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Different from other alloys, the observation in this work on the dendritic mushy zone shows that the freckles are formed in two different regions before and after peritectic reaction in directional solidification of Sn–Ni peritectic alloys. In addition, the experimental results demonstrate that the dendritic morphology is influenced by the temperature gradient zone melting and Gibbs–Thomson effects. A new Rayleigh number (RaP) is proposed in consideration of both effects and peritectic reaction. The prediction of RaP confirms the freckle formation in two regions during peritectic solidification. Besides, heavier thermosolutal convection in samples with larger diameter is also demonstrated.

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 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.

Embedded the thermal and solutal buoyancy into the momentum conservation equation as an additional force term using the Boussinesq approximation, a 2D CA-FVM model is extended to simulate the dendritic growth with thermosolutal convection. The model is firstly validated by comparison of numerical predictions with the benchmark test of Rayleigh – Benard convection and the analytical solutions of the stagnant film model for the free dendritic growth with thermosolutal convection, and good agreements between the numerical results with analytical solutions are obtained. Later, numerical simulations for both the equiaxed and columnar dendritic growth of Fe-0.82wt%C binary alloy with thermosolutal convection are performed. The results show that, for the equiaxed dendritic growth in an undercooled melt, the dendrite tip growth rapidly decreases from the high velocity to a relative low steady-state value. With the further growth of dendrite, the thermosolutal convection induced by the solute rejection and latent heat release is enhanced and four vortexes are developed between the dendrite arms. Thus, the asymmetries of the dendrite morphology, temperature and solute profiles are intensified. For the columnar dendritic growth with thermosolutal convection under the unidirectional solidification process, the thermosolutal convection transports the rejected solute downward and makes the solute enrich at the interdendritic region. The thermosolutal convection facilitates the upstream dendritic growth, but inhibits the downstream dendritic growth. Moreover, with the increase of deflection angle of gravity, the advection on the top region and the clock-wise vortex flow at the interdendritic region intensified, and finally the columnar dendrite morphology becomes more asymmetrical.

Using a perturbation method, we solve asymptotically the nonlinear partial differential equations that govern double-diffusive convection (with heat and solute diffusing) in a two-dimensional rectangular domain near a critical point in parameter space where the linearized operator has a quadruple-zero eigenvalue. The asymptotic solution near this codimension-four point is found to depend on two slow-time-dependent amplitudes governed by two nonlinearly-coupled Van der Pol–Duffing equations. Through numerical approximation of the 3-dimensional Poincare map in the four-dimensional state space of the amplitude equations, we detect and analyze the bifurcations of the amplitude equations as the thermal Rayleigh number, R T , is increased (for R S ≪ R T , the solute Rayleigh number) with all other parameters fixed. The bifurcations observed include: Hopf, pitchfork and Neimark–Sacker bifurcations of limit cycles, symmetric and asymmetric saddle–node bifurcations of 2-tori, and reverse torus-doubling cascades. In addition, chaotic solutions are found numerically to emerge via two different types of routes: (1) a route involving a homoclinic explosion in the Poincare map and; (2) type-I intermittency routes near saddle–node bifurcations of 2-tori. The homoclinic explosion occurs when two unstable 2-tori form homoclinic connections with a saddle limit cycle, thereby creating a homoclinic butterfly in the Poincare map that leads to a discrete Lorenz-like attractor.

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 present study simulates the 3D unsteady double-diffusive natural convection subject to opposing thermal and solutal buoyancy forces (N

The unsteady double-diffusive natural convection flow in a rectangular enclosure filled with soft rocks which are subjected to humid air, including water vapor absorption and thermoelasticity, is studied numerically. The high order compact finite difference schemes are adopted for better simulation of this problem, and a Darcy–Brinkman–Forchheimer extended model combined with the absorption and thermoelasticity effects is introduced. The effects of the thermal and solutal Rayleigh numbers, hygroscopicity, Darcy numbers and thermoelasticity on the flow are investigated in detail. Results are presented in the form of streamlines and isolines of temperature and mass fraction as well as the plots of average Nusselt and Sherwood numbers over the walls under different conditions. The flow structure develops from conduction-dominated to steady convection-dominated as increasing Rayleigh number or increasing buoyancy ratio as well as increasing Darcy numbers. The thermoelasticity effects of soft rocks play an important role in the analysis of thermal convection flow by the change of temperature and permeability, while the water vapor absorption effects may have a slight effect on the flow in the beginning and vanish with the absorption effects becoming weak. Nevertheless, the effect may significant reduce the mechanical strength properties of soft rocks.

