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The instability of the double-diffusive convection of an Oldroyd-B fluid in a vertical Brinkman porous layer caused by temperature and solute concentration differences with the Soret effect is studied. Based on perturbation theory, an Orr–Sommerfeld eigenvalue problem is derived and numerically solved using the Chebyshev collocation method. The effects of dimensionless parameters on the neutral stability curves and the growth rate curves are examined. It is found that Lewis number Le, Darcy–Prandtl number PrD, and normalized porosity η have critical values: When below these thresholds, the parameters promote instability, whereas exceeding them leads to suppression of instability. In addition, for Le < Lec2 (a critical value of Le), Sr strengthens the instability of the flow, while for Le > Lec2, Sr suppresses it. These results highlight the complex coupling of heat and mass transfer in Oldroyd-B fluids within porous media. [ABSTRACT FROM AUTHOR]

This study investigates how thermal radiation, viscous dissipation, double-diffusive convection, and slip boundaries collectively affect the peristaltic movement of a magneto-pseudoplastic nanofluid within a uniform channel. The inclusion of slip boundary conditions at the channel walls helps to accurately represent the flow behavior of the nanofluid near these boundaries. The magneto-pseudoplastic nanofluid exhibits peculiar rheological features to flow dynamics due to pseudoplastic characteristics of nanoparticles in its composition and exposure to magnetic force. The mathematical formulation of motion equations is done through appropriate technique combining the properties of heat radiation, magnetic flux, double diffusion convection, and rheological features. The equation is further simplified by suitable method. The current study aims to evaluate the peristaltic movement under influence of slip boundaries characteristics, sort of concentration, heat radioactivity, flux properties, and temperature profile. Moreover, it will assess the flow dynamics with ratio of mass and heat exchange under the effect of critical parameters which include Prandtl number, Grashof number, slip limitations, and Hartmann number. So, the research will widen the theoretical underpinning of complex fluid transportation of magneto-pseudoplastic nanofluids under peristaltic flux and explicate the practical outcomes in terms of slip boundary settings in such systems. The results and conclusions are imperative for restructuring and devising biomedicine engineering, microfluidic equipment and gadgets, manufacturing techniques for complex fluid with peristaltic flow under the influence of slip limitations and magnetic force. [ABSTRACT FROM AUTHOR]

Mesoscale warm‐core rings, known as Loop Current rings (LCRs) reshape the Gulf of Mexico water masses by redistributing large amounts of heat and salt laterally. LCRs also transform water masses via diapycnal mixing, but the mechanisms by which this occurs are poorly measured. Here, we present glider‐MicroPod turbulence observations that reveal enhanced mixing below the mixed layer, along the eddy edges, driving the LCR's heat, salt, and oxygen exchanges. Interleavings of adjacent water masses may be interpreted mainly as a manifestation of submesoscale processes through stirring of the spice gradients, which facilitates double‐diffusive mixing that transforms Subtropical Underwater into Gulf Common Water. Our findings highlight the need for ocean models to parameterize double‐diffusive mixing processes directly resulting from submesoscale tracer stirring, which may be important at basin scale in the presence of LCRs in the Gulf of Mexico. Plain Language Summary: In the Gulf of Mexico (GoM), anticyclonic eddies, known as Loop Current rings (LCRs) carrying warm and salty water shape the basin's water mass properties, which in turn, affects the regional climate and marine life. The water mass properties are altered by turbulent mixing. However, the mechanisms leading to the mixing of GoM waters are still under debate due to a lack of observations. Here, we use an autonomous underwater vehicle (glider) equipped with a turbulence sensor to assess the nature of LCR mixing and its impact on water properties. The breaking of internal waves in the ocean is often thought to be responsible for turbulent mixing in the ocean interior. However, our findings demonstrate that a process called double‐diffusive convection is responsible, where turbulence is forced by differences between the temperature and salinity of adjacent water parcels. We found that double‐diffusive convection was the main driver in mixing heat, salt, and oxygen along the eddy edges, producing Gulf Common Water. These findings highlight the need to include double diffusive processes in ocean models for more accurate simulations. Key Points: Direct observations of turbulence reveal the distribution of mixing across a Gulf of Mexico Loop Current RingSubtropical Underwater is transformed into Gulf Common Water through double‐diffusive convection on the edges of the eddy [ABSTRACT FROM AUTHOR]

