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The influence of Rayleigh friction and chemical reaction on the onset of double‐diffusive convection in a Navier–Stokes–Voigt (NSV) fluid layer is investigated by conducting linear instability and nonlinear stability analyses. The fluid layer is subjected to isothermal conditions and chemical equilibrium at the boundaries. The solubility of the dissolved component exhibits a linear dependency on temperature. The analysis is conducted for two distinct cases: the fluid layer is heated and salted from the bottom (case‐1), and the fluid layer is heated from the bottom and salted from the top (case‐2). Analytical expressions for the thermal Rayleigh number are obtained for both linear and nonlinear theories, and these expressions depend on Kelvin–Voigt, Rayleigh friction, solutal Rayleigh, Lewis, Prandtl, and Damkohler numbers. Including the Rayleigh friction term in the NSV fluid model improves the stability of the system and hence instability occurs with less ease. For lower solutal Rayleigh numbers, convection commences in the stationary mode and subsequently transitions to the traveling wave mode occurred in case‐1. The Damkohler number plays a significant role in the linear instability thresholds. It is also found that the Kelvin–Voigt number acts as a stabilizing factor for oscillatory mode convection. The comparison between linear and nonlinear thresholds unveils the region characterized by subcritical instability. [ABSTRACT FROM AUTHOR]

Geothermal gradients and heterogeneous permeability are commonly observed in natural geological formations for underground CO $_2$ sequestration. In this study, we conduct three-dimensional direct numerical simulations on the double-diffusive convection with both unstable temperature and concentration gradients in homogeneous and heterogeneous porous media. For homogeneous porous media, the root-mean-squared velocity increases linearly with density ratio defined as the buoyancy ratio by temperature and concentration differences. The flow structures show no remarkable changes when temperature Rayleigh number ${Ra}_T$ is less than its critical value, but alter from sheet-like to cellular structures as ${Ra}_T$ surpasses this threshold. The concentration wavenumber scales approximately as $k_{rS}\sim {Ra}_e^{0.47}$ with a defined effective Rayleigh number ${Ra}_e$. By using a scale analysis, the concentration flux exhibits a consistent linear relation with the total driving forces for all simulations. For heterogeneous porous media, where the Dykstra–Parsons coefficient $V_{DP}$ and correlation length $l_{r}$ determine the spatial distribution of the permeability field, the flow is strengthened in places with higher permeability. The velocity and concentration flux are less affected by $l_{r}$ than that by $V_{DP}$. For small correlation length, the flow structures coarsen and their characteristic width generally increases with increasing heterogeneity. For large correlation length, small structures emerge in the regions with large permeability, which can be attributed to the intensified local Rayleigh number triggering more vigorous convection there. The variations of concentration flux with $l_{r}$ and $V_{DP}$ can be explained by the portion of area covered by high concentration with large vertical velocity near the boundaries. [ABSTRACT FROM AUTHOR]

The current article focuses on the examination of nonlinear instability and dynamic transitions in a double-diffusive rotating couple-stress fluid layer. The analysis was based on the newly developed dynamic transition theory by T. Ma and S. Wang. Through a comprehensive linear spectrum analysis and investigation of the principle of exchange of stability (PES) as the thermal Rayleigh number crosses a threshold, the nonlinear orbital changes during the transition were rigorously elucidated utilizing reduction methods. For both single real and complex eigenvalue crossings, local pitch-fork and Hopf bifurcations were discovered, and directions of these bifurcations were identified along with transition types. Furthermore, nondimensional transition numbers that signify crucial factors during the transition were calculated and the orbital structures were illustrated. Numerical studies were performed to validate the theoretical results, revealing the relations between key parameters in the system and the types of transition. The findings indicated that the presence of couple stress and a slow diffusion rate of solvent and temperature led to smoother nonlinear transitions during convection. [ABSTRACT FROM AUTHOR]

This article explains the heat and mass transfer of electrically conducting Newtonian fluid in double‐diffusive magnetoconvective flow. We have considered two infinite horizontal plates at a constant distance apart under the concentration‐modulated boundary condition. A constant magnetic field is considered in vertically upward directions, which generates an induced magnetic field. We have used the weakly nonlinear analysis to obtain the heat and mass transfer rate using the Ginzburg–Landau equation. The software MATHEMATICA is used to determine the solution of the Ginzburg–Landau equation by inbuilt function. The effects of physical parameters that occurred in the study on the Nusselt number and Sherwood number have been examined graphically. Modulation has a negligible effect on the threshold value of the thermal Rayleigh number, that is, on stationary convection. Moreover, it was found that the Chandrasekhar number, magnetic‐Prandtl number, amplitude of modulation, and frequency of modulation are proportional to the heat and mass transports. [ABSTRACT FROM AUTHOR]

In the present work, the influence of the aspect ratio of the rectangular cavity (length > width) and the built-in rectangular blockage (length > width) on the local and global entropy generation (EG) characteristics due to double-diffusive convection and external magnetic field have been explored. Particularly, the effect of the pertinent parameters, such as the aspect ratio of the cavity (A R = 2 − 4) and blockage (a r = 2 − 4) , Lewis number (L e = 2 − 10) , Rayleigh number ( 10 3 ≤ R a ≤ 10 5) , Hartmann number (0 ≤ H a ≤ 100) , and buoyancy ratios (− 2 ≤ N ≤ 2) on the EG characteristics have been explored. The working fluid is considered to be a liquid metal-sodium–potassium alloy (Pr = 0.054). Lattice Boltzmann method numerical scheme is employed to solve the double-diffusive natural convection phenomenon. The increase in Ra induces an enhancement in the localized EG terms, whereas the augmentation in Ha diminishes the local total EG (STotal) for a given Ra. The dominance of thermal and species transport irreversibility (B e avg > 0.5) in the cavity was noticed for A R = 2 , N = 2. Conversely, for AR = 4, the significance of flow friction irreversibility within the cavity was observed ( B e avg ≤ 0.5 ). The results of the work are also summarized in terms of simpler empirical correlations of S F F , S C , and ST, which might be useful for possible engineering design purposes. [ABSTRACT FROM AUTHOR]

In this article, the onset of double-diffusive convection with the effect of viscous dissipation in a horizontal fluid-saturated porous layer is examined. Two impermeable isothermal and isosolutal walls bound the porous layer, and Darcy's law models the flow. The onset of convective instability is studied by two approaches: the linear stability analysis and the nonlinear stability analysis. The nonlinear stability analysis is performed by utilizing the energy method. The literature on the nonlinear stability analysis of onset of convective instability with the viscous dissipation effect is limited. The present article aims to fill this gap. It is observed that, when the fluid is at rest, the effect of viscous dissipation does not influence the critical thermal Rayleigh number corresponding to both the linear and nonlinear stability analyses. Moreover, sub-critical instabilities do not occur when R a S > 0 . But in contrast, the region of sub-critical instabilities increases along the negative R a S direction. [ABSTRACT FROM AUTHOR]

