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According to research, exposing a person to a magnetic field enhances blood flow and minimizes their risk of suffering a heart attack. Ferrohydrodynamics is the study of fluid motion mechanics that is affected by strong magnetic polarisation forces (FHD). Ferrofluids may transmit heat in a variety of ways by using magnetic fluids. This behaviour is demonstrated by liquid-cooled speakers, which utilise less ferrofluid to prevent heat from reaching the speaker coil. This modification boosts the coil's ability to expand, which enables the loudspeaker to create high-fidelity sound. It is investigated how the fluid dynamics of spinning, squeezing plates are affected by thermosolutal convection and a magnetic field dependent (MFD) viscosity. Standard differential equations are used to represent the equations of the modified form of Navier Stokes, Maxwell's, and thermosolutal convection. The magnetic field, modified velocity field equations, and thermosolutal convection equations all yield suitable answers. Additionally computed and thoroughly detailed are the MHD torque and fluid pressure that are imparted to the top plate. To create a technique with quick and certain convergence, the resulting equations for uniform plates are solved using the Homotopy Analysis Method (HAM) with appropriate starting estimates and auxiliary parameters. The validity and reliability of the HAM outcomes are shown by comparing the HAM solutions with the BVP4c numerical solver programme. It has been found that a magnetic Reynolds number lowers the temperature of the fluid as well as the tangential and axial components of the velocity field. Additionally, when the fluid's MFD viscosity rises, the axial and azimuthal components of the magnetic field behave in opposition to one another. This study has applications in the development of new aircraft take-off gear, magnetorheological airbags for automobiles, heating and cooling systems, bio-prosthetics, and biosensor systems. [ABSTRACT FROM AUTHOR]

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

Highlights • The increase in power-law index provokes heat and mass transfer to drop gradually. • The enhancement of Carreau number decreases heat and mass transfer. • The rise of Carreau number decreases the total irreversibilities. • The rise of Carreau-Yasuda parameter increases the total irreversibilities. Abstract 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 = 10 4 and 10 5 ), 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. [ABSTRACT FROM AUTHOR]

The thermosolutal convection in Rivlin-Ericksen elastic-viscous fluid in porous medium is considered to include the effect of suspended particles in the presence of uniform magnetic field, uniform rotation and variable gravity field. It is found that for stationary convection, the stable solute gradient has stabilizing effect on the system. Rotation has stabilizing effect as gravity increases upward and destabilizing effect as gravity decreases upward whereas suspended particles have destabilizing effect as gravity increases upward and stabilizing effect as gravity decreases upward. The medium permeability has stabilizing/destabilizing effect depending on the rotation parameter. The magnetic field has a stabilizing effect in the absence of rotation whereas in the presence of rotation it has a stabilizing/destabilizing effect under certain conditions. The principle of exchange of stabilities is satisfied in the absence of magnetic field, rotation and stable solute gradient. The presence of magnetic field, rotation and stable solute gradient introduces oscillatory modes into the system. [ABSTRACT FROM AUTHOR]

The thermosolutal convection in a porous medium saturated with an aqueous solution near the temperature of the density maximum is studied. The fixed temperatures applied to vertical walls include the density maximum. The formulation of the problem is based on the Darcy-Brinkman model and the density variation is governed by a nonlinear approximation. The equations are solved by a finite-volume method. The numerical model is validated through experimental results. We show that the nonlinear variation of the density influences strongly the flow structure and the heat transfer. The structures of this flow show that the density maximum generates a complex flow structure of two contrarotating cells of unequal importance. [ABSTRACT FROM AUTHOR]

Presents numerical solutions for thermosolutal convection in a vertical concentric cavity partly filled with a porous medium. Effects of the controlling parameters on the flow patterns and heat and mass transfer behavior; Zones in the closed partly porous cavity in which steep velocity, temperature and concentration gradients are present; Effect of aspect ratio.