Thermosolutal convection with reaction in a porous media of Darcy type is studied using the energy method. The effect of the reaction terms on the temperature and salt Rayleigh numbers are presented graphically. Furthermore, nonlinear energy stability boundaries for different values of the reaction terms are compared with the linear instability boundaries obtained by Pritchard and Richardson (2007).

A stability analysis is carried out to investigate the onset of thermosolutal convection in a horizontal porous layer when the solid and fluid phases are not in a local thermal equilibrium, and the solubility of the dissolved component depends on temperature. To study how the reaction and thermal non-equilibrium affect the double-diffusive convection, the effects of scaled inter-phase heat transfer coefficient H and dimensionless reaction rate k on thermosolutal convection are discussed . The critical Rayleigh number and the corresponding wave number for the stability and overstability convections are obtained. Specially, asymptotic analysis for both small and large values of H and k is presented, and the corresponding asymptotic solutions are compared with numerical results. At last, a nonlinear stability analysis is presented to study how H and k affect the Nusselt number.

The mechanism for thermosolutal convection and the coupling effects of flow, temperature and solute fields during the vertical Bridgman growth of Hg1−xCdxTe single crystals have been numerically analyzed. The calculations take into account the thermophysical properties and their dependence on temperature and composition. The results show that there are two main thermal convection cells in the melt caused by two temperature gradients during the growth of Hg1−xCdxTe single crystals. The stabilizing axial solute gradient in the melt will significantly damp the thermal convection cells when the absolute value of the solute Rayleigh number is close to the value of the thermal Rayleigh number. When there is a large solute gradient in the melt, the thermosolutal convection will become unstable, and the upper flow cell will evolve into a two-cell flow pattern. During the growth of Hg1−xCdxTe single crystals, the radial solute segregation in the melt develops non-monotonically with two minima values. Thus, the methods that solely aim at either damping or enhancing the thermosolutal convection are not always able to improve the radial solute segregation.

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 M"1 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.

Combined effect of thermodiffusion and lateral heating on double diffusive natural convection in a horizontal porous layer, filled with a binary fluid and subjected to uniform fluxes of heat and mass on its long sides, is studied analytically and numerically. The short sides of the layer are impermeable to mass transfer and exposed to a perturbating constant heat flux. The governing parameters of problem under study are the Rayleigh number R T , the Lewis number Le , the buoyancy ratio N , the separation parameter φ , the ratio of the horizontal to vertical heat flux a and the aspect ratio A r of the layer. The thermodiffusion effect on the multiplicity of solutions is studied. It is demonstrated that the φ – N plane can be divided into four regions presenting different behaviors. The heat transfer is found to be considerably affected by the Soret effect.

Thermosolutal convection during vertical Bridgman directional solidification of Ga 1-x In x Sb alloys has been studied by numerical simulation. The transient analysis of heat, momentum and species transport has been performed by using the finite element code FIDAP R . In the case of vertical Bridgman configuration, the thermal convection is driven by the radial temperature gradients. The solute (InSb) rejected at the solid-liquid interface, which is heavier than the GaSb component, damps the thermally driven convection. The solutal effect on the melt convection has been analyzed for low (x = 0.01) and high (x = 0.1) doped Ga 1-x In x Sb alloys. It is found that the damping effect is negligible for Ga 0.99 In 0.01 Sb alloy grown at low pulling rates (V = 1 μm/s), but cannot be neglected if the pulling rate is increased. In the case of concentrated alloys, the low level of convection intensity leads to an increase of radial segregation and interface curvature during the whole growth process as also shown by experiments. The effect of solutal buoyancy force on the melt convection is analyzed for the horizontal Bridgman configuration under microgravity conditions. An inverse but lower solutal effect on the melt convection, as compared with vertical Bridgman arrangement, is observed. The results are in good agreement with the experimental data, and show that convective transport can be observed even for low (2 x 10 -6 g 0 ) residual gravity levels.