The analysis of entropy generation provides valuable information for the design and optimization of thermal systems. Solar stills are used for water desalination and purification. Using renewable energies, they provide a sustainable solution for drinking water supply in remote areas and off-grid situations. This work focuses on the 3D numerical study of entropy generation in a two-stage solar still subjected to the natural double diffusion convection phenomenon in the presence of CNT nanoparticles. The effects of Rayleigh number, buoyancy ratio, and nanofluid concentration on thermal, solutal, and viscous irreversibilities and flow structure were studied. The results show that increasing the buoyancy ratio leads to an increase in thermal and solutal entropy generation. The results of this study also show that total entropy is minimal for positive volume force ratios, N, at a nanoparticle volume fraction of around 3%, and for negative N ratios, at a volume fraction of around 4%. [ABSTRACT FROM AUTHOR]

The influence of the throughflow and gravity fluctuation on thermosolutal convection in an anisotropic porous bed with the Darcy–Brinkman effect is considered numerically. The critical Rayleigh numbers for the onset of stationary and oscillatory modes have been found via linear instability analysis. The impact of various gravitational functions in the presence of throughflow on stability is studied. The analysis has been carried out for decreasing and increasing gravity fluctuations. The convective problem has been numerically analyzed using a single-term Galerkin approach. The results show that the mechanical anisotropy parameter and Lewis number have a destabilizing effect, while the thermal anisotropy parameter, Darcy number, solutal Rayleigh number, throughflow parameter, and gravity parameter have a stabilizing effect on stationary and oscillatory convection. It is clear that the system changes in a way that makes it more stable for case (iii) gravity fluctuation and more unstable for case (iv) gravity fluctuation. [ABSTRACT FROM AUTHOR]

The present analysis mathematically investigates the thermohaline convection problem in viscoelastic fluid layer saturating porous media by utilizing the modified Boussinesq approximation. By performing linear stability analysis, the Darcy–Rayleigh numbers for stationary and oscillatory modes of convection are derived. The effects of different parameters describing the problem are studied numerically. In nonlinear stability analysis, the heat and mass transfer rates in the form of Nusselt and Sherwood numbers, respectively, are obtained for oscillatory convection using the derived Ginzburg–Landau equation. From the results, it is observed that overstability is the preferred mode of instability in linear stability. It is found that in linear double‐diffusive convection problems, the stress relaxation imparts a destabilizing effect whereas the strain retardation time, the coefficient of specific heat variation due to temperature, and the concentration gradient have a stabilizing effect on the system's stability. The numerical values of heat and mass transfer rates varied with the coefficient of specific heat showing that the heat transport decreases while the mass transport increases. Also, the stress relaxation time, the concentration gradient, and the gravity modulation's amplitude increase while the strain retardation time decreases the heat and mass transfer rates. The wavelength of oscillations remains unaltered with the variation of specific heat variation due to temperature. The modulation frequency does not affect the heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency. [ABSTRACT FROM AUTHOR]

In this paper, simulations of two-dimensional (2D) double-diffusive convection in an inclined cavity were conducted using a high-accuracy numerical method. The cavity is gradually turned in the range 0 ° – 90 ° to study how the initial conditions affects the flow mode transition, as well as heat and mass transfer. Rayleigh numbers in the range of 1 0 3 ≤ R a ≤ 1 0 5 , the Prandtl number (P r) ranging from 0.1 to 5.0, the Lewis number (L e) from 0.2 to 20 and the buoyancy ratio (N) from 0 to 2 are considered in the computations. For R a = 1 0 3 , only one vortex fills the cavity, and the efficiency of heat and mass transfer decreases monotonically with increasing inclination angle (α). As the Rayleigh number increases to R a = 1 0 4 and R a = 1 0 5 , the flow becomes more complex, with the presence of either one or two vortices exhibiting different convective intensities within the cavity. Due to the highly nonlinear nature of the system, hysteresis is observed, resulting in two branches of the solution in the range of α ∈ (67 ° , 72 °) for R a = 1 0 4 and α ∈ (69 ° , 90 °) for R a = 1 0 5 . Except for α = 90 ° , the efficiency of heat and mass transfer first decreases and then increases with increasing N from 0 to 2. With increasing Prandtl number, the heat and mass transfer become higher and higher in the oscillation, and two branches of the solution are observed in the range of P r ∈ (0. 1 , 5 ] for R a = 1 0 4 and P r ∈ [ 0. 1 , 0. 9) for R a = 1 0 5 . Similarly, the heat and mass transfer increase with increasing Lewis number, and two branches of the solution are obtained in the range of 1. 0 < L e < 5. 0 for the considered Rayleigh numbers. • Bifurcation in convection at inclination angles of 60°–90°. • Two-vortex heat transfer exceeds single at 70°–90° by 25%. • Enhanced heat and mass transfer with increasing P r or L e. • Bifurcation occurs in liquid metals heat/mass transfer at specific inclination angles. [ABSTRACT FROM AUTHOR]

This work employs single-mode equations to study convection and double-diffusive convection in a porous medium where the Darcy law provides large-scale damping. We first consider thermal convection with salinity as a passive scalar. The single-mode solutions resembling steady convection rolls reproduce the qualitative behavior of root-mean-square and mean temperature profiles of time-dependent states at high Rayleigh numbers from direct numerical simulations (DNS). We also show that the single-mode solutions are consistent with the heat-exchanger model that describes well the mean temperature gradient in the interior. The Nusselt number predicted from the single-mode solutions exhibits a scaling law with Rayleigh number close to that followed by exact 2D steady convection rolls, although large aspect ratio DNS results indicate a faster increase. However, the single-mode solutions at a high wavenumber predict Nusselt numbers close to the DNS results in narrow domains. We also employ the single-mode equations to analyze the influence of active salinity, introducing a salinity contribution to the buoyancy, but with a smaller diffusivity than the temperature. The single-mode solutions are able to capture the stabilizing effect of an imposed salinity gradient and describe the standing and traveling wave behaviors observed in DNS. The Sherwood numbers obtained from single-mode solutions show a scaling law with the Lewis number that is close to the DNS computations with passive or active salinity. This work demonstrates that single-mode solutions can be successfully applied to this system whenever periodic or no-flux boundary conditions apply in the horizontal. [ABSTRACT FROM AUTHOR]

