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This article deals with the effects of thermophoresis on thermosolutal mixed convection in a vertical wavy porous cavity. Three distinct flow features are chosen by changing the directions of the moving horizontal borders. A nonuniform temperature, as well as concentration distributions, are introduced to the bottom wall while keeping cold temperature and low concentration for the other walls. The governing equations are modeled to describe thermosolutal phenomena. These equations are solved by reconstructing a recently developed compact scheme. Furthermore, the significance of well-defined parameters influencing the fluid rotation and thermosolutal transfer, namely Richardson number ( 0.01 ≤ Ri ≤ 100 ), Buoyancy ratio (N = 1), number of undulations ( 0 ≤ d ≤ 2 ) of the wavy walls, Lewis number ( 1 ≤ Le ≤ 10 ), thermophoretic coefficient ( 0.0 ≤ K T ≤ 1.0 ), Darcy number ( 0.001 ≤ Da ≤ 0.1 ), and porosity of the porous medium ( 0.1 ≤ ε ≤ 1.0 ) are performed generously. Results are displayed in terms of streamlines, isotherms, iso-concentrations, Nusselt, and Sherwood numbers to evoke the thermosolutal phenomena for various physical parameters. It is observed that thermophoresis is effective in certain circumstances. In addition, heat and mass transfer enhancement is noted with decreasing Richardson number while heat and mass transfer reduction is noted with increasing undulation number of the wavy walls. We have noticed that for the change in Le from 1 to 10, heat transfer is diminished up to 2.91% in Case-1, 3.03% in Case-2, and 2.20% in Case-3 while mass transfer is enhanced by 162.85% in Case-1, 164.05% in Case-2, and 87.03% in Case-3. [ABSTRACT FROM AUTHOR]

We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or penetrative convection effects which result in spatially dependent coefficients. This spatial dependence usually requires numerical solution even in the linearized case. In this work, we demonstrate that regardless of the size of the Rayleigh number, the perturbation solution will decay exponentially in time for the superdiffusion case. In addition, we establish a similar result for convection in a bidisperse porous medium where both macro- and microporosity effects are present. Moreover, we demonstrate a similar result for thermosolutal convection. [ABSTRACT FROM AUTHOR]

This work presents nonlinear and linear analyses of the rotating Navier–Stokes–Voigt fluid layer that is simultaneously heated and soluted from below, considering different boundary surfaces. The energy method is used to form the eigenvalue problem for nonlinear analysis, whereas the normal mode analysis is used for the linear analysis. The Rayleigh number is numerically calculated by employing the Galerkin technique. Both nonlinear and linear analyses yield the same Rayleigh number, indicating the absence of subcritical regions and implying global stability. The Kelvin–Voigt parameter doesn't affect the Rayleigh number for stationary convection. However, the crucial role of this parameter is established through an energy argument. The presence of rotation, Kelvin–Voigt parameter, and solute gradient give rise to oscillatory modes. Also, the effects of rotation and solute gradient are stabilizing on the system, whereas the stabilizing effect of the Kelvin–Voigt parameter becomes evident when convection exhibits an oscillatory behavior. [ABSTRACT FROM AUTHOR]

The current work establishes research into the non-Newtonian Casson fluid's linear and weakly non-linear stability analysis under the influences of internal heating and gravitational modulation. The study is confined to stationary convection, where marginal stability is determined by the critical Rayleigh number, which is derived from linear stability analysis. The marginal stability curves are plotted to observe the onset of convection due to different parameters that exist in the problem. Heat and mass transfer are measured in terms of the Nusselt number (Nu) and Sherwood number (Sh), respectively, in the non-linear stability analysis. These measurements are based on the Ginzburg-Landau (GL) equation. One of the main outcomes of this stability analysis is that the internal Rayleigh number and Casson parameter behave similarly for mass transport in a fluid whereas it operates oppositely for heat transfer in a fluid. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of the linear and non-linear stability of thermosolutal convection within a porous medium saturated by a non-Newtonian binary fluid. The power-law model is utilized for modeling the behavior of the working medium. The given statement implies that the horizontal boundaries experience thermal and solutal flow rates, whereas the vertical walls are impermeable and thermally isolated. The relevant factors that govern the problem being investigated are the Rayleigh number, , the power-law index, , the cavity aspect ratio, , the Lewis number, , and the buoyancy ratio, . An analytical solution is obtained for shallow enclosures ( ) using the parallel flow approximation and a modified form of the Darcy equation. By solving the entire set of governing equations, a numerical investigation of the same phenomenon was conducted. One of the most intriguing discoveries from this research is that it identifies a bi-stability phenomenon, this particular phenomenon signifies the existence of two stable solutions. The results obtained from both methods demonstrate a good level of agreement across a diverse range of these governing parameters.

