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The aim of this work is to numerically and theoretically model thermosolute natural convection in porous, isotropic and saturated media filled with Casson nanofluids (aluminum nanoparticles) under the influence of a magnetic field. Calculations were performed for various parameters relevant to our model, namely Casson fluid parameters (between 0.1 and 1), thermal Rayleigh number (between 10 and 100000), Geometric aspect ratio number (between 1 and 3),Buoyancy ratio number (between 1 and 10), Soret and Dufour numbers (between 0.2 and 1.2), conductivity ratios (between 1 and 3) and Hartmann numbers (between 0 and 100). The horizontal walls of the enclosure maintain uniform temperature and concentration, while the side walls are rigid, watertight, and insulated. Casson nanofluid flow occurs in porous layers and is described by the extended Darcy law of Brinkman-Forchheimer. The finite volume method was used to spatially discretize the obtained system of equations. Therefore, we investigated the effect of different parameters on the heat transfer rate and concentration. we observe that heat and mass transfer increases with increasing Casson fluid parameter; this increase is significant for the case of β between 0.1 and 0.4. And it also increases with the increase in the number of thermal conductivity ratios, the number of thrust ratios and with the increase in the thermal Rayleigh number. The latter remain unchanged when the thermal Rayleigh number is below the threshold . In the Opposite, we notice an uneven decrease in the thermosolutal transfer with the increase in the Hartmann Soret and Dufour numbers.

This numerical analysis investigates the behavior of magnetohydrodynamics (MHD) thermosolutal convection in a hybrid nanofluid made up of multi-wall carbon nanotube (MWCNT)-Fe3O4 and water along a vertical wavy surface with wall heat and mass flux conditions. The mathematical model is developed using the conservation equations of mass, momentum, energy, and energy. The governing equations are converted into a non-dimensional form using the appropriate transformation, and the implicit finite difference technique is used to solve them. The effects of various parameters, such as the Schmidt number (Sc), nanoparticles volume fraction (ϕ), wavy amplitude (a), magnetic parameter (M), buoyancy ratio (Br), on the velocity, temperature, concentration distribution (Φ), streamlines, isotherms, local skin friction coefficient (Cf), local Nusselt (Nu) number, local Sherwood number (Sh) are investigated. Results show that higher amplitude and the addition of hybrid nanofluids volume fraction slow down the heat and mass transport rate, as indicated by declining local Nusselt and Sherwood numbers. However, enhancing the buoyancy ratio increases the fluid flow’s skin friction, heat, and mass transport. The velocity, temperature, concentration distribution, skin friction, and convective heat transport within the wavy surface is weakened by the addition of the magnetic parameter M.

Abstract This article explores the influence of Joule heating and viscous dissipation on the unsteady three-dimensional squeezing flow of Newtonian fluid. The flow in a rotating channel with a lower stretched permeable wall is observed under the influence of a uniform magnetic field. The impact of thermal radiation is also considered. The effects of mass and heat transfer on the squeezing flow of Newtonian fluids are observed and modelled using the four fundamental governing equations of fluid flow: the mass equation, momentum equation, concentration equation, and energy equation. Using the appropriate similarity transformations, the resultant non-linear partial differential equations are then transformed into ordinary differential equations. The analytical strategy is developed using the homotopy analysis method to obtain the series solution. The influence of several physical parameters, including the squeezing parameter, the suction parameter, the magnetic number, the rotation parameter, the Eckert number, the Prandtl number, the Dufour number, the Soret number, the radiation parameter, and the Schmidt number, on the velocity profile, energy, and concentration are also discussed through graphs. Additionally, it is observed that enhancing the top plate’s squeezing impact causes a rise in the velocity profile while lowering the temperature and concentration distribution. It is also found that for the velocity field, increasing the magnetic number shows a decrease in the value of the velocity field along the y- and z-axis, whereas the velocity field along the x-axis exhibits dual behavior, such that it initially falls as the magnetic number intensifies but starts to rise in the upper region of the channel. The impact of the Dufour, Soret, and Eckert numbers on temperature and concentration distribution is also studied. It is found that while these numbers directly affect the temperature distribution, the mass distribution follows the opposite trend. Also, it is noticed that the thermal radiation parameter is an increasing function of temperature and mass distribution. Further, graphs and tables are presented to illustrate an error analysis.

The fractional of a time derivative for the incompressible smoothed particle hydrodynamics (ISPH) method is adopted to handle thermal radiation on thermosolutal convection in a porous cavity barred by nanoencapsulated phase change materials (NEPCMs). A novel work on the rotational velocities of two rods during thermosolutal convection of NEPCMs within a novel cavity of two connected circular cylinders is introduced. The management of heat-mass transfer and velocity magnitude inside distinct designed materials below various boundary conditions carries improvements for energy efficiency. The physical factors are thermal radiation Rd = 0 − 3 , Fusion temperature θ f = 0. 0 5 − 0. 8 , Rayleigh number Ra = 1 0 3 − 1 0 6 , hot source length L Hot = 0. 4 − 1 , Darcy number Da = 1 0 − 2 − 1 0 − 5 , and fractional order parameter α = 0. 9 5 − 1. This study reported the role of thermal/solutal conditions in varying the dual convection flow and heat capacity contour. The lower Da provides an elevated porous resistance which decelerates the nanofluid velocity. The fusion temperature alters a heat capacity contour. [ABSTRACT FROM AUTHOR]