A linear stability theory is performed to investigate the stability of the quiescent state and fully developed thermosolutal convection within a vertical porous enclosure subject to horizontal opposing gradients of temperature and solute. The fluid motion is modeled using the unsteady form of Darcy's law coupled with energy and species conservation equations. The effect of different thermal and solutal boundary conditions is considered. The linearized governing equations are solved numerically using a finite element method. The thresholds for oscillatory and stationary convection are determined as functions of the governing parameters. It is concluded that the porosity and the acceleration parameter of the porous medium have a strong effect on the onset of overstability for a confined enclosure and on the wave number for an infinite enclosure. The stability analysis of fully developed flows within a slender enclosure reveals that an increase in the porosity and the acceleration parameter of the porous media delays the appearance of oscillatory finite amplitude flows. A nonlinear numerical solution is also computed by solving the full governing equations using a finite element method. Within the overstable regime, nonlinear traveling waves exist within slender enclosures, subject to Dirichlet thermal and solutal boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract: Thermosolutal natural convection induced in a vertical porous layer heated and salted with uniform fluxes is studied analytically and numerically. The study is focused on a specific case where the separation coefficient is identical to the ratio of buoyancy forces. Analytical results, describing both pseudo-conductive and boundary layer regimes, are discussed. Specific behaviour, corresponding to this particular situation, is presented. To cite this article: M. Er-Raki et al., C. R. Mecanique 336 (2008). [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

Abstract: Heat transfer by natural convection and surface condensation in two-dimensional enclosures in contact with a cold external ambient through a wall of finite thickness was studied numerically. Special attention was given on the modeling of the flow of a binary mixture consisting of humid air. Low-Mach number assumption was introduced in order to account for decreases in mixture mass and average pressure within the enclosure between the initial and steady states. The computations show that thermodynamic balances are satisfied within the accuracy of the numerical procedure. The heat and fluid flows with and without condensation are compared for various operating conditions. It is shown that vapor condensation increases the heat transfer rate at the cold wall at the early stage of the transient regime. The decrease in the average density of the mixture leads to significant variable''s reductions at steady-state which, in turn, causes lower overall heat transfer rate than for dry air. [Copyright &y& Elsevier]

Soret effect on fluid flow and heat and mass transfer induced by double-diffusive natural convection in a square porous enclosure, submitted to cross gradients of temperature and concentration, is studied numerically. The cavity is heated from below and cooled from the top, while its vertical walls are adiabatic and maintained at constant but different concentrations. Numerical results are presented for governing parameters varying in the following ranges: 40 ≤ R T ≤ 1,000, Le = 10, - 0.2 ≤ N ≤ 0.2 and - 30 ≤ M ≤ 30, where R T , Le, N , and M are the thermal Rayleigh number, the Lewis number, the buoyancy ratio, and the Soret parameter, respectively. The effect of the buoyancy ratio and the Soret parameter on the maintenance and disappearance of the multiple steady-state solutions obtained in the case of purely thermal convection is analyzed. It is found that only one monocellular flow mode persists at large values of N (or - N ), both in the presence and in the absence of the Soret effect. Some flow modes are destroyed by the solutal buoyancy forces in the absence of the Soret effect ( M = 0) but reappear in some range of the parameter M . The Soret effect may affect considerably the heat and mass transfer in the medium; it leads to an enhancement or to a reduction of the mass transfer, depending on the flow structure and the sign of M . There are situations where a solution transfers the solute toward the wall with the highest concentration. Such behavior is observed when the temperature gradient and the magnitude of the Soret parameter M are such that the thermodiffusion flux opposes and overcomes the convection flux, resulting in a net mass flux directed from the least concentrated wall toward the most concentrated one. [ABSTRACT FROM AUTHOR]

Presents information on a study which investigated the occurrence of stationary and oscillatory solutions in a horizontal layer of fluid in the presence of horizontal and vertical temperature gradients. Formulation of the problem; Approximate solution of the stability problem; Results and discussion; Conclusions.