The onset of thermosolutal convection due to thermal diffusion in a fluid saturated isotropic porous layer, subject to a gravity gradient is investigated using the Galerkin technique. Results reveal that the Soret parameter affects the pattern of convection only when its magnitude is large, both in the presence and absence of variable gravity field.

This article investigates the effect of thermosolutal convection in liquid phase electroepitaxial (LPEE) growth of GaAs through a two-dimensional numerical simulation model. The model accounts for heat transfer and electric current distribution with Peltier and Joule effects, diffusive and convective mass transport including the effect of electromigration, and fluid flow coupled with temperature and concentration fields. Simulations are performed for two growth cell configurations and the results are analyzed to determine growth rates, substrate shape evolution, and relative contributions of Peltier cooling and electromigration. The simulations predict and help explain a number of experimentally observed features which previous diffusion-based models fail to reproduce. In general, electromigration is found to be the dominant growth mechanism, but the contribution of Peltier cooling to the overall growth rate is found to be significantly enhanced by thermosolutal convection in the solution, and Peltier cooling can in fact become the dominant growth mechanism for certain growth conditions and growth cell configurations. The overall growth rate is found to increase with increasing furnace temperature and applied electric current density. The thermosolutal convection model predicts increased non-uniformity of the grown layers compared with the pure-diffusion model. The shape of the grown layers is also shown to be very sensitive to changes in growth cell configurations.

The purpose of this paper is to investigate the influence of the Soret effect on natural convection in a vertical cavity filled with a binary liquid. The two vertical walls of the cavity are subject to constant fluxes of heat while the two horizontal ones are adiabatic. The analysis deals with the particular situation where the buoyancy forces induced by the thermal and solutal effects are opposing each other and of equal intensity. In the limit of tall enclosures an analytical model is derived on the basis of a parallel flow approximation. The study is completed by a numerical solution of the full governing equations.

A numerical study is carried out on double-diffusive natural convection within a vertical circular porous annulus. Motions are driven by the externally applied constant temperature and concentration differences imposed across the vertical walls of the enclosure. In the formulation of the problem, use is made of the Brinkman extended Darcy model which allows the no-slip boundary condition on a solid wall, to be satisfied. The flow is assumed to be laminar and two dimensional. The density variation is taken into account by the Boussinesq approximation. The control-volume approach is used for solving the governing equations. Solutions for the flow fields, temperature and concentration distributions and Nusselt, Nui and Sherwood, Shi numbers are obtained in terms of the governing parameters of the problem. The effect of both the Darcy number, Da, and the radius ratio, κ, on Nui and Shi is found to be significant. Results for a pure viscous fluid and a Darcy (densely packed) porous medium emerge from the present model as limiting cases.

The onset of double diffusive convective flows in an inclined fluid layer, when constant fluxes of heat and mass are applied on the two oposing boundaries of the layer, is investigated. The case of equal and opposing buoyancy forces is considered. A numerical linear stability theory is used to determine the critical Rayleigh number for the onset of convection. The existence of a subcritical Rayleigh number, for the onset of finite amplitude convection, is demonstrated on the basis of the parallel flow approximation.

Two dimensional, thermosolutal convection in molten Pb-Sn housed within a square enclosure, is simulated using a spectral method. The predictions illustrate two regimes of liquid convection which develop in response to simultaneous horizontal temperature and species concentration gradients applied to the system. Sherwood numbers for the high Schmidt number fluid are quite high, and change markedly depending upon the regime of operation. Heat transfer rates are only moderately affected by convection due to the low Prandtl number of the melt. The predictions at relatively large Rayleigh number and buoyancy ratio display highly oscillatory behavior in a manner consistent with previous experimental observations.

