solve the phase-field equation, the advection–diffusion equations of heat and solute, and the lattice Boltzmann equations for fluid flow. Furthermore, we implemented parallel computations using multiple graphics processing units (GPUs) to accelerate the large-scale simulation. Through the application of the multiple mesh and time step method, the computation was accelerated by approximately one hundred times compared to the case using a constant mesh and time step for all equations. Moreover, we confirmed that the developed parallel-GPU computation combined with the multiple mesh and time step method could achieve good acceleration and scaling through increasing the number of GPUs. We also confirmed that the developed method could simulate multiple dendrite growth with thermosolutal convection.

International audience; The present work deals with an analytical solution based on the parallel flow assumption obtained in the case of a vertical porous layer heated and salted from the long vertical sides with uniform fluxes of heat and mass, respectively. The study concerns a specific case for which the buoyancy ratio and the separation coefficient are identical. For this particular situation, the external mass flux is compensated by the Soret effect, which leads to zero concentration gradient on the vertical walls. The problem is first analyzed by solving numerically the full governing equations and the aspect ratio required to satisfy numerically the parallel flow conditions is determined. Analytical solutions for the pseudo-conductive and boundary layer regimes are proposed and discussed. The N-Le plane is divided into regions with specific behaviors and the results obtained are presented in terms of boundary layer thickness, heat transfer (Nusselt number), and mass transfer (Sherwood number) versus the main governing parameters.

In this paper, an analytical study is reported on double-diffusive natural convection in a shallow porous cavity saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. A Cartesian coordinate system is chosen with the x- and y- axes at the geometrical center of the cavity and the y’-axis vertically upward. The top and bottom horizontal boundaries are subject to constant heat (q) and mass (j) fluxes. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. The permeabilities along the two principal axes of the porous matrix are denoted by K1 and K2. The anisotropy of the porous layer is characterized by the permeability ratio K*=K1/K2 and the orientation angle φ, defined as the angle between the horizontal direction and the principal axis with the permeability K2. The viscous dissipations are negligible. Based on parallel flow approximation theory, the problem is solved analytically, in the limit of a thin layer and documented the effects of the physical parameters describing this investigation. Solutions for the flow fields, Nusselt and Sherwood numbers are obtained explicitly in terms of the governing parameters of the problem.

The paper is concerned with designing an experimental scheme for studying convection of moist air under conditions closely approximating the atmospheric conditions. Detailed numerical estimates, necessary conditions and dimensionless gas-dynamic parameters characteristic of the problem of dry and moist air convection are presented and analyzed. The distinctive features of convection of dry and wet air at constant pressure caused by changes in the concentration of water vapor as a result of its evaporation (condensation) are discussed. The effect of water vapor concentration on the convective instability of moist air is analyzed in the context of solutal convection, characterized by the Rayleigh concentration number. The obtained numerical estimates are used to demonstrate the possibility of differentiating and comparing between the processes of convective heat and mass transfer in humid and dry air under laboratory conditions. In future, this will allow researchers to obtain experimental data on the influence of the water-vapor phase transition on the intensity of convective motion in moist air. The structure and detailed technical characteristics of the constructed experimental setup designed for studying convection in moist air in the temperature range from 10 to 30 C are described.

In the present study analysis has been performed for thermosolutal convection in a fluid-porous composite medium, consisting of a fluid-saturated porous medium followed by an overlaying clean medium. The fluid-porous composite medium is subjected to both a horizontal solutal and a thermal gradient. Top and bottom walls of the fluid-porous composite medium are assumed to be impermeable and adiabatic. The Darcy-Brinkman-Forchheimer model is used to study the flow through the fluid-porous composite medium. A single domain approach is taken into consideration for numerical simulation. The solution is done by control volume integration. A comprehensive analysis has been performed for various pertinent parameters to delineate their behavior. Results of the transport phenomenon have been provided in graphical and tabular form, for the complete understanding of the complex phenomenon. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21048

We use the energy method to obtain the non-linear stability threshold for thermosolutal convection porous media of Brinkman type with reaction. The obtained non-linear boundaries for different values of the reaction terms are compared with the relevant linear instability boundaries obtained by Wang and Tan (Phys Lett A 373:776–780, 2009). Using the energy theory we obtain the non-linear stability threshold below which the solution is globally stable. The compound matrix numerical technique is implemented to solve the associated system of equations with the corresponding boundary conditions. Two systems are investigated, the heated below salted above case and the heated below salted below case. The effect of the reaction terms and Brinkman term on the Rayleigh number is discussed and presented graphically.