This paper discusses the theoretical aspects of the effect of salt fingers on heat transfer for different non‐uniform concentration profiles in a micropolar liquid layer kept between two parallel plates of infinite extent separated by a thin layer, heated and soluted from above. The onset of salt finger convection (convection due to the salt finger process) is studied through the linear stability analysis theory. The system of partial differential equations is solved numerically using the normal mode analysis method and the required solution is found by applying the Galerkin method. The effect of heat transfer and concentration of micropolar liquid is obtained for (i) free–free, (ii) rigid–rigid, and (iii) rigid–free isothermal, permeable with no‐spin boundary conditions. The effect of different micropolar parameters (i.e., coupling parameter, micropolar heat conduction parameter, couple stress parameter, and inertia parameter) has been analyzed on the onset of stationary convection, and the results are depicted graphically. It is shown that different non‐uniform concentration gradients, diffusivity ratio, coupling parameter, and solutal Rayleigh number influence the heat transfer in the system. The phase of concentration flow for different boundary conditions is compared and analyzed. [ABSTRACT FROM AUTHOR]

A three-dimensional computational study of double-diffusive natural convection was conducted to explore the impact of tilt on the thermal and solutal performance of a floating pyramidal solar still filled with an air-steam mixture. In the present work, the still is cooled from the upper walls and is maintained at a low vapor concentration. The bottom wall of the still is maintained at a hot temperature and high concentration. Four different models of baffles placed in the upper region of the solar still have been studied. The mathematical formulation of the equations governing the problem is based on the vector current potential -vorticity formalism. The numerical method of finite volumes is used. The effect of Rayleigh and tilt angle of the floating solar still on the flow structure, iso-temperatures, iso-concentrations, and heat and mass transfer rates were examined. The most relevant results of this study are (i) an uncooled air-vapor mixture outlet was observed during tilting for the solar still equipped with a small, flat baffle, (ii) triangular and curvilinear baffle configurations are suitable to guide the air-vapor mixture towards the cold walls during the tilting of the solar still floating on the sea, and (iii) the triangular baffle configuration is the most relevant design, enhancing thermal and solutal performance by 20%. [ABSTRACT FROM AUTHOR]

• The Soret and Dufour effects of double-diffusive convection over a rough surface are studied by using a TRT-LB model. • A sudden enhancement or attenuation in heat and mass transfer causes changes in the state and structure of flow. • Unexpected changes in the flow structure from reversal to period were identified after its long-term evolution. • Heat and mass transfer as well as the flow structure are most intimately related to the compactness of rough elements. This study examines the Soret and Dufour effects of double-diffusive convection (DDC) over a rough surface by using a lattice Boltzmann (LB) model with two-relaxation-time (TRT) collision operators, where the cross-diffusion terms are modeled by introducing additional collision operators that can be used to avoid the need for special treatment of the gradient terms. The TRT model is applied to improve the stability of the LB method for flows at high Rayleigh numbers. We investigate how rough surfaces with different distributions and compactness of rough elements affect heat and mass transfer as well as the flow structure of the DDC system with the Soret and Dufour effects. We examined five rough models with different spatial distributions of the triangular rough elements as well as different values of the Rayleigh number (R a = 10 6 and 10 9), Prandtl number (P r = 0.7), Lewis number (L e = 1 and 2), buoyancy ratio (− 2 ≤ N c ≤ 6.5), Soret factor (0 ≤ S T C ≤ 1), Dufour factor (0 ≤ D C T ≤ 1), and the height of the roughness (1 / 96 ≤ h ≤ 1 / 2). Specifically, the influence of the buoyancy ratio on the DDC system was investigated, and the relationship of heat and mass transfer with the buoyancy ratio was divided into four stages: conduction-dominated, transition, steady convection-dominated, and oscillatory convection-dominated stages. The rough surfaces reduced heat and mass transfer at low Rayleigh numbers and low height of the roughness, and the third rough model (Model III) yielded the highest reduction. The flow showed periodic behavior after long-term reversals in some cases, which appear to have not been observed in previous research. Moreover, the effects of the Soret and Dufour factors were examined, and it was found that mass and heat transfer could be enhanced in most cases by increasing their values. To enhance heat and mass transfer, the height of the roughness should be increased as well. Model III delivered the best performance, with a scenario completely opposite to that in case of a low roughness height. Finally, approximate values of the critical height of the roughness with different rough models were obtained such that heat and mass transfer were enhanced only when the height of the roughness was greater than a critical value. [ABSTRACT FROM AUTHOR]

This paper reports a numerical study of double-diffusive natural convection through an annular space delimited by a square cylinder on the outside and a cylindrical cylinder on the inside covered by a porous layer. The Darcy-Brinkmann-Forchheimer is used for modeling flow in both fluid and porous areas. The annular space is partially or completely filled with an isotropic porous medium. A finite volume method, using the Patankar-Spalding technique is used for solving the discretization of the dimensionless equations governing the problem. The effects of simultaneously applied thermal and solutal buoyancy forces on heat and mass transfer are shown in the results for a large range of buoyancy ratios, Rayleigh number, and thermal conductivity. Streamlines, isotherms, and iso-concentrations are presented to analyze the flow structure transition from mass species dominated to thermal dominated flow. Results show that the buoyancy ratio can change the flow pattern and the increased thermal conductivity ratio can improve heat and mass transfer. A good agreement was obtained between the present results and those published were found. [ABSTRACT FROM AUTHOR]

Linear and weakly nonlinear stability analyses of double-diffusive convection in two-component liquids with either potassium chloride (KCl) or sodium chloride (NaCl) aqueous solution, and heat being present is investigated in the paper for free, and rigid, isothermal, iso-solutal boundaries. Using the thermophysical values of the aqueous solutions, we have shown that the stationary convection is the preferred mode at onset and that sub-critical motion is possible. We found that the critical thermal Rayleigh number for water + NaCl + heat is higher compared to that of water + KCl+ heat. The study shows that for water + KCl + heat, the transition from convective motion to chaotic motion occurs at r H = 27.2 for free boundaries and at 48.5 for rigid boundaries. Here, r H denotes the Hopf thermal Rayleigh number. Further, the existence of windows of mildly chaotic points and fully periodic intervals are reported using Lyapunov exponents and bifurcation diagrams. Chaotic motions in both the aqueous solutions are nearly identical. The percentage increase in heat transport in the double-diffusive system involving NaCl is nearly 1% more than that of KCl in the case of free boundaries, whereas in the case of realistic boundaries it is nearly 1.6%. The comparison of the Nusselt and the Sherwood numbers between water + KCl and water + NaCl leads us to the conclusion that the aqueous solution with lower Lewis number transports maximum heat in the case of free boundaries and opposite is seen in the case of rigid boundaries due to the boundary effect. The many qualitative similarities between the results of artificial and realistic boundaries are highlighted. [ABSTRACT FROM AUTHOR]