The rate of layer growth during thermosolutal convection in a square enclosure is studied both experimentally and analytically. The thermosolutal convection is induced by the combined thermal and solutal buoyancies which either augment or oppose each other. The layer growth process is attributable to the vertical solutal boundary flow which accumulates and stratifies along the horizontal wall. A mathematical model, based on the filling box process used to predict the layer growth rate, is developed. The solutal boundary flow that enters or exits the stratified layer is calculated by using an integral solution for natural convection due to combined thermal and solutal buoyancies along a vertical plate. Comparison of layer growth rate between the prediction and the data is made, and the agreement is excellent if the actual thickness of the solutal boundary layer flow at the inlet and the outlet of the stratified layer can be accurately determined. The actual thickness of the solutal boundary layer flow at the inlet and the outlet is found to increase with increasing buoyancy ratio.

Numerical solutions are presented for the problem of thermosolutal convection in a rectangular enclosure subjected to simultaneous heating of the bottom and sidewalls. A steady model based on primitive variables and an unsteady model solved using a high-accuracy numerical scheme are used to study the problem. Effects of the Lewis number, buoyancy ratio, aspect ratio and the Rayleigh number on flow and heat and mass transfer rates are studied. Details of oscillatory solutions and flow bifurcations are presented.

This paper reports the numerical simulations of double diffusive natural convection flows in a binary fluid contained in a two-dimensional enclosure, with imposed horizontal temperature and concentration differences between the vertical walls. The analysis concerns the influence of the different parameters governing the problem in the heat transfer characteristics and on the flow structure. The study is focused on steady-state solutions in the cooperating situation. At high Lewis numbers, numerical simulations show that heat transfer decreases with increasing buoyancy ratios. This phenemenon is analysed on the basis of the flow structure, and a scale analysis is provided to estimate the decrease in heat transfer. Then, the influence of the parameters on the formation of a multicellular flow structure is discussed.

This paper reports the analytical and numerical results on double diffusive natural convection in a binary fluid contained in a two-dimensional enclosure where horizontal temperature and concentration differences are specified. A numerical code, based on a finite volume procedure, and a scaling law approach are used to analyse the influence of the different parameters which characterize those thermosolutal flows: in this first paper, the mass transfer problem is studied in the steady-state. A general mass transfer correlation is proposed, which is valid over a wide range of parameters.

This paper focuses on the effect of natural convection on the accuracy of diffusion coefficient measurements in concentrated liquid alloys. This convective effect is modelled using the concept of effective diffusivity, introduced in a former work for the case of dilute systems. Our computer simulations support the validity of this approach and show that it is very difficult in practice to reach conditions of negligible convective solute transport. The possibility of realizing the measurements of diffusion coefficients in microgravity is also discussed.

We consider the dynamical system associated with two-dimensional thermosolutal convection and show the existence of a maximal attractor. We derive estimates on the Lyapunov exponents, the Hausdorff and fractal dimension of the attractor.

Observations of the macroscopic shape of the solid-liquid interface and radial solute segregation have been carried out on quenched Pb-30 wt%TI alloys which were grown upwards, that is, for the case for which thermosolutal convection may take place. The solidification front exhibits a structure which is composed of solid plateaux separated by liquid channels and whose amplitude presents a maximum when plotted versus growth rate, which suggests a concomitant maximum in the level of thermosolutal convection. The convective flow adjacent to the solidification front has then been deduced.

The influence of laminar thermosolutal convection on solute segregation and heat transfer in the floating zone crystal growth of a dilute binary alloy is considered. The solute gradient is assumed to be destabilizing, and the thermal gradient is assumed perpendicular to it. The evolution of non-linear states from the critical points predicted by linear theory is studied. For vanishing thermal Rayleigh numbers, two solutions, corresponding to upflow and downflow at the meniscus, are obtained. The presence of side heating establishes upflow as the preferential direction; the downflow solution is found to persist for low thermal Rayleigh numbers. Flow and heat transfer for high thermal Rayleigh numbers are also computed.

When a solution containing a non-linear profile of solute concentration is heated from below, convection can occur in layers. Observations of this phenomenon are presented, and these are compared with calculations based on a simple model. It is concluded that the model contains the essential features of the process.