Thermosolutal convection in a square cavity filled with Boussinesq fluid is numerically investigated. The cavity is heated along the active walls whereas the two other walls of the cavity are adiabatic and insulated. Entropy gen- eration due to heat and mass transfer, fluid friction and magnetic effect has been determined in transient state for laminar flow by solving numerically the continuity, momentum energy and mass balance equations, using a Control Volume Fi- nite-Element Method. The structure of the studied flows depends on six dimensionless parameters which are the Prandtl number, the thermal Grashof number, the buoyancy ratio, the Lewis number, the Hartman number and the inclination angle of the magnetic field. Results show that the magnetic field parameter has reducing the flow in the cavity and this lead to a decrease of entropy generation, Temperature decreases with increasing the value of the magnetic field parameter. The av- erage Nusselt number increases with the Prandtl number and, in particular, its effect is more evident at high Hartmann numbers.

In this paper, the thermosolutal convection in compressible Walters' (model B′) elastico-viscous fluid permeated with suspended particles in a porous medium is considered. For the porous medium, the Brinkman model is employed. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the medium permeability, suspended particles, gravity field and viscoelasticity introduce oscillatory modes. For stationary convection, it is observed that the Darcy number and stable solute gradient have stabilizing effects whereas the suspended particles and medium permeability has destabilizing effects on the system. The effects of Darcy number, stable solute gradient, suspended particles and medium permeability has also been shown graphically.

Transient thermosolutal convection of Boussinesq fluid with moving heating and cooling blocks placed at the bottom wall in a square cavity was numerically investigated subject to vertical gradient of thermosolutal conditions at the top or bottom walls. With the progress in time, due to the interactions among thermal and solutal buoyancy and stratification together with forced block movement, a complex flow structure was formed in the cavity as well as the corresponding transient heat and mass transports. At steady state, the absolute values of average Nusselt and Sherwood numbers remained almost constant with time as an increase of the velocity of the blocks. Furthermore, the cooling phase took more time than heating phase to reach the steady state, and time to reach the steady state decreased as an increase in the moving velocity of the block.

In this study, the linear stability analysis is used to determine the onset of thermosolutal convection in fluids confined in rotating annular Hele-Shaw cell. The fluid layer is submitted to radial gradients of temperature and concentration. The effects of both Coriolis force and curvature parameter on the stationary and oscillatory convection are investigated when the Prandtl number is of the order of unity or larger than unity.

PurposeThe motivation for this work is to establish a model that not only includes the main factors resulting in macrosegregation but also retains simplicity and consistency for the sake of potential application in casting practice.Design/methodology/approachA mathematical model for the numerical simulation of thermosolutal convection and macrosegregation in the solidification of multicomponent alloys is developed, in which the coupled macroscopic mass, momentum, energy and species conservation equations are solved. The conservation equations are discretized by using the control volume‐based finite difference method, in which an up‐wind scheme is adopted to deal with the convection term. The alternative direction implicit procedure and a line‐by‐line solver, based on the tri‐diagonal matrix algorithm, are employed to iteratively solve the algebraic equations. The velocity‐pressure coupling is handled by using the SIMPLE algorithm.FindingsBased on the present study, the liquid flow near the dendritic front is believed to play an important role in large‐scale transport of the solute species. The numerical or experimental results in the literatures on the formation of channel segregation, especially those about the location of the initial flow as well as the morphology of the liquidus front, are well supported by the present investigation.Research limitations/implicationsThe modelling is limited to dealing with the thermosolutal convection of two‐dimensional cases. More complicated phenomena (e.g. crystal movement) and 3D geometry should be considered in future research.Practical implicationsThe present model can be used to analyze the effects of process parameters on macrosegregation and, with further development, could be applied as a useful tool in casting practice.Originality/valueThe numerical simulation demonstrates the capability of the model to simulate the thermosolutal convection and macrosegregation in alloy solidification. It also shows that the present model has good application potential in the prediction and control of channel segregation.