In the present work, double-diffusive convection of salt finger is numerically investigated. A computational code based on the finite volume method with high-order accuracy and high resolution in space, implying a fifth-order scheme WENO5 for the nonlinear convective terms, a fourth-order centered scheme for the viscous terms, and the third-order TVD Runge–Kutta method used to approximate the unsteady term, was employed to solve the two-dimensional Navier–Stokes equations for a wide range of buoyancy ratio ( R ρ = 1.5 - 20 ) and thermal Rayleigh numbers ( R a T ∼ 10 3 - 10 8 ). In this framework, we focused on the evolution of salt fingers structures emphasizing the salt fingers/mixed layers interaction. This paper aims at analyzing the evolution of finger structures, by mean of both integrated and local quantities. The results show that for higher buoyancy ratio the dynamical behavior of blobs is governed by two symmetric counter-rotating vortices (dipolar structure) with circular-shapes. Whereas, for lower ratio the blobs are constituted of by two asymmetric counter-rotating vortices with stretch-shape. For the moderate Rayleigh number, it is also found that when the buoyancy ratio is higher, the system does not lead to the generation of new fingers. However, for the small buoyancy ratio, new finger generation was observed. The results obtained from the simulations were shown that for high Rayleigh number fingers length scale are proportional to the buoyancy ratio. We also find that fingers develop rapidly, their dynamic complexity increases with Rayleigh number. Furthermore, at high Rayleigh number, the intensity of the convection in the mixed layers is well formed and it is stronger at the beginning leading to the formation of salt-finger zone, sandwiched between them, and then it eventually decreases over time and allows the penetration of the fingers again especially for lower buoyancy ratio. Moreover, the more vigorous convection in the low buoyancy ratio cases distorts the fingers more and limits their length. In contrast, at low Rayleigh numbers no-shearing convection in the layers was created for both configurations lower and higher buoyancy ratio, while overturning the finger system was well observed. The mixing behavior is also investigated in this work using the probability density function of the salinity PDF(S*). It is shown that thermal Rayleigh number and buoyancy ratio have a large effect on the mixing properties of double-diffusive convection of salt fingers. [ABSTRACT FROM AUTHOR]

Purpose: The problem aims to find the effects of coupled cross-diffusion in micropolar fluid oversaturated porous medium, subjected to Double-Diffusive Chandrasekhar convection. Design/methodology/approach: Normal mode and perturbation technique have been employed to determine the critical Rayleigh number. Non-linear analysis is carried out by deriving the Lorenz equations using truncated Fourier series representation. Heat and Mass transport are quantified by Nusselt and Sherwood numbers, respectively. Findings: Analysis related to the effects of various parameters is plotted, and the results for the same are interpreted. It is observed from the results that the Dufour parameter and Soret parameter have an opposite influence on the system of cross-diffusion. Originality/value: The effect of the magnetic field on the onset of double-diffusive convection in a porous medium coupled with cross-diffusion in a micropolar fluid is studied for the first time. [ABSTRACT FROM AUTHOR]

The onset of double-diffusive convection in an electrically conducting fluid-saturated porous layer is studied. The convective flow in the porous medium is induced by horizontal temperature and concentration gradients with net horizontal mass throughflow. The effect of magnetic field on the instability of convection is taken into consideration. The stability of the steady-state solution is investigated in two different approaches, namely the linear instability analysis and nonlinear stability analysis. The nonlinear stability analysis is performed by constructing the energy functional. The eigenvalue problems which are derived from the stability analyses are numerically integrated using the shooting and Runge–Kutta methods. The variation in the critical thermal Rayleigh number against each flow governing parameter is shown graphically. It is observed that Hartman number H a 2 delays the onset of convection to commence and helps to reduce the region of subcritical instabilities. When the solute is concentrated at lower boundary of the porous layer, the onset of convection is in the form of stationary modes, but it switches to oscillatory mode of convection when the solute is concentrated at upper boundary. Interestingly, Hartman number H a 2 plays an important role in delaying this transition from stationary mode to oscillatory mode of convection. [ABSTRACT FROM AUTHOR]

When fluid stratification is induced by the vertical gradients of two scalars with different diffusivities, double-diffusive convection (DDC) may occur and play a crucial role in mixing. Such a process exists in many natural and engineering environments. Especially in the ocean, DDC is omnipresent since the seawater density is affected by temperature and salinity. The most intriguing phenomenon caused by DDC is the thermohaline staircase, i.e., a stack of alternating well-mixed convection layers and sharp interfaces with very large gradients in both temperature and salinity. Here we investigate DDC and thermohaline staircases in the salt finger regime, which happens when warm saltier water lies above cold fresher water and is commonly observed in the (sub)tropic regions. By conducting direct numerical simulations over a large range of parameters, we reveal that multiple equilibrium states exist in fingering DDC and staircases even for the same control parameters. Different states can be established from different initial scalar distributions or different evolution histories of the flow parameters. Hysteresis appears during the transition from a staircase to a single salt finger interface. For the same local density ratio, salt finger interfaces in the single-layer state generate very different fluxes compared to those within staircases. However, the salinity flux for all salt finger interfaces follows the same dependence on the salinity Rayleigh number of the layer and can be described by an effective power law scaling. Our findings have direct applications to oceanic thermohaline staircases. [ABSTRACT FROM AUTHOR]

The model of thermosolutal convection in a fluid‐saturated bidisperse porous medium of Darcy type is studied in this paper. The permeability is allowed to be horizontally isotropic for both the macro‐ and microphases. The linear instability and nonlinear stability are analyzed by taking the Soret effect into account. Furthermore, the effect of anisotropy parameter, Soret coefficient, and other physical parameters on the stability of the system are investigated. It is shown that the linear instability boundaries and the energy stability boundaries do not coincide when the layer is heated and salted from below, where a region of potential subcritical instability occurs. The results reveal that the horizontal to vertical permeability ratio plays a crucial role in the stability of the system. It is also observed that for large values of the salt Rayleigh number, the onset of thermal convection is more likely to be via oscillatory convection rather than stationary convection. Furthermore, the onset of stationary convection is significantly influenced by the presence of the Soret coefficient. [ABSTRACT FROM AUTHOR]

We investigate the double-diffusive instability in an inclined porous layer with a concentrationbased internal heat source by conducting linear instability and nonlinear energy analyses. The effects of different dimensionless parameters, such as the thermal (RaT) and solutal (RaS) Rayleigh numbers, the angle of inclination (f), the Lewis number (Le) and the concentration-based internal heat source (Q) are examined. A comparison between the linear and nonlinear thresholds for the longitudinal and transverse rolls provides the region of subcritical instability. We found that the system becomes more unstable when the thermal diffusivity is greater than the solute and the internal heat source strength increases. It is observed that the system is stabilized by increasing the angle of inclination. While the longitudinal roll remains stationary without the region of subcritical instability, as the angle of inclination increases, the transverse roll switches from stationary-oscillatory-stationarymode. Our numerical results show that for RaS <0, for all Q values, the subcritical instability only exists for transverse rolls. For RaS ≥ 0, however, the subcritical instability appears only for Q=0 and Q ≥ 0, respectively, for longitudinal and transverse rolls. [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]