Corrigendum to this publication: http://hal.archives-ouvertes.fr/hal-00528029; International audience; This call describes a numerical comparison exercise for the simulation of ingot solidification of binary metallic alloys. Two main steps are proposed, which may be treated independently: 1. The simulation of the full solidification process. First a specified 'minimal' solidification model is used and the contributors are provided with the corresponding sets of equations. The objective is to verify the agreement of the numerical solutions obtained by different contributors. Then different physical solidification models may be compared to check the features that allow for the best possible prediction of the physical phenomena. 2. A separate preliminary exercise is also proposed to the contributors, only concerned with the convective problem in the absence of solidification, in conditions close to those met in solidification processes. Two problems are considered for the case of laminar natural convection: transient thermal convection for a pure liquid metal with a Prandtl number on the order of 10(-2), and double-diffusive convection in an enclosure for a liquid binary metallic mixture with a Prandtl number on the order of 10(-2) and a Lewis number on the order of 10(4).

Experiments were carried out to test the existence of solutal or thermosolutal convection and its effect on the solute distribution in the solid. Dilute Al-Mg binary alloys were solidified unidirectionally upward in the planar growth range and the temperature variations in the melt ahead of the solidification front were measured by differential thermal analysis (DTA). The Solidification interface was revealed by quenching and the solute distribution in the solid was analyzed. The almost flat solidification interface at the macroscopic scale indicated that thermal convection due to a radial temperature gradient was minimal. Temperature fluctuations in the melt were very small. However, the concentration profile along the axis of the crystal showed macroscopic segregation due to convection, which was more pronounced at slower growth rates and at higher concentration. The character of the convection is discussed in terms of solutal and thermosolutal convection, and a convection criterion is proposed which combines the solutal Rayleigh number, Ra s , and the thermal Rayleigh number, Ra T .

A transient two-dimensional ISPH method based on the time-fractional derivative was applied for emulating thermosolutal convection of the nano-encapsulated phase change material (NEPCM) embedded in an annulus between an inner wavy shape and outer hexagonal-shaped cavity. The impacts of a magnetic field and double rotations amongst an inner wavy shape and outer hexagonal-shaped cavity on the heat and mass transmission of NEPCM in an annulus have been conducted. Effects of a time parameter τ (0.01 − 1), frequency parameter ω (1 − 7), fractional time derivative α (0.95 − 1), Darcy parameter Da (10−2 − 10−4), Hartmann number Ha (0 − 100), fusion temperature θf (0.05 − 0.8), and Rayleigh number Ra (103 − 105) on the contours of temperature, heat capacity, concentration, and velocity field as well as profiles of Nu ¯ and Sh ¯ are investigated. The main findings signaled that the double rotations plays effectively in speed up the nanofluid movements, and changing the features of temperature, concentration, and heat capacity inside an annulus. An augmentation in a frequency parameter boosts the nanofluid speed by 128.57%. A decline in α from 1 to 0.95 enhances the maximum nanofluid velocity by 13.73%. The nanofluid movements within an annulus are reduced according to an increase in Ha and a decrease in Da. The power in the Rayleigh number enhances the nanofluid movements within an annulus.

A numerical model is developed to simulate the temperature field, the thermosolutal convection, the solute segregation and the growth interface morphology during the growth of ZnTe crystal from Te rich solution by the temperature gradient solution growth (TGSG) technique. Effects of the temperature gradient on the transport phenomena, the growth interface morphology and the growth rate are examined. The influences of the latent heat and the thermal conductivity of ZnTe crystal on the transport phenomena and the growth interface are also discussed. We find that the mass transfer of ZnTe in the solution is very slow because of the low diffusion coefficient and the lack of mixing in the lower part of the solution. During the growth, dilute solution with high density and low growth temperature accumulates in the central region of the growth interface, making the growth interface change into two distinct parts. The inner part is very concave, while the outer part is relatively flat. Growth conditions in front of the two parts of the growth interface are different. The crystalline quality of the inner part of the ingot is predicted to be worse than that of the outer part. High temperature gradient can significantly increase the growth rate, and avoid the diffusion controlled growth to some extent.