Motivated by studies of the cylinder wake, in which the vortex-shedding frequency can be obtained from the mean flow, we study thermosolutal convection driven by opposing thermal and solutal gradients. In the archetypal two-dimensional geometry with horizontally periodic and vertical no-slip boundary conditions, branches of traveling waves and standing waves are created simultaneously by a Hopf bifurcation. Consistent with similar analyses performed on the cylinder wake, we find that the traveling waves of thermosolutal convection have the RZIF property, meaning that linearization about the mean fields of the traveling waves yields an eigenvalue whose real part is almost zero and whose imaginary part corresponds very closely to the nonlinear frequency. In marked contrast, linearization about the mean field of the standing waves yields neither zero growth nor the nonlinear frequency. It is shown that this difference can be attributed to the fact that the temporal power spectrum for the traveling waves is peaked, while that of the standing waves is broad. We give a general demonstration that the frequency of any quasi-monochromatic oscillation can be predicted from its temporal mean.

The present study addresses the interaction effect of participating media radiation with the onset of double-diffusive convection in a square enclosure. Vertical walls are imposed with constant temperature and concentration, and the horizontal walls are impermeable and adiabatic. The boundaries of the enclosure are diffuse-gray, and the enclosed fluid isotropically scatters, emits, and absorbs thermal radiation. Numerical simulations have been performed for both aiding and opposing buoyancy conditions. The buoyancy ratio has been varied to simulate the effect of buoyancy driven flow and compositionally driven flow, along with transition of flow between the above. Optical properties like opacity of medium, scattering albedo, Planck number, and wall emissivity have been varied to depict their influence on flow and heat transfer. The modified MAC method is used for the solution of convective transport equations. Gradient dependent consistent hybrid upwind scheme of second order (GDCHUSSO) is used for the discretization of the convective terms. The discrete ordinate method, with S8 approximation, is used to solve the radiative transport equation. The parametric results are provided in graphical and tabular form. Flow lines, isotherms, and isoconcentration contour maps are provided to bring clarity in the understanding of the momentum, heat, and solute transport phenomenon. The stabilization effect of thermal radiation at critical buoyancy ratio for buoyancy opposed flow is observed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21108

The effect of an anisotropic inertia coefficient in the Darcy equations is studied. How such anisotropy affects the critical Rayleigh number for the onset of convective motion in a porous layer with thermal and solutal effects is analyzed quantitatively. The mathematical analyses employed involve both linear instability techniques and the energy method for nonlinear stability.

This investigation presents numerical treatment of governing equations pertaining to thermosolutal flow within an annulus and an application of a model describing the important physical phenomenon as found in muffle furnace. The inner side of the annulus is exposed to high temperature and high solute concentration while the outer side of the annulus is maintained at low temperature and low solute concentration. Darcy-Brinkman-Forchheimer model is used to study the flow, heat and solute transfer in a non-Darcian saturated porous media. The solution is obtained upon application of control volume integration. Modified MAC method is used for the numerical solution of governing equations. Gradient dependent consistent hybrid upwind scheme of second order (GDCHUSSO) is used for discretization of the convective terms. The parameters such as Rayleigh-Darcy number, Darcy number, buoyancy ratio and width ratio, that govern the flow phenomenon have been identified and their effects are critically examined. The fluid flow pattern in the annular space and the associated heat and mass transfer are conceptualized from the obtained isoconcentration, isotherm and flowline contour maps.

Thermosolutal convection and macrosegregation formation during the solidification of steel ingots are numerically simulated in three dimensions. The simulation is based on a fully coupled model for mass, momentum, energy, and species conservation equations. The interdendritic flow in the mushy zone is governed by Darcy's law, and the permeability term is discretized using an interpolated liquid fraction method. The numerical results for a benchmark test of macrosegregation in a Pb-Sn alloy are compared with experimental data taken from the literature. The present model is applied to simulate the solidification of industrial steel ingots. Preliminary predictions are obtained, including the positive segregation in the hot top, and the conically shaped negative segregation zone at the bottom of the ingot. The predicted variation of the segregation ratio in carbon along the vertical centreline of an ingot is compared with measurements, and generally good agreement is observed. Future attention should be paid to the precision of prediction by considering complex solidification issues, such as the sedimentation of free equiaxed grains and the formation of shrinkage cavity.