With the high-precision and high-resolution numerical method, the dynamics of double-diffusive convection of different liquid metals in a long cavity under external magnetic fields in 2 directions was directly simulated, to reveal the influences of the fluid property parameter of Prandtl number Pr, the magnetic field direction and the magnetic field intensity on the flow and the heat and mass transfers. The results indicate that, within the range of the considered Pr values, the flow transitions from periodic to steady with the increase of Pr for weak magnetic fields. Specifically, when the Pr is 0.03, the convective system will have unsteady solution, and the flow will be periodic. The efficiency of heat and mass transfers initially increase rapidly, then slowly. For the moderately strong magnetic field, the flow remains steady, and the growth rate of the heat and mass transfer efficiency slows down further with Pr increasing. For the strong magnetic field, the flow is always steady, and the efficiency of the heat and mass transfer hardly changes with the Pr. Under the same magnetic field intensity, compared with the inclined magnetic field with a direction of 45° and the horizontal magnetic field, the vertical magnetic field has a weaker suppressive effect on the heat and mass transfer efficiency. [ABSTRACT FROM AUTHOR]

This article depicts the heat and mass transport of the double-diffusive convective flow of Walter-B viscoelastic fluid in highly permeable porous media with an internal heat source. We used weakly nonlinear analysis to quantify the nature of heat and mass transport using the Ginzburg–Landau equation. The Ginzburg–Landau equation has been derived in terms of the amplitude of the stream function. The effect of physical parameters has been examined on Nusselt and Sherwood numbers, which has represented graphically. According to the boundary condition, we have discussed the four scenarios based on the phase angles. Our study has demonstrated that internal heat plays a significant role in heat transfer processes. Furthermore, the elastic parameter leads to a transient augmentation in the heat and mass transfer rate. The main output of the current study is that the highest transport was found when both the modulations were put in out-phase condition (Scenario 1).

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]

In this work, a coupled representative elementary volume scale lattice Boltzmann method (LBM) is developed to investigate double-diffusive convection in a porous cavity, taking into account Dufour and Soret effects. The governing equations comprise the incompressible Navier-Stokes equations and the coupled convection diffusion equations with cross diffusion terms, which pose challenges to the numerical methodology. To accurately handle the cross diffusion term, a comprehensive collision operator is introduced in the proposed LBM. By means of multi-scale Chapman-Enskog analysis, the coupled LBM successfully recovers the governing equations. Several benchmark double-diffusive convection problems are simulated to verify the reliability of the proposed LBM, showing good agreement with established data from previous research. Furthermore, the impacts of the Darcy number, Rayleigh number, and Soret and Dufour factors on heat and mass transfer rates are thoroughly examined, yielding calculations of average Nusselt number and Sherwood numbers under these dimensionless quantities. The numerical results underscore the capability of the developed LBM for simulating double-diffusive convection in porous media with Dufour and Soret effects. [ABSTRACT FROM AUTHOR]

The work focuses on developing a detailed understanding of the effects of initial composition (Cin) and bottom cooling temperatures (TB) on different characteristics of double-diffusive convection during unidirectional solidification of water-NH4Cl solution in a complete non-intrusive manner. The qualitative investigation, simultaneous quantification of transported parameters (composition and temperature) and fluid velocities associated with flow patterns are carried out using rainbow schlieren deflectometry, dual-wavelength interferometry and PIV (particle image velocimetry) technique respectively. The dependence of the characteristics of double-diffusive convection for different Cin and TB is explained on the basis of real-time whole-field investigation using a combination of aforementioned imaging techniques. [ABSTRACT FROM AUTHOR]

This paper’s goal is to investigate the oscillatory flow of double-diffusive convection in a Voigt fluid. We re-design the basic equations of the channel flow, which initially appear dimensional, in a dimensionless manner using non-dimensional variables. The oscillation technique transforms the governing equations into coupled ordinary differential equations (CODEs). We have derived the analytical expressions for velocity, temperature, and concentration distribution by solving the CODEs using the direct analytical method. The study focuses on how physical factors, like the thermal Grashof number, the solutal Grashof number, the Prandtl number, the Lewis number, and the Voigt fluid parameter, affect different aspects of flow, such as speed, temperature, concentration, rate of heat transfer, and mass transfer. Notably, the study finds that skin friction increases on both channel plates with increasing injection on the heated plate. The significance of double-diffusive oscillatory flow lies in its ability to improve heat and mass transfer rates, as well as its impact on pattern formation and stability, which influences a wide range of applications from engineering design to environmental studies. [ABSTRACT FROM AUTHOR]