International audience; A special case that stands out in thermosolutal convection is that for which the thermal and solutal convection forces are equal and generate opposite effects (N = -1). This antagonistic effect between the two buoyancy forces is expected to generate unpredictable and unique behaviors when combined with thermodiffusion and internal heating phenomena. The present numerical study is dedicated to this particular case considering a binary mixture confined in a vertical rectangular cavity with an aspect ratio A = 2. The lattice Boltzmann method with multiple relaxation time is used to analyze the effect of the control parameters which are the Soret parameter (Sr = -0.5, 0 and 0.5), and the internal to external Rayleigh numbers ratio (0

An analysis of thermosolutal convection and entropy generation considering Soret and Dufour effects inside an inclined rectangular enclosure attached with porous wall has been investigated. The physical parameters are in the ranges such as buoyancy ratio (-10 ≤ N ≤ 10), permeability (10−9 ≤ Da ≤ 10−1) and thickness (0 ≤ d ≤ 1.0) of porous wall, enclosure inclination angle (0° ≤ Φ ≤ 90°), Soret number (0 ≤ Sr ≤ 1.5) and Dufour number (0 ≤ Du ≤ 1.5). Heatlines and masslines taking Soret and Dufour effects into account are obtained as effective tools that visualizes the heat and species transported paths. Results demonstrate that Soret number has mild impact on heat transfer rate and promotes moisture transportation, while increasing Dufour number could boot heat transfer rate and reduce moisture transfer rate. Furthermore, increasing Soret numbers enhances entropy generation induced by heat transfer and fluid friction, while entropy generation induced by fluid friction, heat and moisture transfer is dropped with stronger Dufour effect. Present work can benefit the heat and moisture transfer performance and entropy generation minimization of thermal storage wall system.

Under a NASA (National Aeronautics and Space Agency)-ESA (European Space Agency) collaborative research project, MICAST (Microstructure formation in casting of technical alloys under a diffusive and magnetically controlled convection conditions), three Al-7 wt% Si samples (MICAST-6, MICAST-7 and MICAST2-12) were directionally solidified aboard the International Space Station (ISS) to determine the effect of mitigating convection on the primary dendrite array morphology. MICAST-6 was processed with a step-increase in the growth speed from 5 to 50 µm s−1, MICAST-7 with a step-decrease from 20 to 10 µm s−1, and MICAST2-12 with constant speed of 40 µm s−1. Nearest-neighbor primary dendrite arm spacings and primary dendrite trunk diameters were measured on transverse sections taken at approximately 5 mm intervals along the length of the MICAST samples. In MICAST samples, especially in the steady-state growth regime, the observed primary dendrite nearest-neighbor spacings show a good agreement with predictions from the Hunt-Lu numerical model. The maximum to minimum (highest 10% to lowest 10%) nearest-neighbor spacing ratio in MICAST samples is 2.10 ± 0.27 in agreement with Hunt-Lu model, which assumes pure diffusive transport. Trunk diameters in MICAST samples also agree well with predictions from a coarsening based model. The terrestrial-grown equivalent samples, on the other hand, display smaller nearest-neighbor spacing, and larger primary dendrite trunk diameters than those predicted from the models. Thermosolutal convection appears to increase the dendrite tip radius, causing the trunk diameter to increase, while simultaneously reducing the primary dendrite spacing. This requires verification-experiments involving directional solidification followed by rapid quenching of the liquid-solid interface in metallic alloys in a low gravity environment. The International Space Station currently does not have on-board hardware to conduct such experiments.

Hypoeutectic Al-7 wt .% Si alloys were directionally solidified vertically downward in cylindrical molds that incorporated an abrupt cross-section decrease (9.5 mm to 3.2 mm diameter) which, after 5 cm, reverted back to 9.5 mm diameter in a Bridgman furnace; two constant growth speeds and thermal gradients were investigated. Thermosolutal convection and cross-section-change-induced shrinkage flow effects on macrosegregation were investigated. Dendrite clustering and extensive radial macrosegregation was seen, particularly in the larger cross-sections, before contraction and after expansion, this more evident at the lower growth speed. This alloy shows positive longitudinal macrosegregation near cross-section decrease followed by negative macrosegregation right after it; the extent of macrosegregation, however, decreases with increasing growth speed. Primary dendrite steepling intensified as solidification proceeded into the narrower section and negative longitudinal macrosegregation was seen on the re-entrant shelves at expansion. A two-dimensional model accounting for both shrinkage and thermo-solutal convection was used to simulate solidification and the resulting mushy-zone steepling and macrosegregation. The experimentally observed longitudinal and radial macrosegregation associated with the cross-section changes during directional solidification of an Al–7Si alloy is well captured by the numerical simulations.