The present study analyzes numerically the mixed thermosolutal convection in a vertical partly porous annular cavity. The fluid motion in the porous matrix is described by the generalized Darcy-Brinkman-Forchheimer model. The results show that the composite porous layer tends to improve the heat transfer and moderately reduce the transfer of aqueous solution compared to the case of a homogeneous porous partition. This conclusion is valid for all characteristic values (Da, ) or the flow modes set up in the porous matrix.

This study attempts to examine convection caused by the combined effects of temperature and concentration gradients in an annular enclosure with steps. An experimental study of thermosolutal convection of a CuSO4+ H2SO4+ H2O solution in a horizontal annular enclosure with steps is conducted using an electrochemical system that enables either opposing or cooperating in temperature and concentration gradients to be imposed. The shadowgraph recording technique is utilized to visualize and analyze the flow field phenomenon. The large difference between the thermal and solutal diffusion rates causes the flow to exhibit double-diffusive characteristics. In both cooperating and opposing cases, some finger-type flow can be visualized in the layered flow structure. Furthermore, Sh (mass transfer rate) increased with increasing Grt for fixed Grm and S*. Sh is larger in the cooperating case than in the opposing case for given Grt and Grm values.

On the basis of Brinkman model, the onset of double-diffusive (thermosolutal) convection with a reaction term in a horizontal sparsely packed porous media is studied using the normal mode analysis. The effects of Brinkman term, the reaction term, the normalized porosity e and Lewis number Le on the Rayleigh number for stationary and oscillatory case are presented graphically. The Darcy number destabilize the system in case of both stationary and oscillatory mode. The effects of Lewis number and reaction term depend on the value of the values of solutal Rayleigh number. Furthermore, some results of Darcy model can be recovered in limit cases.

In this article, we extend the analysis of Diaz and Brevdo (J. Fluid Mech. 681:567–596, 2011) of the absolute/convective instability dichotomy at the onset of convection in a saturated porous layer with either horizontal or vertical salinity and inclined temperature gradients to studying the influence of the Soret effect on the dichotomy in a similar model. Only longitudinal modes are considered. We treat first normal modes and analyze the influence of the Soret effect on the critical values of the vertical thermal Rayleigh number, R v, wavenumber, l, and frequency, ω, for a variety of values of the horizontal thermal Rayleigh number R h, and the vertical salinity Rayleigh number, S v. Our results for normal modes agree well with relevant results of Narayana et al. (J. Fluid Mech. 612:1–19, 2008) obtained for a similar model in a different context. In the computations, we use a high-precision pseudo-spectral Chebyshev-collocation method. Further, we apply the formalism of absolute and convective instabilities and compute the group velocity of the unstable wavepacket emerging in a marginally unstable state to determine the nature of the instability at the onset of convection. The influence of the Soret effect on the absolute/convective instability dichotomy present in the model is treated by considering the destabilization for seven values of the Soret number: S r = −1, −0.5, −0.1, 0, 0.1, 0.5, 1, for all the parameter cases in the treatment of normal modes.

PurposeThe purpose of this paper is to present a numerical and an analytical study of the thermohaline convection with Soret effect in a square enclosure filled with a binary fluid mixture.Design/methodology/approachThe horizontal boundaries of the enclosure are impermeable and heated from below while its vertical walls are assumed to be adiabatic and impermeable. The Navier‐Stokes equations under the Boussinesq‐Oberbeck approximation are solved numerically. The results are given for different values of the separation ratio. The critical Rayleigh number at the onset of convection is determined analytically and numerically. The Hopf frequency at the onset of convection is obtained.FindingsThe existence of two stable stationary bifurcation branches is illustrated. Furthermore, it is shown that the existence of stable traveling waves in the transition from one branch to the other depends on the value of the separation ratio. For some values of Rayleigh number, asymmetric flows are observed. A good agreement is found between the numerical solution and analytical analysis.Originality/valueThe present work is the first to consider thermosolutal convection with Soret effect in a square enclosure.

A theoretical and numerical study of the effect of thermodiffusion on the stability of a gradient layer is presented. It intends to clarify the mechanisms of fluid dynamics and the processes which occur in a salinity gradient solar pond. A mathematical modelling is developed to describe the thermodiffusion contribution on the solar pond where thermal, radiative, and massive fluxes are coupled in the double diffusion. More realistic boundary conditions for temperature and concentration profiles are used. Our results are compared with those obtained experimentally by authors without extracting the heat flux from the storage zone. We have considered the stability analysis of the equilibrium solution. We assumed that the perturbation of quantities such as velocity, temperature, and concentration are infinitesimal. Linearized equations satisfying appropriate prescribed boundary conditions are then obtained and expanded into polynomials form. The Galerkin method along with a symbolic algebra code (Maple) are used to solve these equations. The effect of the separation coefficient y is analyzed in the positive and negative case. We have also numerically compared the critical Rayleigh numbers for the onset of convection with those obtained by the linear stability analysis for Le = 100, µa = 0.8, and f = 0.5.