In this research article, we investigated the weakly non-linear effect of gravity modulation for the temperature dependent viscous fluid in a horizontal porous layer in the presence of internal heat source. We use power series expansion in terms of the amplitude of gravity modulation, which is considered to be small for double-diffusive convection in porous media. We graphically show the effect of internal heat source, solute Rayleigh number, Lewis number, Vadász number, thermo-rheological parameter, the amplitude of gravity modulation, the frequency of modulation on the heat and mass transfer using Ginzburg-Landau equation. The effect of gravity modulation is found significant and is more effective for the low values of frequency of modulation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the well‐posedness of the initial and boundary value problem for the double‐diffusive convection system in a bounded domain Ω ⊂ R 3. We first prove the local existence of the unique strong solution with large initial data in H 0 1 ( Ω ) and then extend it to a global one provided the L2 norm of the initial data is small. [ABSTRACT FROM AUTHOR]

We numerically simulate the initiation of an average convective flow in a system composed of a horizontal binary fluid layer overlying a homogeneous porous layer saturated with the same fluid under gravitational field and vibration. In the layers, fixed equilibrium temperature and concentration gradients are set. The layers execute high-frequency oscillations in the vertical direction. The vibration period is small compared with characteristic timescales of the problem. The averaging method is applied to obtain vibrational convection equations. Using for computation the shooting method, a numerical investigation is carried out for an aqueous ammonium chloride solution and packed glass spheres saturated with the solution. The instability threshold is determined under two heating conditions—on heating from below and from above. When the solution is heated from below, the instability character changes abruptly with increasing solutal Rayleigh number, i.e., there is a jump-wise transition from the most dangerous shortwave perturbations localized in the fluid layer to the long-wave perturbations covering both layers. The perturbation wavelength increases by almost 10 times. Vibrations significantly stabilize the fluid equilibrium state and lead to an increase in the wavelength of its perturbations. When the fluid with the stabilizing concentration gradient is heated from below, convection can occur not only in a monotonous manner but also in an oscillatory manner. The frequency of critical oscillatory perturbations decreases by 10 times, when the long-wave instability replaces the shortwave instability. When the fluid is heated from above, only stationary convection is excited over the entire range of the examined parameters. A lower monotonic instability level is associated with the development of perturbations with longer wavelength even at a relatively large fluid layer thickness. Vibrations speed up the stationary convection onset and lead to a decrease in the wavelength of most dangerous perturbations of the motionless equilibrium state. In this case, high enough amplitudes of vibration are needed for a remarkable change in the stability threshold. The results of numerical simulation show good agreement with the data of earlier works in the limiting case of zero fluid layer thickness. [ABSTRACT FROM AUTHOR]

A linear stability problem for mechanical equilibrium in an inhomogeneous fluid-saturated porous layer underlying a horizontal binary fluid layer is numerically simulated. The layers are subjected to high-frequency vertical vibration in a gravity field. Different values of temperature and concentration are fixed at the outer impermeable boundaries of the two-layer system. Porosity of a porous layer linearly depends on a transverse z -coordinate. Permeability is given by the Carman-Kozeny formula. To describe a fluid flow in layers, we use the vibrational convection equations written in the Boussinesq approximation and obtained by the averaging method. It is shown that when the fluid is heated from below, vibration effectively increases the equilibrium stability threshold and wavelength of its most dangerous perturbations. If a temperature gradient coincides with the direction of a concentration gradient for the heavier component of binary fluid, average convection is excited in an oscillatory manner. In the opposite case, there is a monotonic instability of equilibrium. Effects of the dimensionless porosity gradient m z and vibrational parameter p v on the instability threshold are studied. For p v < 0.0134 and a fixed solutal Rayleigh number ( - 5 ⩽ R mc ⩽ 15 ) an abrupt jump-like transition from the long-wave to short-wave most dangerous perturbations occurs as m z grows in the range of 0.030–0.162. Long-wave perturbations penetrate both layers. Short-wave perturbations mainly locate in the fluid layer. The transition is smoothed for p v > 0.0134 . When the fluid is heated from above, wavelength of critical perturbations smoothly varies with a change in p v and m z . A convective fluid flow arises monotonously and mostly in the form of long wavelength rolls (a wave number is of k < 3.3 ). Vibration weakly lowers the equilibrium stability threshold in layers. The effect is most pronounced at high enough Rayleigh numbers ( R m = - 40 ) for a porous medium with the porosity increasing with depth at m z = - 0.2 . [ABSTRACT FROM AUTHOR]

A numerical study of the 3-D double-diffusive natural convection in an inclined solar distiller was established. The flow is considered laminar and caused by the interaction of thermal energy and the chemical species diffusions. The governing equations of the problem, are formulated using vector potential-vorticity formalism in its 3-D form, then solved by the finite volumes method. The Rayleigh number is fixed at Ra = 105 and effects of the buoyancy ratio and inclination are studied for opposed temperature and concentration gradients. The main purpose of the study is to find the optimum inclination angle of the distiller which promotes the maximum mass and heat transfer. [ABSTRACT FROM AUTHOR]

• Transient numerical simulation of double diffusive convection. • Long duration simulations revealing complete life-span of layers. • Regimes of successive and spontaneous layering and merger. • Effect of layering on heat transfer characteristics. A recent observation revealed that alternating layers of milk and coffee-enriched regions are formed when espresso is poured into steamed milk Xue et al. This is generally known as double-diffusive convection (DDC), often seen in oceans, solidifying mixtures, etc. Inspired by this observation, we report an extensive numerical investigation of DDC, for a system having a linearly stable solute stratification of an aqueous solution exposed to lateral thermal cooling from a sidewall. The phenomenon is analyzed with the help of finite-volume-based numerical solutions of the conservation equations (continuity, momentum, energy, and species) for two-dimensional, unsteady, laminar convection. A large number of simulations, covering a wide range of thermal Rayleigh numbers ( 10 5 ≤ R a T ≤ 10 8) and solutal Rayleigh numbers (10 6 ≤ R a S ≤ 10 8) , revealed the transitions between four different flow regimes in the form of correlations of the two Rayleigh numbers. The analysis of the overall time of survival of double-diffusive layers (DDLs) for a wide range of R a S & R a T established that the time of survival follows the same proportionality with R a S & R a T as the curve of onset of the spontaneous layered regime. In addition to the transient evolution of flow and transport variables (composition, temperature and density fields), the heat transfer coefficients at the sidewalls were obtained for the whole life-span of DDLs. While the influence of DDLs in rendering an alternating high and low wall heat transfer was evident, the overall heat transfer was also found to be significantly lower when compared with the absence of DDC. These findings explain why a layered latte remains hotter for a larger duration. [ABSTRACT FROM AUTHOR]