A numerical study is made of double-diffusive convection in a square cavity with a sliding top lid in the presence of combined vertical temperature and concentration gradients. The bottom lid and other two walls are kept fixed. The side walls are adiabatic and impermeable to solute while the top and bottom lids are kept at constant but distinct temperature and concentration. The governing unsteady Navier-Stokes equations combined with the heat and mass transport equations are solved numerically through a finite volume method on a staggered grid system using QUICK scheme for convective terms. The resulting equations are then solved by an implicit, time-marching, pressure correction-based algorithm. The flow configuration is classified into four cases depending on positive/negative values of thermal Grashof number and solutal Grashof number. A detailed comparison of the four flow configurations is made in this paper. In conclusion, these four flow configurations can be brought to either stably or unstably stratified field. Furthermore, the possibility of salt-fingering and double-diffusive instability in the absence of the top lid motion is explored and the effect of the lid motion is clearly exhibited. The dependence of the average rates of heat and mass transfer from the top and bottom lids on the flow parameters is also investigated in the presence of top lid motion. [ABSTRACT FROM AUTHOR]

Segregation is a serious defect in alloy ingots which severely deteriorates materials performance. The segregation defect in Mg-6Gd alloy is studied by coupling macro thermal-solutal-convection transport and micro dendrite growth. The macroscopic fluid dynamics and mass transfer equations are resolved to forecast the segregation behavior under conditions of continuous temperature variation during the solidification process. The numerical model is validated by testing double-diffusive natural convection in a closed square cavity. A phase field model is then applied to simulate the micro dendrite growth, using macro undercooling and liquid flow velocity as boundary conditions. Results show that the multiscale segregation behavior, including macro solute distribution and micro dendritic morphology, is strongly dependent on the temperature condition and the liquid convection, which provides guidance for reducing and eliminating the segregation defect. [ABSTRACT FROM AUTHOR]

Numerical continuation is used to investigate stationary spatially localized states in two-dimensional thermosolutal convection in a plane horizontal layer with no-slip boundary conditions at top and bottom. Convectons in the form of 1-pulse and 2-pulse states of both odd and even parity exhibit homoclinic snaking in a common Rayleigh number regime. In contrast to similar states in binary fluid convection, odd parity convectons do not pump concentration horizontally. Stable but time-dependent localized structures are present for Rayleigh numbers below the snaking region for stationary convectons. The computations are carried out for (inverse) Lewis number τ = 1/15 and Prandtl numbers Pr = 1 and Pr>1. [ABSTRACT FROM AUTHOR]

Soret-driven thermosolutal convection within a shallow porous or fluid layer subject to a vertical gradient of temperature is investigated analytically and numerically. The bridging between a clear fluid and Darcy porous media problems is conducted using the Brinkman–Hazen–Darcy model in its transient form. The analytical solution is derived on the basis of the parallel flow approximation, and validated numerically using a finite difference method by solving the full governing equations. The study is focused on the thermal diffusion effects on the flow intensity, and on the heat and mass transfer rates. In particular, a comparative study is made for the two limiting cases that emerge from the present investigation, namely the low porosity Darcy porous medium and the clear fluid medium. The flow behavior for both cases is qualitatively similar. The critical Rayleigh numbers for the onset of subcritical, oscillatory and stationary convection are determined explicitly as functions of the governing parameters for infinite and finite layers. At the onset of instabilities, the wavenumber is equal to zero and the oscillation frequency vanishes at the onset of Hopf bifurcation. For a finite aspect ratio enclosure, the frequency is finite and decreases as the aspect ratio increases. The codimension-2 point exists and different flow regimes are delineated. For constant heat flux boundaries, only standing oscillatory and steady waves are found to exist. The analytical and numerical results are found to be in good agreement, within the range of the governing parameters considered in the present study. The thermal diffusion effect on the flow intensity and on the heat and mass transfer is more enhanced for Darcy medium compared to the clear fluid, for which the viscous effects are significant. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This study investigates the stability analysis of Rayleigh-Bénard configuration for a viscoelastic fluid subject to thermorheological effects, using the D 2 -Chebyshev- τ method. The fluid is modeled as a third-order viscoelastic fluid. This study accentuates how salting the fluid layer affects the thresholds for the onset of instability in a fluid of third order encompassing physically realistic rigid boundaries. The dynamic model incorporates advection-diffusion of temperature and solute concentration and a modified Navier–Stokes equation. We determine instability thresholds for the complex non-Newtonian fluid by analyzing the linear stability of the steady-state conduction solution. Our analysis proves the strong form of the principle of exchange of stabilities, demonstrating that convective motions can only occur through stationary motion. Additionally, a nonlinear stability analysis using the energy method is performed, deriving an unconditional nonlinear stability criterion. The results provide a comprehensive understanding of how variable viscosity and viscoelasticity impact system stability. Both the viscosity parameter and the third-grade fluid parameter exhibit stabilizing effects. Notably, we observe a discrepancy between the linear and global nonlinear stability results, indicating the presence of a subcritical instability region. This study contributes to the understanding of complex fluid dynamics in non-linear mechanical systems, with potential applications in various industrial and natural processes. • A system of differential equations models the double-diffusive convection in viscoelastic fluid. • The effect of temperature-dependent viscosity on the onset of convection is examined. • The strong form of principle of exchange of stabilities is proved. • Linear analysis determines thresholds above which steady solutions become unstable. • Nonlinear analysis proves the total perturbed energy of the system decays asymptotically. [ABSTRACT FROM AUTHOR]