Lattice Boltzmann simulations of double-diffusive convection in a rectangular cavity differentially heated and salted are conducted in the presence of internal heat generation and Dufour and Soret effects. The study is performed for an aspect ratio A = 2, an external Rayleigh number RaE = 105, a Lewis number Le = 2, a buoyancy ratio N = -1, and a Prandtl number Pr = 0.71: The study focuses mainly on the effect of Dufour number (Du = 0 and 0.5) to measure its impact on the ranges of steady/unsteady solutions reported in a previous study for the Soret parameter ranging from -0.5 to 0.5 and internal to external Rayleigh numbers ratio ranging from 0 to 80. Compared to Du = 0, the results obtained show that the presence of Dufour mechanism with a positive value leads to a destabilizing effect by widening the ranges of instability observed for the considered values of Sr: The combinations (Sr, Du) the most stabilizing/destabilizing are identified and discussed in this study. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of the linear and non-linear stability of thermosolutal convection within a porous medium saturated by a non-Newtonian binary fluid. The power-law model is utilized for modeling the behavior of the working medium. The given statement implies that the horizontal boundaries experience thermal and solutal flow rates, whereas the vertical walls are impermeable and thermally isolated. The relevant factors that govern the problem being investigated are the Rayleigh number, RT, the power-law index, n, the cavity aspect ratio, A, the Lewis number, Le, and the buoyancy ratio, N. An analytical solution is obtained for shallow enclosures (A >> 1) using the parallel flow approximation and a modified form of the Darcy equation. By solving the entire set of governing equations, a numerical investigation of the same phenomenon was conducted. One of the most intriguing discoveries from this research is that it identifies a bi-stability phenomenon, this particular phenomenon signifies the existence of two stable solutions. The results obtained from both methods demonstrate a good level of agreement across a diverse range of these governing parameters. [ABSTRACT FROM AUTHOR]

AbstractThermosolutal natural convection originates in a fluid when the density changes due to the presence of two distinct components with varying rates of diffusion. This convection is driven by buoyancy resulting from concurrent temperature and concentration gradients. This study focuses on the thermosolutal free convection flow within a parallelogrammic enclosure. The functioning fluid under consideration is non-Newtonian and formulated by the viscosity model (power-law). The top and bottom walls of the chamber are adiabatic and are assumed to be impermeable. The temperature and concentration on the left side are maintained at a high level, while the conditions on the right side are cold and low. The controlling parameters for the present case include Rayleigh number (105≤Ra≤106), Lewis number (Le = 5, 10), Prandtl number (Pr = 6.2), buoyancy ratio (N = 0.8, −0.8) along with power-law index (n = 0.6, 1, 1.4). The results obtained from this numerical study are validated with existing results and indicate the correctness of the code. The output of the study is shown in terms of velocity and temperature profiles, streamlines, isotherms, and iso-concentrations, the average rate of heat and mass transmission in terms of the average Nusselt number (Nu¯) and the average Sherwood number (Sh¯). The correlation equation derived from the RSM approach demonstrates the relationship between the output responses and the input parameters. It concludes that n negatively affects both heat and mass transfer, while Ra affects positively. The findings of this study could be helpful for understanding of thermosolutal natural convection behavior of non-Newtonian (power-law) fluid in an enclosure and therefore accelerate the industrial application of such fluid in the relevant field, such as HVAC (heating, ventilation, and air conditioning) system. [ABSTRACT FROM AUTHOR]

In a composite system possessing rigid‐rigid boundaries, the significance of thermal diffusion on the onset of triple diffusive convection is analyzed. The Darcy–Brinkman–Rayleigh–Benard model is employed to model the porous media. The regular perturbation methodology has been used to solve the governing equations of the composite system with the Boussinesq approximation. The critical thermal Rayleigh number, which determines the stability of the system, is estimated analytically. A graphical assessment of the impact of multiple physical attributes on the stability of the system is made. It is observed that the Soret parameters and solute Rayleigh numbers have a stabilizing effect, whereas the Darcy number exhibits a destabilizing effect upon the onset of triple diffusive convection in the composite system. [ABSTRACT FROM AUTHOR]