The thermosolutal instability of couple-stress fluid in the presence of uniform vertical rotation is considered. Following the linearized stability theory and normal mode analysis, the dispersion is obtained. For the case of stationary convection, the stable solute gradient and rotation have stabilizing effects on the system, whereas the couple-stress has both stabilizing and destabilizing effects. The dispersion relation is also analyzed numerically. The stable solute gradient and the rotation introduce oscillatory modes in the system, which did not occur in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

A new combined numerical model of the BFC (Boundary Fitted Coordinate) system and moving boundary technique has been developed for the analysis of macrosegregation phenomena during alloy solidification. This new model'is applied to a Pb-Sn alloy solidification process in a two-dimensional confined rectangular mold to study the effects of thermosolutal convection on the formation of macrosegregation. The basic equations are solved using the Continuum Model theory with the SIMPLE algorithm adopting the new combined method of time-dependent and boundary-fitted coordinate system to treat the moving (possibly irregular shaped) interface. Not only the effect of the buoyancy-driven flow due to temperature and liquid composition gradients but also the effects of the cooling condition, magnitude of gravity, and interaction between liquid and mushy zones on the macrosegregation are examined using the new combined model.

The effect of uniform magnetic field on the Dufour-driven thermosolutal convection of an electrically conducting fluid completely confined in an arbitrary region bounded by rigid walls is considered. Some general qualitative results concerning the character of marginal state, stability of oscillatory motions and limitations on the oscillatory motions of growing amplitude, are derived. The results for the horizontal layer geometry in the present case follow as a consequence.

The impact of thermosolutal convection during directional solidification is explored via results of numerical investigations. Results from fully transient numerical simulations of directional solidification in a differentially heated cavity under terrestrial conditions and Bridgman cytstal growth in space are discussed. The pivowl role ofboth thermaland solutal convection in the solidifaction process is illustrated by examining these two cases. In particular, radical and longitudinal macrosegregation resulting from this thermosolutal convection is discussed.

Double diffusive natural convection within a vertical porous enclosure with localized heating and salting from one side is numerically studied by the finite element based finite volume method. In the formulation of the problem, use is made of the Darcy model, which allows the slip boundary condition on a solid wall to be satisfied. Comparisons with benchmark solutions for natural convection in fluid saturated porous enclosures are first presented to validate the code. Following that, an extensive series of numerical simulations is conducted in the range of −55 ⩽ N ⩽ + 55 and 0.125 ⩽ L ⩽ 0.875, where N and L are the buoyancy ratio and the element location, respectively. Streamlines, heatlines, masslines, isotherms and iso-concentrations in the system are produced to illustrate the flow structure transition from solutal dominated opposing to thermal dominated and solutal dominated aiding flows, respectively. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting element.

An experimental study of thermosolutal convection in an inclined rectangular enclosure with a partition is presented in this article. Aspect ratio, partition ratio, and inclination angle were kept constant at Ar =0.5, Ap = 0.25 and φ = 30°, respectively. The convective flow is generated by both inclined temperature and concentration gradients under limiting current condition. Both the thermal and solutal buoyancies, which either cooperated or opposed one another, were induced from the copper plates. The temperature gradient was maintained and controlled using two separate constant temperature baths that circulated heated or cooled water through a heat exchanger. We used copper sulphate-sulfuric acid solution as both the working fluid and the electrolyte. An electrochemical method based on a diffusion-controlled electrode reaction was employed to create the concentration gradient. We used the shadowgraph recording technique to visualize and analyze the flow field phenomenon. Thermal Grashof numbers ranging from 8.16 × 105 to 16.32 × 105 and a solutal Grashof number Grm = 4.36 × 106 were investigated. It is demonstrated that the mass transfer rate increases with the increasing thermal Grashof numbers within our experimental ranges. Multilayer structures are found in the cooperating case or the opposing case.

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.