Analytical and numerical investigations were performed to study the influence of the Soret and Dufour effects on double-diffusive convection in a vertical porous layer filled with a binary mixture and subject to horizontal thermal and solute gradients. In particular, the study was focused on the effect of Soret and Dufour diffusion on bifurcation types from the rest state toward steady convective state, and then toward oscillatory convective state. The Brinkman-extended Darcy model and the Boussinesq approximation were employed to model the convective flow within the porous layer. Following past laboratory experiments, the investigations dealt with the particular situation where the solutal and thermal buoyancy forces were equal but acting in opposite direction to favor the possible occurrence of the rest state condition. For this situation, the onset of convection could be either supercritical or subcritical and occurred at given thresholds and following various bifurcation routes. The analytical investigation was based on the parallel flow approximation, which was valid only for a tall porous layer. A numerical linear stability analysis of the diffusive and convective states was performed on the basis of the finite element method. The thresholds of supercritical, RTCsup, and overstable, RTCover, convection were computed. In addition, the stability of the established convective flow, predicted by the parallel flow approximation, was studied numerically to predict the onset of Hopf's bifurcation, RTCHopf, which marked the transition point from steady toward unsteady convective flows; a route towards the chaos. To support the analytical analyses of the convective flows and the numerical stability methodology and results, nonlinear numerical solutions of the full governing equations were obtained using a second-order finite difference method. Overall, the Soret and Dufour effects were seen to affect significantly the thresholds of stationary, overstable and oscillatory convection. The Hopf bifurcation was marked by secondary convective flows consisting of superposed vertical layers of opposite traveling waves. A good agreement was found between the predictions of the parallel flow approximation, the numerical solution and the linear stability results. [ABSTRACT FROM AUTHOR]

Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating spherical shell can exhibit a rather large number of behaviours often distinct from that of the single diffusive system. In order to understand how the differences in thermal and compositional molecular diffusivities determine the dynamics of thermo-compositional convection we investigate numerically the linear onset of convective instability in a double-diffusive setup. We construct an alternative equivalent formulation of the non-dimensional equations where the linearised double-diffusive problem is described by an effective Rayleigh number, , measuring the amplitude of the combined buoyancy driving, and a second parameter, α, measuring the mixing of the thermal and compositional contributions. This formulation is useful in that it allows for the analysis of several limiting cases and reveals dynamical similarities in the parameters space which are not obvious otherwise. We analyse the structure of the critical curves in this space, explaining asymptotic behaviours in α, transitions between inertial and diffusive regimes, and transitions between large-scale (fast drift) and small-scale (slow drift) convection. We perform this analysis for a variety of diffusivities, rotation rates and shell aspect ratios showing where and when new modes of convection take place. [ABSTRACT FROM AUTHOR]

Presents a study which provided an improved fluid flow and heat-transfer modeling of float-zone growth. Derivation of numerical simulations for heat transfer modeling; Complexities of the float-zone models; Role of fluid and thermal fields in the control of crystal quality.