This paper deals with thermosolutal convection in an inclined enclosure inserted with heat-generating porous blocks under the influence of magnetic field. The general Brinkman-extended Darcy model is adopted to formulate the fluid flow in the enclosure. An extensive series of numerical simulations is investigated in the range of parameters 0 ≤ Ha ≤ 150, 103 ≤ Ra ≤ 107, −10.0 ≤ N ≤ 10.0, 10−9 ≤ Da ≤ 10−1, 0.1 ≤ Kr ≤ 10 and −90° ≤ Φ ≤ 90°. Streamline, isotherms, isoconcentrations and masslines are produced to illustrate the fluid, heat and moisture flow structures. It is founded that overall Nusselt number is an increasing function of Ra, N, Da and Kr in the vertical enclosure, while decreasing with Ha. The permeability and thermal conductivity of porous blocks have no significant effect on moisture transfer rate. The Nusselt and Sherwood curves for different inclination angle are presented to be parabolic, and the maximum are near at Ф = −10° and 30°, respectively. In addition, correlations of the overall Nusselt and Sherwood numbers depending on thermal Rayleigh number, buoyancy ratio, Hartmann number and inclination angle have been obtained, which are beneficial to determine heat and moisture transfer rates in electrical devices.

The residual accelerations that are typically present in microgravity environments (g-jitters) contain a broad spectrum of frequencies and may be modeled as stochastic processes. Their effects on the quality of the semiconductor crystals are analyzed here quantitatively with direct numerical simulation. In particular we focus on the dopant segregation effects due to thermosolutal convection as a function of the parameters characterizing the statistics of the stochastic force. The numerical simulation is specified for material parameters of two doped semiconductors (Ge:Ga and GaAs:Se) in realistic conditions of actual microgravity environments. As a general result, we show that the segregation response is strongly dominated by the low-frequency part of the g-jitter spectrum. In addition, we develop a simplified model of the problem based on linear response theory that projects the dynamics into very few effective modes. The model captures remarkably well the segregation effects for an arbitrary time-dependent acceleration of small amplitude, while it implies an enormous reduction of computer demands. This model could be helpful to analyze results from real accelerometric signals and also as a predictive tool for experimental design.

Experiments are carried to investigate free dendritic growth of succinonitrile–acetone alloys in an undercooled melt. The measurements include the steady dendrite tip velocity and radius, the non-axisymmetric amplitude coefficient of the fins near the tip, and the envelope width, projection area, and contour length of the sidebranch structure far from the tip. It is found that the measured dendrite tip growth Peclet numbers agree well with the predictions from a stagnant film model that accounts for thermosolutal convection in the melt. The measured tip selection parameter, σ ⁎ , is verified to be independent of the alloy composition, but shows a strong dependence on the imposed undercooling. The universal amplitude coefficient, A 4 , is measured to be equal to 0.004, independent of the undercooling, but the early onset of sidebranching prevents its accurate determination for more concentrated alloys. For the self-similar sidebranch structure far from the tip, scaling laws are obtained for the measured geometrical parameters. While melt convection causes some widening of the sidebranch envelope, and the early onset of sidebranching for alloy dendrites results in a 25% upward shift of the envelope width, the projection area and, hence, the mean width of a sidebranching dendrite, as well as its contour length in the sidebranch plane, obey universal power laws that are independent of the convection intensity and the alloy composition.