AbstractEnclosures that contain both fluid and porous regions are utilized in various industries and geophysical processes to enhance heat and mass transfer. These enclosures find applications in fields such as geothermal engineering, drying of porous solids, cooling of electronics, metal solidification, and many others. In line with the motivation behind these applications, the present study explores double diffusion in the naturally convective flow of water-based nano fluid saturated in the trapezoidal porous enclosure and containing Copper (Cu) nano particles. The impact of uniformly applied radiative heat flux and nano particle shape factor is also accounted. A numerical investigation was carried out using a finite difference methodology integrated into a computational MATLAB code for numerical simulation. The simulation aimed to study the effect of nanoparticle shape factor on the effectiveness of a porous medium, which is exposed to two distinct objectives: enhancing heat transfer and optimizing mass transfer within a fluid-saturated porous medium. This research conducts a meticulous parametric exploration, underscoring the pivotal roles played by Darcy number (Da), nanofluid shape factor (m), Rayleigh number (Ra), thermal radiation (Rd), buoyancy ratio (Nr), and Lewis number (Le) in shaping the dynamics of flow, heat, and concentration transfer. The analysis of Nusselt and Sherwood numbers reveals that changing the shape of nano-particles from spheres to bricks increases the heat flux and mass flux coefficients by approximately 0.33% and 1.37% respectively. The results show a significant increase in Nusselt and Sherwood numbers, with blade-shaped nanoparticles demonstrating approximately a 2.97% and 10.82% improvement, respectively, compared to sphere-shaped nanoparticles. The outcome of this analysis yields an exhaustive dataset encompassing Nusselt and Sherwood numbers can be written as mathematical functions based on the parameters we talked about earlier. [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]

The effects of vertical throughflow, rotation, cross‐diffusion, and vertical heterogeneous permeability on the onset of double‐diffusive convection in a finite vertical porous cylinder have been studied. The fluid in the cylinder is warmed and salted from below with its top and lower walls considered to be isothermal, isosolutal, and permeable. In the model, the Brinkman model was adopted, coupled with the Oberbeck–Boussinesq approximation. The normal mode technique is used for linear stability analysis and a single‐term Galerkin method is used to solve the eigenvalue problem. Further, the influence of parameters such as the thermal and solute Rayleigh, Taylor, and the Soret and Dufour numbers on the fluid system instability have been investigated. Among other results, we found that vertical heterogeneity may either stabilize or destabilize a fluid system. The stabilization of the throughflow remains consistent irrespective of the orientation in the absence of a cross‐diffusion effect. The dual effect of throughflow is observed when there are cross‐diffusion effect. We found that increasing the Dufour parameter delays the onset of both stationary and oscillatory convection. The positive Soret number has a stabilizing effect on stationary convection and a destabilizing effect on the oscillatory convection case. [ABSTRACT FROM AUTHOR]

Combined buoyancy shifts from temperature and concentricity gradients create double-diffusive convection. Complex Crown form enclosure with heat and mass source brings originality and practicality by enhancing use in a broad variety of technical, industrial, and geophysical operations. Current artifact is to explore thermosolutal diffusion in buoyantly driven flowing of viscid liquid contained in a crown enclosure with the installation of a uniformly heated and soluted circular cylinder. Novel physical characteristics of inclining magnetic field are introduced, and distributions affected by cylinder radius change are compared. Dimensionless PDEs are solved numerically using finite elements. Grid independence test ensures simulation mesh level. Hybrid meshing with triangular and rectangular components discretizes domain. Linear interpolating polynomials approximate pressure, whereas quadratic polynomials approach velocity, temperature, and concentricity. PARDISO solves a non-linear system of equations efficiently. Average Nusselt and Sherwood numbers are estimated by comparing relevant parameters to cylinder radius change. Heat transference rate rises to 40% and mass transport upsurges to 60% when radius of cylinder is increased from 0.1 to 0.2. Hartmann number tends to affect a decline in Nusselt and Sherwood quantities. Reduction in thermal and solutal boundary layers near surface of the cylinder is observed against the improve in radius of cylinder. [ABSTRACT FROM AUTHOR]