The main purpose of our work is to show the impact of some pertinent parameters; such Lewis and solutal Rayleigh numbers as well as the buoyancy and the aspect ratios; on a viscoplastic materials’ double-diffusive convection which occurs within an SiC annulus; contained between a cold “and less concentric” outer circular cylinder and a hot “and concentric” inner one, to come out with innovative correlations what predict the mean transfer rates into 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. To handle the cylinder shape in Cartesian coordinates; the Cartesian Cut-Cell approach was adopted. Subsequently, inclusive correlations of overall transfers within such viscoplastic porous annulus are set forth as a function of the governing parameters; which foresee with ±2 to ±3% the numerical predictions. Noted that the validity of the computing code was ascertained by comparing its results with experimental data and numerical ones; already available in the literature. [ABSTRACT FROM AUTHOR]

Abstract: In this work, the STEP scheme and several schemes based on the normalized variable diagram (NVD), such as MINMOD, GAMMA, CLAM, NOTABLE, MUSCL, CUBISTA, SMART, WACEB, and VANOS schemes, are evaluated for solving the radiative transfer equation. Two‐dimensional and three‐dimensional rectangular enclosures containing transparent, emitting–absorbing, emitting–absorbing–scattering, or nonhomogeneous participating media are investigated using the modified FTn finite volume method. Although the NVD schemes are much more accurate than the STEP scheme, but they have more time‐consuming and require more iterations. Moreover, most of them often necessitate underrelaxation to ensure convergence. Results show that the MINMOD and GAMMA schemes are still much less accurate than other NVD schemes, but they converge the fastest of the NVD schemes, and do not require underrelaxation. Although the VANOS, WACEB, and SMART schemes give more accurate solutions, they are not competitive with other NVD schemes. However, the CLAM, NOTABLE, and CUBISTA schemes are relatively fast and accurate. [ABSTRACT FROM AUTHOR]

Three-dimensional thermosolutal natural convection and entropy generation within an inclined enclosure is investigated in the current study. A numerical method based on the finite volume method and a full multigrid technique is implemented to solve the governing equations. Effects of various parameters, namely, the aspect ratio, buoyancy ratio, and tilt angle on the flow patterns and entropy generation are predicted and discussed. [ABSTRACT FROM AUTHOR]

The onset of double-diffusive convection in a horizontal fluid-saturated porous layer is examined by taking the Soret effect into consideration. The linear and nonlinear stability analyses are derived, and the corresponding eigenvalue problems are solved. The nonlinear stability analysis is achieved by using the energy method. In both the cases of linear and nonlinear stability theories, the onset criterion for all possible modes is derived analytically. For numerical computations of the eigenvalue problem, the Chebyshev tau method is employed. It is observed that the effect of stabilization or destabilization caused by the Soret parameter is significant for the Soret parameters which are less than Sr=2. In the absence of the Soret effect, the linear and nonlinear stability thresholds coincide. [ABSTRACT FROM AUTHOR]

A volume average solidification model is extended to incorporate fragmentation as the source of equiaxed crystals during mixed columnar-equiaxed solidification. This study is to use this model to analyze the role of fragmentation in the formation of as-cast structure. Test simulations are made for the solidification of a model alloy (Sn-10wt.%Pb) with two different geometries. The first one is a 2D rectangular domain (50 × 60 mm2) as cooled from the top boundary. Solidification starts unidirectionally as columnar structure from the top. The solute (Pb) enriched interdendritic melt is heavier than the bulk melt, and sinks downwards, hence leads to solutal convection. Fragmentation phenomenon occurs near the columnar tip front. The fragments are transported out of the columnar region, and they continue to grow and sink, and finally settle down and pile up at the bottom. The growing columnar structure from the top and pile-up of equiaxed crystals from the bottom finally lead to a mixed columnar-equiaxed structure, in turn leading to a columnar-to-equiaxed transition (CET). The second geometry is a 3D plate, 100 × 60 ×10 mm³, as cooled laterally from one side. It was cast experimentally and analyzed for the as-cast structure. The equiaxed fragments are produced in the solidification front and transported into the bulk melt, leading to a special pattern of as-cast structure: columnar structure in the cool wall side and equiaxed structure in the upper left corner near the hot wall side, extending downwards to the middle bottom region. Numerically calculated as-cast structures agree with the experiment results. [ABSTRACT FROM AUTHOR]