In this paper, double-diffusive convection of power-law nanofluids in rectangular enclosures is investigated in detail with regularized lattice Boltzmann method. In order to appropriately treat the external force appears in the fluid field, a unified forcing term is also incorporated in the evolution equation such that the Navier–Stokes equations can be recovered correctly. The fluid in the cavity is a water-based nanofluid containing Cu nanoparticles, and the numerical simulations presented here span a wide range of thermal Rayleigh number ( 10 4 ⩽ Ra ⩽ 10 6 ), volume fraction of nanoparticles ( 0 ⩽ ϕ ⩽ 0.1 ), power-law index ( 0.5 ⩽ n ⩽ 1.5 ), buoyancy ratio ( - 1.0 ⩽ Nc ⩽ 1.0 ), Lewis number ( 1 ⩽ Le ⩽ 50 ) and aspect ratio ( 0.125 ⩽ AR ⩽ 8 ) to identify the different flow patterns, temperature and concentration distributions. The results show that the augmentation of the nanoparticle volume fraction increases the average Nusselt number but reduces the average Sherwood number. In addition, the average Nusselt and Sherwood numbers are generally decrease with an increase in the power-law index. Further, it was observed that the average Nusselt and Sherwood numbers increase with increasing AR up to an aspect ratio value of AR max at which the maximum values of Nu av and Sh av are obtained. For AR > AR max , the mean Nusselt and Sherwood numbers start to decrease with increasing AR . What’s more, we also found that the average Nusselt number obtained in some shallow enclosures is abnormally increased with the increase of power-law index. [ABSTRACT FROM AUTHOR]

Development of a real-time Mach–Zehnder based dual wavelength interferometry technique for studying the double-diffusive convection phenomena is presented. The interferometer employs two different monochromatic light sources with wavelengths of λ 1 = 632.8 nm and λ 2 = 457.9 nm. A high resolution color CCD sensor has been employed to record the interferograms that carry phase information pertaining to the coupled effects of the two wavelengths used. Phenomenon of double-diffusive convection has been set up in a two-layered salt-stratified solution that is destabilized by isothermal heating at the bottom wall of the test cell. The resultant changes in the thermal and solutal fields have been simultaneously captured using the developed interferometric technique. Experiments have been performed at a stability ratio of R ρ = 1.02 and thermal Rayleigh number of Ra T = 6.0 × 10 5 . The work presents a detailed methodology for quantitative determination of temperature and/or concentration fields from a single dual wavelength interferogram. Results have been presented in the form of dual color interferometric images and contours of whole-field temperature distribution as a function of experimental run time. The two-dimensional contours of concentration field at time instant t = 0 min have been presented. The observed variations in the fringe patterns are primarily due to thermal gradients prevailing in the fluid layer. In addition to the quantitative studies, interferometer also acts as a flow visualization tool and fringe patterns give qualitative insights into the flow field. The fringe patterns indicate towards the possibility of the existence of mechanical coupling between the two fluid layers wherein the direction of circulatory movement of fluids in each layer is oppositely oriented. [ABSTRACT FROM AUTHOR]

• A comprehensive and detailed solution of double-diffusive natural convection of Casson fluids in an enclosure is obtained. • The influence of the governing parameters on fluid flow, morphology of yielded/unyielded regions, and heat and mass transfer are thoroughly examined. • The unyielded regions grow with decreasing buoyancy ratio and increasing the yield number. • The Lewis number has different effects on unyielded areas depending on the flow parameters. • Correlations for average Nusselt and Sherwood numbers are provided. This study investigates the double-diffusive natural convection of the non-Newtonian Casson fluid in a square cavity based on the original viscoplastic stress model without simplification. Therefore, yield stress plays an essential role in understanding fluid behavior. The finite element approach provided a numerical solution to continuity, momentum, energy, and species governing equations. The governing parameters for this problem are Rayleigh number, Ra , yield number, Y , buoyancy ratio number, Nr , and Lewis number, Le. The influence of these parameters on heat and mass transfer, the morphology of yielded/unyielded regions, and fluid flow are thoroughly examined. The results show that unyielded regions increase at high Rayleigh numbers, despite the increase in buoyancy force and consequently increased heat and mass transfer. On the other hand, as the buoyancy ratio drops, the flow's strength and heat and mass transmission diminish, leading to an increase in plug regions. Accordingly, the mechanisms influencing the growth of unyielded regions are complex and follow different patterns. However, the plug regions always grow with increasing Y. The results indicate that increasing the Lewis number (mass transfer) reduces the effect of the buoyancy ratio on flow, heat transfer, and the unyielded regions in every case. Quantitative analysis of the results indicates that, while buoyancy ratio affects heat and mass transfer almost equally, the Lewis number increases mass transfer up to three times the heat transfer. Meanwhile, changing the buoyancy ratio can increase the maximum yield stress to 400%, while changing the Lewis number has a maximum effect of 20%. [Display omitted] [ABSTRACT FROM AUTHOR]

Direct atmospheric greenhouse gas emissions can be greatly reduced by CO 2 sequestration in deep saline aquifers. One of the most secure and important mechanisms of CO 2 trapping over large time scales is solubility trapping. In addition, the CO 2 dissolution rate is greatly enhanced if density-driven convective mixing occurs. We present a systematic analysis of the prerequisites for density-driven instability and convective mixing over the broad temperature, pressure, salinity and permeability conditions that are found in geological CO 2 storage. The onset of instability (Rayleigh–Darcy number, Ra ), the onset time of instability and the steady convective flux are comprehensively calculated using a newly developed analysis tool that accounts for the thermodynamic and salinity dependence on solutally and thermally induced density change, viscosity, molecular and thermal diffusivity. Additionally, the relative influences of field characteristics are analysed through local and global sensitivity analyses. The results help to elucidate the trends of the Ra , onset time of instability and steady convective flux under field conditions. The impacts of storage depth and basin type (geothermal gradient) are also explored and the conditions that favour or hinder enhanced solubility trapping are identified. Contrary to previous studies, we conclude that the geothermal gradient has a non-negligible effect on density-driven instability and convective mixing when considering both direct and indirect thermal effects because cold basin conditions, for instance, render higher Ra compared to warm basin conditions. We also show that the largest Ra is obtained for conditions that correspond to relatively shallow depths, measuring approximately 800 m, indicating that CO 2 storage at such depths favours the onset of density-driven instability and reduces onset times. However, shallow depths do not necessarily provide conditions that generate the largest steady convective fluxes; the salinity determines the storage depth at which the largest steady convective fluxes occur. Furthermore, we present a straight-forward and efficient procedure to estimate site-specific solutal Ra that accounts for thermodynamic and salinity dependence. [ABSTRACT FROM AUTHOR]