The viscoelastic effects on the double diffusive oscillatory flow in a fluid-saturated porous layer are investigated. A modified Darcy–Oldroyd-B model is used to characterize the non-Newtonian fluid behavior flow in a porous layer. Analytic solutions of the dimensionless governing equations of fluid flow are obtained and the effects of the flow parameters on temperature, concentration, velocity profiles, skin friction and rate of heat transfer are discussed and shown graphically. It is interesting to note that skin friction increases on both channel plates as injection increases on the heated plate. Increase in the strain retardation parameter is to decrease the fluid velocity, while an opposite trend is noticed with increasing stress relaxation parameter. The study reiterates that the consideration of viscoelastic fluid is very important in proper considerate of oscillatory flow in double diffusive fluid systems. [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]

The outcomes of partial slip on double-diffusive convection of Johnson–Segalman nanofluids in an asymmetric peristaltic path are presented in this research with the effect of inclined magnetic field. The mathematical formulation of Johnson–Segalman nanofluids is also discussed with double-diffusive convection and inclined magnetic field. To simplify extremely nonlinear partial differential equations, a lubricant approach is applied. The numerical calculations are obtained to the equations for the stream function, concentration, pressure gradient, temperature, velocity, nanoparticle volume fraction, and pressure rise. The impact of prominent hydro-mechanical parameters such as Brownian motion, thermophoresis, Soret, Dufour, and slip constraints on the axial velocity, trapping, volumetric fraction, pressure gradient, temperature, pressure rise, and concentration functions is evaluated graphically. It is noted that slip effect in the channel causes the fluid particles to stray, slowing the fluid velocity. Moreover, it has been noted that as thermophoretic effects and Brownian motion increase, nanoparticles rapidly move from the wall into the fluid, significantly raising temperature. [ABSTRACT FROM AUTHOR]

Abstract This research work reports the numerical investigation of magnetohydrodynamics (MHD) characteristics around the near-wall blockage ( NWB ) for various separation distances owing to double-diffusive convection (DDC) in a rectangular cavity. The distance between the bottom wall of the cavity and the lower wall of blockage is called separation distance S d , and it has varied from ( H / 4 ≤ S d ≤ H / 8 ) , where H is the height of the cavity. The working fluid is considered as liquid metal - Sodium-Potassium alloy ( P r = 0.054 ). The numerical computations are conducted by using an in-house developed lattice Boltzmann method ( LBM ) solver. The simulations are conducted for the steady-state, laminar, incompressible, and Newtonian fluid flow. The effect of NWB has been explored for a range of parameters, such as Rayleigh number ( R a = 10 4 and 10 5 ) , Lewis number ( 0.5 ≤ L e ≤ 1.5 ) , buoyancy ratio ( − 1.5 ≤ N ≤ 1 ) and Hartmann number ( 0 ≤ H a ≤ 300 ) . The variation and contour plots show the higher heat and mass transfer (HMT) rates for S d = H / 4 at constant Ra. As S d increases, HMT rates enhance. The increase in Ra, N, and Le induces multiple-cell formation inside the cavity for a given S d . As Ha augments HMT rates get decreased monotonically. For H a ≥ 150 , negligible or slight variation was observed in the rate of HMT. As the obstruction between the bottom wall of the blockage and the adiabatic bottom wall of the cavity increases, shear force occurs, and the buoyancy-driven flow decreases. The outcomes of the numerical investigation are summarized in the form of empirical correlation of N u Total for Ra = 10 4 and 10 5 at various separation distances, which might be utilized for probable design purposes. [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]

This paper aims to investigate the transient behavior of a salinity gradient solar pond (SGSP) under Mediterranean climate. For this purpose, a 2D numerical model is developed in which the absorption of solar radiation by different layers of saline water, the wind effect at the SGSP free surface, the heat losses from the SGSP free surface, and the development of the double-diffusive convection in the lower and upper convective zones are considered. The governing equations of continuity, momentum, thermal energy, and diffusion are solved using the finite volume method with SIMPLE algorithm. The validity of the numerical model developed in fortran 95 programing language is achieved through the comparisons of the results computed with the available numerical and experimental results obtained by literature studies. Results show that the developed numerical model can predict transient behavior of the SGSPs with a good accuracy. As an application of this model, the temperature, salt concentration, energy stored, and storage efficiency variations of a proposed SGSP are analyzed under Mediterranean climate. The results show that the lower convective zone (LCZ) temperature increases from 15 °C to around 95 °C whereas the temperature of the upper convective zone (UCZ) varies sinusoidally depending on that of the ambient air. Furthermore, the salt concentration of the LCZ decreases from 250 kg/m³ to around 248 kg/m³ while that of the UCZ increases from 50 kg/m³ to about 52 kg/m³. Additionally, the thermal energy stored is around 135 MJ with an efficiency of about 38%, which confirms the capacity of the SGSP to store thermal energy as sensible heat. [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]