This article provides theoretical conditions for the use and meaning of a stability analysis around a mean flow. As such, it may be considered as an extension of the works by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336-382) to non-parallel flows and by Turton et al. (Phys. Rev. E, vol. 91 (4), 2015, 043009) to broadband flows. Considering a Reynolds decomposition of the flow field, the spectral (or temporal Fourier) mode of the fluctuation field is found to be equal to the action on a turbulent forcing term by the resolvent operator arising from linearisation about the mean flow. The main result of the article states that if, at a particular frequency, the dominant singular value of the resolvent is much larger than all others and if the turbulent forcing at this frequency does not display any preferential direction toward one of the suboptimal forcings, then the spectral mode is directly proportional to the dominant optimal response mode of the resolvent at this frequency. Such conditions are generally met in the case of weakly non-parallel open flows exhibiting a convectively unstable mean flow. The spatial structure of the singular mode may in these cases be approximated by a local spatial stability analysis based on parabolised stability equations (PSE). We have also shown that the frequency spectrum of the flow field at any arbitrary location of the domain may be predicted from the frequency evolution of the dominant optimal response mode and the knowledge of the frequency spectrum at one or more points. Results are illustrated in the case of a high Reynolds number turbulent backward facing step flow. [ABSTRACT FROM AUTHOR]

Certain flows denominated as amplifiers are characterized by their global linear stability while showing large linear amplifications to sustained perturbations. As the forcing amplitude increases, a strong saturation of the response appears when compared to the linear prediction. However, a predictive model that describes the saturation of the response to higher amplitudes of forcing in stable laminar flows is still missing. While an asymptotic analysis based on the weakly nonlinear theory shows qualitative agreement only for very small forcing amplitudes, the linear response to harmonic forcing around the mean flow computed by direct numerical simulations presents a good prediction of the saturation also at higher forcing amplitudes. These results suggest that the saturation process is governed by the Reynolds stress and thus motivate the introduction of a simple self-consistent model. The model consists of a decomposition of the full nonlinear Navier-Stokes equations in a mean flow equation together with a linear perturbation equation around the mean flow, which are coupled through the Reynolds stress. The full fluctuating response and the resulting Reynolds stress are approximated by the first harmonic calculated from the linear response to the forcing around the aforementioned mean flow. This closed set of coupled equations is solved in an iterative manner as partial nonlinearity is still preserved in the mean flow equation despite the assumed simplifications. The results show an accurate prediction of the response energy when compared to direct numerical simulations. The approximated coupling is strong enough to retain the main nonlinear effects of the saturation process. Hence, a simple physical picture is formalized, wherein the response modifies the mean flow through the Reynolds stress in such a way that the correct response energy is attained. [ABSTRACT FROM AUTHOR]

In this study, mixed convection in a cavity that has a fluid and superposed porous medium with an adiabatic rotating cylinder is numerically investigated. The bottom horizontal wall is heated and the top horizontal wall is cooled while the remaining walls are assumed to be adiabatic. An adiabatic rotating cylinder is inserted inside the cavity. The governing equations are solved by the Galerkin weighted residual finite element method. The effects of Rayleigh number (between 103and 106), angular rotational speed of the cylinder (between 0 and 6,000), Darcy number (between 10−5and 10−2), cylinder sizes (betweenR = 0.1 andR = 0.3) and three different vertical locations of the cylinder on the fluid flow and heat transfers characteristics are numerically investigated. It is observed that the cylinder size has a profound effect on the local and averaged heat transfer. The local and averaged heat transfers generally increase and the convection is more effective in the upper half of the cavity as the Rayleigh number and Darcy number enhance. The averaged heat transfers increases with the cylinder size untilRa = 105. The averaged heat transfer increases almost linearly with the angular rotational velocity of the cylinder and the increase rate becomes higher as the cylinder size increases. The local and averaged heat transfers enhances/deteriorate as the cylinder approaches the upper/lower wall of the cavity. [ABSTRACT FROM AUTHOR]