Abstract: A model for double-diffusive convection in an anisotropic porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear threshold accurately predicts on the onset of instability in the steady state throughflow. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold. [Copyright &y& Elsevier]

Abstract: Double-diffusive convection of a binary mixed fluid in a rectangular enclosure with horizontal temperature and concentration gradients is numerically investigated. The problem with thermal Rayleigh numbers of and , the Prandtl number being range of [0.015,12], the Lewis number being range of [0.05,100], the buoyancy ratio of , and the height-to-width aspect ratio of 2 are considered. A compact difference method with fully fourth-order accuracy and high resolution in space, involving a, at least, fourth-order upwind compact scheme suggested for approximation of the nonlinear convective terms, a fourth-order symmetrical compact scheme to discretize the viscous terms and the third-order TVD Runge–Kutta method employed for time discretization, is proposed for solving this unsteady double-diffusive convection problem. The effects of Prandtl and Lewis numbers on flow structure, the temperature and concentration distribution are investigated and discussed for and respectively in a rectangular enclosure with the aspect ratio . A bifurcation for the double-diffusive convection is captured with the variation of Prandtl number, and two different types of periodic flow motion with Lewis number in different ranges are observed. [Copyright &y& Elsevier]

In this study, the effect of radiation on double-diffusive natural convection is investigated by considering the phenomena of Soret and Dufour in complex geometry, for the first time. The multi-time relaxation lattice Boltzmann method has been adopted to calculate the momentum, energy, and species equations. The radiative transfer equation has been solved using the finite volume method. Complex boundaries have been simulated by the sharp interface-immersed boundary method. The influences of effective parameters including the optical thickness (τ = 1 to 100), Rayleigh number (Ra = 104 and 105), Planck number (Pl = 0.01 to 1), Buoyancy ratio (Br = − 5 to 5), Soret number (S r = − 1 to 1), and Dufour number (D f = − 1 to 1) have been analyzed on the flow field, heat, and mass transfer in a square cavity with an internal circular cylinder. Moreover, temporal variations of velocity and phase space trajectory have been used to study the effects of radiation on unsteady flow behavior. Results indicate that, the increment in optical thickness significantly reduces radiation, while a sweep behavior occurs in mass and heat transfer. Increasing the Dufour (Soret) parameter depending on the value of the Soret (Dufour) parameter can increase or decrease the mass (heat) transfer. • Double diffuse convection in an irregular geometry • The effects of Soret & Dufour numbers are investigated on Nusselt and Sherwood numbers. • The effects of radiation are studied on flow field, heat and mass transfer. • Time history of velocity and phase space trajectory are analyzed. • The Immersed boundary method has been used to model carved boundary [ABSTRACT FROM AUTHOR]

Abstract: The onset of buoyancy driven convection in a transient boundary layer at large Rayleigh numbers is discussed theoretically by using a minimal yet powerful method proposed by Howard. The method is applied to thermal and Soret-driven convection in bulk fluid layers, in Hele-Shaw geometries and in porous media with, respectively, isothermal as well as constant heat flux boundary conditions. Scaling laws for the onset latency time and the critical boundary layer height are derived for the cases under consideration. The crossover Rayleigh numbers, above which even in a Hele-Shaw geometry the bulk scaling laws apply, are also discussed. [Copyright &y& Elsevier]

The linear and non-linear stability of a rotating double-diffusive reaction-convection in a horizontal anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated considering a Darcy model that includes the Coriolis term. The effect of Taylor number, mechanical, and thermal anisotropy parameters, reaction rate, solute Rayleigh number, Lewis number, and normalized porosity on the stability of the system is investigated. We find that the Taylor number has a stabilizing effect, chemical reaction may be stabilizing or destabilizing and that the anisotropic parameters have significant influence on the stability criterion. The effect of various parameters on the stationary, oscillatory, and finite-amplitude convection is shown graphically. A weak nonlinear theory based on the truncated representation of Fourier series method is used to find the finite amplitude Rayleigh number and heat and mass transfer. [ABSTRACT FROM AUTHOR]

Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy's framework for a porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy--Rayleigh number increases with increasing value of the solutal Darcy--Rayleigh number in the absence of crossdiffusive parameters. The critical Darcy--Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below. [ABSTRACT FROM AUTHOR]

Abstract: Turbulent double-diffusive natural convection in a square cavity represents numerous important problems in practice as well as in fundamental. However up to date the study on it is quite sparse and most previous studies just focus on laminar regime. To the best knowledge of the present authors, only several k–ϵ models were developed to investigate turbulent double-diffusive convection and there is no attempt to use Large Eddy Simulation (LES). In order to deepen our knowledge on turbulent double-diffusive convection in a square cavity, we propose a novel LES-based lattice Boltzmann (LB) model to simulate such turbulent convectional flow. Previous LES-based LB models can be recovered from the present model. We find that the symmetry of the fluid circulation becomes broken since the Rayleigh number Ra =108, although the asymmetry is more clear when Ra ⩾1010. More important, in the present study we find the power-law relationship among the Nusselt (Nu), the ratio of buoyancy forces (N) and the Rayleigh number (Ra) still exists in turbulent regime. The formula among them can be concluded as Nu = a ×(Ra ×∣1− N∣) b + c. The values of parameters a, b and c are given in this work. [Copyright &y& Elsevier]

Linear and nonlinear stability analyses were performed on a fluid layer with a concentration-based internal heat source. Clear bimodal behaviour in the neutral curve (with stationary and oscillatory modes) is observed in the region of the onset of oscillatory convection, which is a previously unobserved phenomenon in radiation-induced convection. The numerical results for the linear instability analysis suggest a critical value γ of γ, a measure for the strength of the internal heat source, for which oscillatory convection is inhibited when γ > γ. Linear instability analyses on the effect of varying the ratio of the salt concentrations at the upper and lower boundaries conclude that the ratio has a significant effect on the stability boundary. A nonlinear analysis using an energy approach confirms that the linear theory describes the stability boundary most accurately when γ is such that the linear theory predicts the onset of mostly stationary convection. Nevertheless, the agreement between the linear and nonlinear stability thresholds deteriorates for larger values of the solute Rayleigh number for any value of γ. [ABSTRACT FROM AUTHOR]