Consequence of thermal and concentration convection on peristaltic pumping of hyperbolic tangent nanofluid in a non‐uniform channel and induced magnetic field is discussed in this article. The brief mathematical modeling, along with induced magnetic field, of hyperbolic tangent nanofluid is given. The governing equations are reduced to dimensionless form by using appropriate transformations. Exact solutions are calculated for temperature, nanoparticle volume fraction, and concentration. Numerical technique is manipulated to solve the highly non‐linear differential equations. The roll of different variables is graphically analyzed in terms of concentration, temperature, volume fraction of nanoparticles, axial induced magnetic field, magnetic force function, stream functions, pressure rise, and pressure gradient. [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 work has mathematically modeled the peristaltic flow in nanofluid by using thermal radiation, induced a magnetic field, double-diffusive convection, and slip boundary conditions in an asymmetric channel. Peristalsis propagates the flow in an asymmetric channel. Using the linear mathematical link, the rheological equations are translated from fixed to wave frames. Next, the rheological equations are converted to nondimensional forms with the help of dimensionless variables. Further, the flow evaluation is determined under two scientific assumptions: a finite Reynolds number and a long wavelength. Mathematica software is used to solve the numerical value of rheological equations. Lastly, the impact of prominent hydromechanical parameters on trapping, velocity, concentration, magnetic force function, nanoparticle volume fraction, temperature, pressure gradient, and pressure rise are evaluated graphically. [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 study is aimed at establishing an effective incremental-iterative framework, for the first time, using reproducing kernel collocation method for solving multi-phase dynamic coupling problems in a porous enclosure. The central difference method is utilized in the temporal discretization while direct collocation with reproducing kernel approximation is adopted in the spatial discretization, in particular, with Newton–Raphson method for nonlinear iteration. Under the proposed numerical framework, a determined and well-conditioned nonlinear system is ensured during nonlinear iteration. In addition to the traditional mesh-based weak-form methods, it is shown that the present study provides an alternative effective approach to solve unsteady-state double-diffusive convection problems. [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]

Over the years, the lattice Boltzmann method (LBM) has been evolved as a substitute and efficient numerical tool to mimic the single/multiphase fluid flow and transport problems. LBM has been mainly advantageous in multi-physics and multiphase flow applications. On the other hand, double-diffusive convection has extensive occurrence in domestic and industrial activities. The type of convection in which the combined effect of temperature and concentration gradients (resulting in the density variation) on fluid's hydrodynamic and thermal characteristics is called double-diffusive convection (DDC). The importance of DDC has been recognized in various engineering applications, and it has thoroughly been investigated experimentally, theoretically, and numerically. This paper is proposed to deliver a brief review of double-diffusive convection by computational approach (mainly lattice Boltzmann method and Navier–Stokes equation-based solvers). This review explores the illustration of some of the practical applications of DDC, studies of DDC in various heated cavities. The paper also gives insights into LBM formulation of DDC under various external force conditions. A table compromising various empirical correlations of the average Nusselt numbers and average Sherwood numbers as a function of different governing parameters has been discussed. [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 influence of linear, parabolic and inverted parabolic temperature gradients on the onset of double-diffusive Rayleigh-Darcy convection is theoretically investigated. The composite system is constrained horizontally by adiabatic and free-free thermal boundaries, and appropriate interfacial boundary conditions are used to connect fluid-porous layers. The regular perturbation approach is used to determine the critical Rayleigh number expression for different temperature gradients. Graphs are used to investigate the significance of a variety of dimensionless characteristics. The couple stress parameter, couple stress viscosity ratio, solute Rayleigh number, and solute diffusivity ratio clearly have a stabilizing effect on the system, whereas the Darcy number and thermal diffusivity ratio destabilize it. [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]