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This study examines the double diffusive convection of a sparsely packed micropolar fluid-saturated porous medium by using a linear stability analysis. The Darcy-Brinkman-Forchheimer model is employed for the porous fluid layer. The stability criterion is sought analytically with the simple free-free, iso-thermal, and iso-solutal boundary conditions. The dependence of stationary or oscillatory convection on the porous parameter, Lewis number, solutal Rayleigh number, and parameters involved in micropolar fluids is drawn and discussed. The results show that the critical wave number is found to be insensitive to the variation of governing parameters except for the porous parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21052 [ABSTRACT FROM AUTHOR]

In this paper, the combined effect of suspended (fine dust) particles and rotation on the onset of double-diffusive convection in a viscoelastic fluid in porous medium is studied. For the porous medium, the Brinkman model is employed and Walters' (model B') model is used to characterize viscoelastic fluid. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, stable solute gradient, suspended particles, gravity field and viscoelasticity introduce oscillatory modes. For stationary convection, it is observed that the rotation, stable solute gradient have stabilizing effect and suspended particles have destabilizing effect on the system whereas Darcy number and medium permeability have stabilizing/destabilizing effects under certain conditions. The effects of rotation, stable solute gradient, suspended particles, Darcy number and medium permeability have also been investigated. [ABSTRACT FROM AUTHOR]

The thermal instability of a couple-stress fluid acted upon by uniform vertical magnetic field and rotation heated from below is investigated. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the nonoscillatory motions which may be neutral or unstable for any combination of free and rigid boundaries at the top and bottom of the fluid. It is proved mathematically that all non-decaying slow motions starting from rest, in a couple-stress fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical magnetic field and rotation opposite to gravity and a constant vertical adverse temperature gradient, are necessarily non-oscillatory, in the regime established. The result is important since it hold for all wave numbers and for any combination of perfectly conducting dynamically free and rigid boundaries. [ABSTRACT FROM AUTHOR]

A numerical study of three-dimensional incompressible viscous flow inside a cubical lid-driven cavity is presented. The flow is governed by two mechanisms: (1) the sliding of the upper surface of the cavity at a constant velocity and (2) the creation of an external gradient for temperature and solutal fields. Extensive numerical results of the three-dimensional flow field governed by the Navier-Stokes equations are obtained over a wide range of physical parameters, namely Reynolds number, Grashof number and the ratio of buoyancy forces. The preceding numerical results obtained have a good agreement with the available numerical results and the experimental observations. The deviation of the flow characteristics from its two-dimensional form is emphasized. The changes in main characteristics of the flow due to variation of Reynolds number are elaborated. The effective difference between the two-dimensional and three-dimensional results for average Nusselt number and Sherwood number at high Reynolds numbers along the heated wall is analyzed. It has been observed that the substantial transverse velocity that occurs at a higher range of Reynolds number disturbs the two-dimensional nature of the flow. [ABSTRACT FROM AUTHOR]

A classification is made for the intrinsic decadal modes of variability in the thermohaline circulation in an oceanic model with steady boundary conditions in a simply-shaped, hemispheric domain with a coarse spatial grid, without the capability of generating any mesoscale eddies. The purpose is to provide an overview of many previous and more specific examples of such variability to better understand its essential characteristics and potential roles in climate change. Various control parameters – including ones expressing the intensities (i.e., Rayleigh numbers) and patterns associated with the surface heat and freshwater forcing – are shown to be important in determining the particular critical values of the thermohaline regime transitions, but they do not modify the overall structure of the bifurcation diagrams. An important categorical distinction is associated with the mathematical form of the surface boundary conditions in determining whether distinguishable decadal variability occurs and, if so, its character. Specified (fixed) patterns for heat and water flux are more permissive of intrinsic decadal variability, and they have a simpler dynamical interpretation for it than do the so-called mixed surface boundary conditions with fixed freshwater flux and thermal relaxation patterns. Both types of boundary conditions are idealizations of the true ocean–atmosphere interactions in climate. The routes to decadal oscillation are quite different for the two types of boundary conditions, namely, a simple Hopf bifurcation for flux conditions and a global bifurcation for mixed conditions. Consequently, with transient forcing distinguishable decadal, variability is evident even for sub-critical parameter values for flux conditions but not for mixed conditions. Furthermore, mixed conditions are more permissive of multiple steady states than are flux conditions. [ABSTRACT FROM AUTHOR]