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

The two-temperature model of local thermal nonequilibrium (LTNE) is utilized to investigate a weakly nonlinear stability of thermosolutal convection in an Oldroyd-B fluid-saturated anisotropic porous layer. The anisotropies in permeability, thermal conductivities of the porous medium, and solutal diffusivity are accounted for by second-order tensors with their principal directions coinciding with the horizontal and vertical coordinate axes. A modified Darcy-Oldroyd model is employed to describe the flow in a porous medium bounded by impermeable plane walls with uniform and unequal temperatures as well as solute concentrations. The cubic-Landau equations are derived in the neighborhood of stationary and oscillatory onset using a modified perturbation approach and the stability of bifurcating equilibrium solutions is discussed. The advantage is taken to present some additional results on the linear instability aspects as well. It is manifested that the solutal anisotropy parameter also plays a decisive role on the instability characteristics of the system. It is found that the stationary bifurcating solution transforms from supercritical to subcritical while the oscillatory bifurcating solution transforms from supercritical to subcritical and revert to supercritical. The Nusselt and Sherwood numbers are used to examine the influence of LTNE and viscoelastic parameters on heat and mass transfer, respectively. The results of Maxwell fluid are outlined as a particular case from this study. [ABSTRACT FROM AUTHOR]

A linear stability analysis is carried out to investigate the onset of thermosolutal convection in a fluid layer overlying a fluid-saturated porous layer under the high-frequency small-amplitude translational vibration with different direction in the gravitational field. Distinct temperatures and concentrations are applied at the external boundaries of the two-layered fluid-porous domain in such a way that the buoyancy ratio (the ratio of density drop due to concentration difference to that due to temperature difference) has a positive value. The numerical calculations show that transverse (vertical) vibration suppresses convection by delaying its onset when the domain is heated from below. There is a jump-like transition from local to large-scale convective regimes with intensifying vibration. In the case of longitudinal (horizontal) vibration the convection onset value varies non-monotonically: it increases initially, reaches a maximum, and then decreases. The noticeable enhancement of convection is observed at the vibrational Rayleigh-Darcy number close to its value in weightlessness. The longitudinal vibration in contrast to the transverse one is additionally capable of creating convection when the two-layered domain is heated from above. In such a situation the flow has exclusively thermosolutal vibrational nature. With strengthening longitudinal vibration, the critical flow patterns replace each other in the following order: local flows – large-scale flows – long-wave flows with the system of vertically ordered vortexes – “super-shortwave” flows. If one applies at least a small concentration difference across the layers, all of the mentioned vibration effects manifest themselves at less temperature difference and vibration acceleration than they are in the case of pure thermal convection. The thermal and concentration density gradients reinforce each other at positive buoyancy ratios, so heat and mass transfer become most effective. [ABSTRACT FROM AUTHOR]

• Heat and mass transfer in a SGSP are investigated experimentally and numerically. • 2D numerical model developed can accurately predict and describe the transfers. • Solar flux influence significantly on the SGSP temperature. • Solar flux influence is insignificant on the SGSP saline concentration. In this paper, experimental and numerical investigations of heat and mass transfer in a Salt Gradient Solar Pond (SGSP) are presented for the first time in the SGSP studies. The experimental approach consists of a thermally insulated parallelipedic tank filled with saline water and exposed under a solar simulator. The numerical model is developed in Fortran 95 basing on 2D Navier-Stokes, thermal energy and diffusion equations with an appropriate treatment of the SGSP boundary conditions. These equations are solved using the implicit Finite Volume Method and the SIMPLE algorithm. The study covers a 10-day period and involves two different values of the sun-like average radiation: 150 W/m2 (case 1) and 500 W/m2 (case 2). Comparisons between experimental and numerical results, for case 1, show that the numerical model developed can accurately predict and describe the heat and mass transfer with the development of the thermosolutal convection in the SGSP. Moreover, the time required to form the linear variation of the SGSP temperature is shorter for case 2 than for case 1 with a difference of 89 h, during which the LCZ temperature increases from 20 °C to 28.82 °C for case 1 and to 48.03 °C for case 2. Therefore, the energy storage takes place after a few days of the SGSP operation. In addition, the salt concentration of the LCZ decreases by about 0.83 kg/m3 and increases in the UCZ by about 1 kg/m3 for both cases. Thus, the sun-like average radiation does not have a significant influence on the mass transfer in the SGSP unlike on the heat transfer. [ABSTRACT FROM AUTHOR]