Two-dimensional (2D) numerical experiments are performed to investigate the flow instabilities and mixing of different nonisothermal counterflowing jets in a passive-mixer. The fluid is modeled as a binary mixture with thermal and solutal buoyancy effects considered through the Boussinesq approximation. The streams are arranged in a thermal and solutal buoyancy aiding configuration. Computations are carried out for three different ratios of the upper jet bulk velocity to the lower jet bulk velocity (VR), namely, VR = 0.5, 1.0, and 2. Within the parametric domain of RiT and RiC defined by region (RiT + RiC) ≤ 3, the instability causing transition from steady to unsteady flow regime is observed for VR = 1 and 2, while no transition is found to occur at VR = 0.5. Using Landau theory, it is established that the transition from steady to unsteady flow regime is a supercRiTical Hopf bifurcation. A complete regime map identifying the steady and unsteady flow regimes, within the parametRiC space of this study, is obtained by plotting the neutral curves of RiC and RiT (obtained using Landau theory) for different values of VR. Proper orthogonal decomposition (POD) analysis of the unsteady flows at VR = 1 establishes the presence of standing waves. However, for VR = 2, the presence of degenerate pairs in the POD eigenspectrum ascertains the presence of traveling waves in the unsteady flows. The standing wave unsteady flow mode is found to yield the highest rate of mixing. [ABSTRACT FROM AUTHOR]

The stability of double-diffusive buoyant flow in a vertical layer of Darcy porous medium whose boundaries are held at different constant temperatures and solute concentrations is investigated. The time evolution of normal mode perturbations superposed onto the basic state is deliberated to determine the stability of fluid flow. The analysis of Gill in proving the stability of fluid flow is found to be ineffective and the eigenvalue problem is solved numerically using the Chebyshev collocation method. The neutral stability curves are found to be closed and the region of instability expands with increasing solute/thermal Darcy–Rayleigh number and the Lewis number. The critical thermal/solute Darcy–Rayleigh number and the corresponding wave number are computed for different values of governing parameters. Depending on the values of Lewis number, there exists a range of solute/thermal Darcy–Rayleigh number prior to which the flow remains stable and beyond which it becomes unstable. [ABSTRACT FROM AUTHOR]

We explore the physical influence of magnetic field on double-diffusive convection in complex biomimetic (peristaltic) propulsion of nanofluid through a two-dimensional divergent channel. Additionally, porosity effects along with rheological properties of the fluid are also retained in the analysis. The mathematical model is developed by equations of continuity, momentum, energy, and mass concentration. First, scaling analysis is introduced to simplify the rheological equations in the wave frame of reference and then get the final form of equations after applying the low Reynolds number and lubrication approach. The obtained equations are solved analytically by using integration method. Physical interpretation of velocity, pressure gradient, pumping phenomena, trapping phenomena, heat, and mass transfer mechanisms are discussed in detail under magnetic and porous environment. The magnitude of velocity profile is reduced by increasing Grashof parameter. The bolus circulations disappeared from trapping phenomena for larger strength of magnetic and porosity medium. The magnitude of temperature profile and mass concentration are increasing by enhancing the Brownian motion parameter. This study can be productive in manufacturing non-uniform and divergent shapes of micro-lab-chip devices for thermal engineering, industrial, and medical technologies. [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 Parameterizations of small‐scale mixing are important in modeling the behavior of the World Ocean. These microstructure mixing processes do not exist in isolation, however, and larger‐scale processes can affect their fluxes, which is an important consideration for general circulation models. We have developed a new pseudo‐spectral hydrodynamic model, the “Rocking Ocean Modeling Environment,” which is able to simulate the effects of some large‐scale processes, such as shear and internal waves. The code induces a time‐dependent shear forcing across a small domain that can accurately resolve the micro‐scale. This configuration presents a challenge for modeling via Fourier‐based algorithms because the typical evolution of such a flow is incompatible with the periodic boundary conditions at the vertical extremities of the computational domain. This complication is addressed by reformulating the governing equations in a new, temporally varying “tilting” coordinate system associated with the background flow as has been done in the past in the field of homogenous turbulence. The code is applied to one such process which is known to show substantial differences in turbulent environments: salt fingers. We simulate salt fingers in the presence of constant and oscillating shear in order to quantify the mixing of heat and salt by these systems under the impacts of large‐scale internal waves. Generally, it is shown that the application of shear can reduce fluxes by a factor of 2 or 3 for typical amplitudes of near‐inertial waves and that the impact of shear decreases as the frequency of the applied shear increases.