Abstract: Our numerical study focuses on convection in a rotating spherical shell with the objective to model combined thermal and compositional convection as proposed for the Earth’s core. Since the core is cooling, a thermal gradient is established, which can drive thermal convection. Simultaneously, due to the solidification of the inner core latent heat is released at the freezing front and the concentration of the light constituents of the liquid phase increases thus providing a source for compositional buoyancy. Typically, the molecular diffusivities of both driving components differ by some orders of magnitude. To account for this difference it is indicated to adopt a double-diffusive convection model in treating Earth’s core dynamics. As opposed to purely thermal or purely compositional convection the double-diffusive system is controlled by two Rayleigh numbers associated with the respective buoyancy sources. Using the Rayleigh numbers as control parameters neutral curves of the linear onset of convection in the rotating shell are determined for different Ekman numbers and diffusivity ratios. It is found that the neutral curves depend significantly on the system parameters. By comparison with the analytical solutions of the rotating cylindrical annulus it is shown that the neutral curves represent a superposition of curves associated with solutions for different azimuthal wave numbers. Furthermore, fully non-linear simulations are presented in order to elucidate the effect of isochemical and fixed chemical flux boundary conditions on the convection. We consider three driving scenarios with varying thermo-chemical forcing ratios. Both the forcing ratio and the chemical boundary condition have distinct effects on the system that are discussed separately. [Copyright &y& Elsevier]

The double-diffusive convection in a horizontal fluid-saturated porous layer, which is heated and salted from below in the presence of Soret and Dufour effects, is studied analytically using both linear and nonlinear stability analyses. The linear analysis is based on the usual normal mode technique, while the nonlinear analysis is based on truncated representation of Fourier series. The generalized Darcy model that includes the time derivative is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effects of solute Rayleigh number, Lewis number, normalized porosity parameter, Vadasz number, Soret and Dufour parameters on the stationary, oscillatory convection, and heat and mass transfers are shown graphically. The Vadasz number has dual effect on the threshold of the oscillatory convection. Some known results are recovered as special cases of the present problem. [ABSTRACT FROM AUTHOR]

Abstract: A nonlinear stability result for a double-diffusive magnetized ferrofluid layer rotating about a vertical axis for stress-free boundaries is derived via generalized energy method. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. The result is compared with the result obtained by linear instability theory. The critical magnetic thermal Rayleigh number given by energy theory is slightly less than those given by linear theory and thus indicates the existence of subcritical instability for ferrofluids. For non-ferrofluids, it is observed that the nonlinear critical stability thermal Rayleigh number coincides with that of linear critical stability thermal Rayleigh number. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of magnetic parameter, M 3, solute gradient, S 1, and Taylor number, , on subcritical instability region have been analyzed. We also demonstrate coupling between the buoyancy and magnetic forces in the nonlinear stability analysis. [Copyright &y& Elsevier]

This paper deals with the theoretical investigation of the effect of rotation in a magnetized ferrofluid with internal angular momentum, heated and soluted from below subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset of convection. The influence of various parameters like rotation, solute gradient, magnetization and internal angular momentum parameters (i.e. coupling parameter, spin diffusion parameter and heat conduction parameter) has been analyzed on the onset of stationary convection. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large values of buoyancy magnetization parameter M1 and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferrofluid with internal angular momentum heated from below in the absence of rotation, coupling between vorticity and spin, microinertia and solute gradient. The oscillatory modes are introduced due to the presence of the rotation, coupling between vorticity and spin, microinertia and solute gradient, which were non-existent in their absence. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability. [ABSTRACT FROM AUTHOR]

Abstract: Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating cylindrical annulus with conical caps is considered with the aim to establish whether a small fraction of compositional buoyancy added to the thermal buoyancy (or vice versa) can significantly reduce the critical Rayleigh number and amplify convection in planetary cores. It is shown that the neutral surface describing the onset of convection in the double-buoyancy case is essentially different from that of the well-studied purely thermal case, and does indeed allow the possibility of low-Rayleigh number convection. In particular, isolated islands of instability are formed by an additional “double-diffusive” eigenmode in certain regions of the parameter space. However, the amplitude of such low-Rayleigh number convection is relatively weak. At similar flow amplitudes purely compositional and double-diffusive cases are characterized by a stronger time dependence compared to purely thermal cases, and by a prograde mean zonal flow near the inner cylindrical surface. Implications of the results for planetary core convection are briefly discussed. [Copyright &y& Elsevier]

Abstract: Turbulent double-diffusive natural convection is of fundamental interest and practical importance. In the present work we investigate systematically the effects of thermal Rayleigh number (Ra), ratio of buoyancy forces (N) and aspect ratio (A) on entropy generation of turbulent double-diffusive natural convection in a rectangle cavity. Several conclusions are obtained: (1) The total entropy generation number (S total) increases with Ra, and the relative total entropy generation rates are nearly insensitive to Ra when Ra ≤ 109; (2) Since N > 1, S total increases quickly and linearly with N and the relative total entropy generation rate due to diffusive irreversibility becomes the dominant irreversibility; and (3) S total increases nearly linearly with A. The relative total entropy generation rate due to diffusive and thermal irreversibilities both are monotonic decreasing functions against A while that due to viscous irreversibility is a monotonic increasing function with A. More important, through the present work we observe a new phenomenon named as “spatial self-copy” in such convectional flow. The “spatial self-copy” phenomenon implies that large-scale regular patterns may emerge through small-scale irregular and stochastic distributions. But it is still an open question required further investigation to reveal the physical meanings hidden behind it. [Copyright &y& Elsevier]

Abstract: Double-diffusive convection in vertical annuluses with opposing temperature and concentration gradients is of fundamental interest and practical importance. However, available literature especially for higher Rayleigh numbers beyond is sparse. In this study, we investigated double diffusion induced convection up to using a simple lattice Boltzmann model. Thanks to the good stability of the present model, a modest grid resolution is sufficient for the present simulations. The influences of the ratio of buoyancy forces , the aspect ratio and the radius ratio on heat and mass transfer characteristics are discussed in detail. [Copyright &y& Elsevier]

Abstract: A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic field-dependent (MFD) viscosity, for stress-free boundaries. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effects of magnetic parameter, M 3, solute gradient, S 1 and MFD viscosity parameter, δ, on the subcritical instability region have also been analyzed. [Copyright &y& Elsevier]

Abstract: Convection in a horizontal fluid layer of a binary mixture is studied analytically and numerically. In the formulation of the problem, use is made of the Boussinesq approximation. Neumman boundary conditions are specified for the temperature on all walls of the cavity. In addition of the Soret contribution, a shear stress, τ, is applied on the upper free surface of the layer. The flows are found to be dependent of the Darcy–Rayleigh number, R T, the Lewis number, Le, the solutal to thermal buoyancy ratio, ϕ, the shear stress, τ and the thermal boundary conditions. Numerical results for finite amplitude convection, obtained by solving numerically the full governing equations, are found to be in good agreement with the analytical solution based on the parallel flow approach. For given sets of the control parameters, the occurrence of multiple steady state solutions is demonstrated. The existence of subcritical bifurcations for both stabilizing and destabilizing mass flux is also demonstrated. [Copyright &y& Elsevier]