Transient thermosolutal convection in a cubical enclosure having finite thickness walls filled with air, submitted to temperature and concentration gradients, is studied numerically. In the first series of numerical simulations, the influence of Rayleigh number on fluid motion and heat and mass transfer ( N = 1, Ra = 10 4 –10 5 ) is analyzed. The second series deals with the effect of the dimensionless time ( N = 1, Ra = 5 × 10 4 , τ = 1–100). In the third series the influence of the conductivity ratio on heat and mass transfer ( N = 1, Ra = 10 5 , k fs = 0.037, 0.0037) is investigated. The fourth series deals with the effect of the mass source sizes on the heat and mass transfer regimes. Comprehensive Nusselt and Sherwood numbers data are presented as functions of the governing parameters mentioned above.

The influence of the thermosolutal convection of the liquid steel in the solidifying core of a 3.3-ton ingot on the formation of banded mesosegregates is investigated by a multiscale solidification model. We first show how the thermosolutal flow structure in the solidifying core depends on the relation between the interacting thermal and solutal buoyancy forces and the coupling by the phase-change kinetics. We further show that banded mesosegregates are triggered by instabilities of the solidification front, that their location is determined by flow instabilities, and that their “A” or “V” orientation depends on the global direction of the flow circulation. Moreover, the results show that local remelting is not necessary to develop a channel mesosegregate. Destabilization of the mushy zone with local variations of the solidification velocity is sufficient.

International audience; An extension of a slightly compressible flow model to double-diffusive convection of binary mixtures 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 work are the statement of the mathematical model used, and the analysis of some significant results showing the influence of density variation on transient solutions for pure thermal or pure solutal convection as well as for thermosolutal convection in the special case where the thermal and solutal buoyancy forces are equal in intensity either for aiding or for opposing cases.

Numerical modeling of convection damping and macrosegregation suppression during solidification of alloys with prominent mushy zones through the use of tailored magnetic fields is demonstrated here. Macrosegregation leads to commonly observed defects such as freckles, channels and segregates in cast alloys that severely affect the performance and suitability of the alloy for further applications. The current work demonstrates the successful use of magnetic fields in suppressing thermosolutal convection and eliminating some of these defects in solidifying metallic alloys. The computational model presented utilizes volume-averaged governing transport equations and stabilized finite element techniques to discretize these equations. A finite-dimensional optimization problem, based on the continuum sensitivity method is considered to design the time history of the imposed magnetic field required to effectively damp convection. The coefficients that determine this time variation are the main design parameters of this optimization problem. Continuum sensitivity equations are derived by design-differentiating the governing equations of the direct problem. The cost functional here is given by the square of the L2 norm of an expression representing the deviation of the volume-averaged velocity corresponding to conditions of convection less growth. The cost functional minimization process is realized through a non-linear conjugate gradient algorithm that utilizes finite element solutions of the continuum direct and sensitivity problems. Design of the time history of the imposed magnetic field is highlighted through different examples with the main objective being the suppression of convection and macrosegregation during alloy solidification.

The microstructural scales of dendrites, such as primary, secondary and tertiary arm spacings, control the segregation profiles and the formation of secondary phases within interdendritic regions, which determine the properties of cast structures. Investigations on tertiary dendritic arms are scarce in the literature, and only a few studies have been conducted in order to analyze the effects of melt convection within the interdendritic region during transient solidification. In this article, the influence of thermosolutal convection on the tertiary dendrite arm spacing is experimentally examined in the downward vertical unsteady-state directional solidification of Al–Cu and Al–Si hypoeutectic alloys.

This paper deals with the theoretical investigation of the effect of dust particles on the thermosolutal convection in ferrofluid subjected to 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, non-buoyancy magnetization and dust particles 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 the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold good for the ferrofluid 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.

Microstructures are the strategic link between materials processing and materials behavior. The microstructural scales of dendrites, such as primary and secondary arm spacings, control the segregation profiles and the formation of secondary phases within interdendritic regions, which determine the properties of cast structures. A small number of studies have been conducted in order to analyze the effects of melt convection within the interdendritic region. In this article, the influence of thermosolutal convection on dendrite arm spacings is experimentally examined in the downward vertical unsteady-state directional solidification of Sn–Pb hypoeutectic alloys. The main predictive theoretical models for dendritic spacings are compared with the experimental observations.