Effect of Hall currents and suspended particles is considered on the hydromagnetic stability of a compressible, electrically conducting Walters' (Model B) elastico-viscous fluid. After linearizing the relevant hydromagnetic equations, the perturbation equations are analyzed in terms of normal modes. A dispersion relation governing the effects of visco-elasticity, magnetic field, Hall currents and suspended particles is derived. It has been found that for stationary convection, the Walters' (Model B) fluid behaves like an ordinary Newtonian fluid due to the vanishing of the visco-elastic parameter. The compressibility and magnetic field have a stabilizing effect on the system, as such their effect is to postpone the onset of thermal instability whereas Hall currents and suspended particles are found to hasten the onset of thermal instability for permissible range of values of various parameters. Also, the dispersion relation is analyzed numerically and the results shown graphically. The critical Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. The visco-elasticity, suspended particles and Hall currents (hence magnetic field introduce oscillatory modes in the system which were non-existent in their absence. [ABSTRACT FROM AUTHOR]

In this paper, a study of double diffusive convection in an anisotropic porous layer, saturated with viscoelastic fluid, heated form below, and cooled from above, has been performed; the fluid and solid phases are not in thermal equilibrium. Extended Darcy model, which includes the time derivative term in the momentum equation, has been used. For the fluid and solid phase temperature fields, a two-field model has been used separately for energy equation. Linear stability analysis is performed, using normal mode technique, and the expression for Rayleigh number has been obtained. It is found that small inter-phase heat coefficient has substantial effect on the stability of the system. The criterion for both stationary and oscillatory convection is derived analytically. The effects of various parameters on the stability of the system have been investigated. A weak nonlinear stability analysis based on the truncated representation of Fourier series is performed to find Nusselt number and Sherwood number. Further, we studied the transient behavior of the Nusselt number and Sherwood number by solving the finite amplitude equations using a numerical method. The results obtained during the analysis have been presented graphically. A study of streamlines, isotherms, and isohalines has been also made for fluid and solid phases. [ABSTRACT FROM AUTHOR]

Combined heat and mass transfer process by natural convection from a wavy vertical surface immersed in a fluid-saturated semi-infinite porous medium due to Soret and Dufour effects for Forchheimer extended non-Darcy model has been analyzed. A similarity transformation followed by a wavy to flat surface transformation is applied to the governing coupled non-linear partial differential equations, and they are reduced to boundary layer equations. The obtained boundary layer equations are solved by finite difference scheme based on the Keller-Box approach in conjunction with block-tridiagonal solver. Detailed simulations are carried out for a wide range of parameters like Groshof number ( Gr*), Lewis number ( Le), Buoyancy ratio ( B), Wavy wall amplitude ( a), Soret number ( S), and Dufour number ( D). Comparison tables local and average Nusselt ( Nu) number, local and average Sherwood ( Sh) number plots are presented. [ABSTRACT FROM AUTHOR]

We study thin film instabilities in liquid films with deformable surface using the lubrication theory. An externally applied vertical temperature gradient may give cause to an instability (Marangoni instability) of the flat motionless film. Contrary to the earlier work where mostly pure fluids were discussed, the focus of the present paper lays on instabilities in mixtures of two completely miscible liquids. We show that the normally found monotonic long-wave instability may turn into an oscillatory one if the two components have a different surface tension and if the Soret coefficient establishes a stabilizing vertical concentration gradient. A systematic derivation of the basic equations in long-wave approximation is given. The character of instabilities is studied using linear stability analysis. Finally, a real system consisting of a water-isopropanol mixture is discussed in some detail. [ABSTRACT FROM AUTHOR]