A full three-dimensional (3D) numerical simulation of solidification was carried out for a benchmark experiment on a binary Sn-10 wt. %Pb alloy. The experiment process involves a melting stage, a first holding stage at constant temperature with electromagnetic stirring, setting a mean horizontal temperature difference (second holding stage), and finally solidification stage by decreasing the temperature under a imposed horizontal temperature gradient. The numerical model is applied only to investigate the solidification stage and compared with the measured temperature fields and macrosegregation obtained from the postmortem analysis. A columnar numerical model based on a two-phase volume-averaged approach is used for the numerical simulation, accounting for thermosolutal convection and assuming perfect microscopic mixing (lever rule) in the mushy zone. It demonstrates that such a model is able to predict stratification in the solute from the liquid phase and mushy zone during the solidification. The effect of the sedimentation on macrosegregations and channel segregation or freckles which develop during the solidification stage is also predicted by the model and compared with experimental data. Emphasis is given to the main factors that have a direct effect on the development and morphology of segregated channels, namely, the remelting phenomenon, dendrite fragmentation, and the solidification front instabilities. [ABSTRACT FROM AUTHOR]

• LBM simulation of thermosolutal convection in a SGSP enclosure with porous layer. • Cross-diffusive effects on thermosolutal convection in this SGSP enclosure are analyzed. • Attaching a porous layer at the bottom inhibits the thermal and solutal transfer processes. • Du enhances both thermal and solutal transfer processes, while Sr boosts the solutal one. • Internal heat generation reduces the positive influence of Soret and Dufour effect. Salt gradient solar pond (SGSP) is a promising alternative for low-temperature industrial applications. Thermal and solutal transfer processes occur simultaneously at SGSP, which induce the cross-diffusive effects and make the internal flow more complicated. In the present work, thermosolutal convection under cross-diffusive effects inside a simplified SGSP enclosure attached with a porous layer are investigated through Lattice Boltzmann Method (LBM). Influences of internal heat generation, buoyancy ratio, thickness and permeability of porous layer combined with Soret and Dufour parameters are considered on the thermal and solutal transport characteristics. Average Nusselt and Sherwood numbers as well as mean temperature and concentration are presented to analyze the thermal and solutal transport processes in the SGSP enclosure. Results indicate that Soret effect mainly boosts the solutal transport process, while Dufour effect can greatly enhance both the thermal and solutal transport processes. Internal heat generation can inhibit the thermal and solutal transport processes and reduce the positive influence of Soret and Dufour effect. Buoyancy ratio can boost thermal and solutal transport processes. In the opposing situations (N < 0), Soret effect weakens the thermal transport process, while Dufour effect is reverse. Furthermore, attaching a porous layer at the bottom wall can suppress the thermal and solutal transfer processes, and then increases the thermal storage capacity. Permeability and thickness of porous layer have a significant influence on thermal and solutal transport processes. Present study is beneficial to the thermal storage enhancement and the future development of SGSP. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper investigates the linear and weakly nonlinear stability of thermosolutal rotating porous convection subject to a lack of thermal equilibrium. Being an example of a triply diffusive fluid system in porous media with multiparameters, some novel results on the linear instability are delineated for a few isolated cases. The otherwise stabilizing factors such as stabilizing solute concentration and rotation are shown to destabilize the system under certain parameters space. Besides, the existence of a completely detached closed convex oscillatory neutral curve from that of the stationary neutral curve is uncovered indicating the requirement of three critical thermal Darcy-Rayleigh numbers to identify the linear instability criteria instead of the usual single critical value. The multivalued nature of the stability boundaries for the case of completely detached oscillatory neutral curves is displayed. The co-dimension-2 points are found through a stability map with the demarcation of stationary and oscillatory convective regions in a plane of Darcy-Taylor and scaled Vadasz numbers. Weakly nonlinear stability theory is carried out for a stationary case by using a modified multi-scale method and thereby the complex Ginzburg-Landau amplitude equation is derived identifying the pitchfork bifurcation. Moreover, heat and mass transport are quantified in terms of average thermal and solute Nusselt numbers, respectively. [ABSTRACT FROM AUTHOR]