The current study investigates Darcy-Brinkman convective instability for a non-Newtonian binary nanofluid layer in the presence of internal heat source. Non-Newtonian fluid behavior is characterized by Casson model. Normal mode technique is employed to convert the relevant PDEs into ODEs and Boussinesq approximation is used. The phenomenon is explored for both stationary as well as oscillatory modes of convection. The novelty and significance of the work lie in the fact that oscillatory motions have come into existence due to the presence of internal heat source term in the thermal energy equation which were non-existent otherwise for top-heavy configuration of nanoparticles. The impact of various nanofluid and solute parameters except solute Rayleigh number is found to destabilize the nanofluid layer while solute Rayleigh number, Darcy number and porosity parameters are found to postpone the onset of convection. Non-Newtonian Casson parameter and internal heat source strength are found to hasten the convection for the present arrangement of nanoparticles. [ABSTRACT FROM AUTHOR]

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

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]

This study unveils a numerical paradigm that amalgamates the partially saturated lattice Boltzmann method (PSLBM) with the non‐isothermal quantitative phase‐field (PF) model. This innovative integration equips us with a prognostic tool ready to elucidate the progression and motion of solid‐air dendritic growth in the presence of both natural and forced convection. The PSLBM is employed to compute the flow of the solution and the interaction forces between the fluid and solid dendrites. Concurrently, the PF model is utilized to simulate the formation of solid‐air dendrites. The reliability of calculating of interaction forces between the fluid and solid was confirmed through a numerical case study involving fluid flow around a stationary cylinder. The results indicate that this model is applicable for simulating the growth and evolution of single/multiple solid‐air dendrites under the influence of convection, whether they are stationary or in motion. The promotion of the upstream side dendritic arms and the inhibition of the downstream dendritic arms increase with the intensification of natural convection. As the initial undercooling is raised, the capacity of natural convection to reshape dendritic morphology gradually diminishes. With the enhancement of forced convection intensity, due to alterations in the flow pattern, the downstream dendritic arms do not consistently exhibit growth suppression. The motion of solid‐air dendrites induced by forced convection counteracts the influence of convection, resulting in slightly faster growth of the downstream dendritic arms compared to the upstream arms. Simultaneously, it fosters the formation of secondary dendritic branches in the upstream zone. [ABSTRACT FROM AUTHOR]

In this article, the phenomenon of thermosolutal convection within a fluid characterized by the Brinkman–Darcy–Kelvin–Voigt (BDKV) model is delved into, while the impact of couple stresses on this process is considered. Both linear instability and nonlinear stability analyses are encompassed in our investigation. Several noteworthy observations have been made. When the fluid layer is heated from below and salt is introduced from above, it is found that the points at which stability and instability thresholds are reached coincide. This alignment is supported by the validity of the linear theory in predicting the initiation of convection under these conditions. However, the scenario changes when the layer is salted from the bottom while being heated. In this case, the stability thresholds remain constant, regardless of variations in the salt Rayleigh number. This discrepancy between the thresholds of linear instability and nonlinear stability is deemed significant. To gain a deeper understanding, numerical computations were conducted to identify and thoroughly discuss the thresholds of linear instability. These findings offer valuable insights into the behavior of the system under study. It is indicated by our results that parameters such as Brinkman, couple stresses, and Kelvin–Voigt contribute to stabilizing the system. Additionally, it was noted that the salt Rayleigh number has a stabilizing effect when the layer is salted from below, whereas it has a destabilizing effect when salt is introduced from above. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present a numerical study along with an exhaustive adsorption investigation in a binary dilute mixture model nearby the solvent’s critical point in a configuration relevant for soil remediation. By means of this model, mass and heat transfer efficiency were qualitatively and quantitatively discussed through this work. The convergence of the solution was evaluated on the values of the Nusselt and Sherwood numbers. The results reveal intense convection expanding into the cavity close to the critical point, thus enabling homogeneous adsorption of the solute. Moreover, the mass fraction perturbation isolines exhibit the existence, along the adsorbent plate, of a thin boundary layer which becomes thinner when approaching the critical point.

The thermosolutal stability of a layer of the Rivlin-Ericksen fluid in a porous medium is considered under varying gravity conditions. It is found that for stationary convection, medium permeability and suspended particles have a destabilizing/stabilizing effect when gravity increases/decreases. The stable solute gradient has a stabilizing effect on the system.

The characteristics of a stationary flow of a volatile liquid driven by a co-current gas flux in a flat horizontal mini-channel upon the non-zero transverse temperature drop are studied. We use an exact solution of the thermosolutal convection equations for describing the heat and mass transfer caused by the combined action of gas pumping, buoyancy, thermocapillarity and linear heating of the channel walls in a two-layer system. The influence of heating from above on the parameters of the ground state and the stability characteristics of the basic flow is explored using an example of the ethanol–air system. We evaluate the thresholds of the linear stability and select the most dangerous modes. Heating from above results in flow stabilization. Instability appears in the form of oscillatory cellular convective patterns.

A model for thermosolutal convection of a category of viscoelastic fluids in a bidisperse porous medium is comprehensively investigated. The Brinkman model is employed in macropores, whereas the Darcy model is utilized in micropores. In the momentum equations, the densities are considered a linear function of temperature and concentration. The concentration of solutes at equilibrium is assumed to be a linear function of temperature. There are two situations considered, where we have study systems that are heated below and salted above and heated and salted below. The fluids are of the Kelvin–Voigt type. The critical Rayleigh numbers for linear instability and nonlinear stability are computed. [ABSTRACT FROM AUTHOR]

The present paper reports on an analytical and numerical study of combined Soret and Dufour effects on thermosolutal convection in a horizontal porous cavity saturated with an electrically conducting binary fluid under a magnetic field. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The main governing parameters of the problem are the Rayleigh, the Hartmann, the Soret, the Dufour and the Lewis numbers, the buoyancy ratio, the enclosure aspect ratio, and the normalized porosity of the porous medium. An asymptotic parallel flow approximation is applied to determine the onset of subcritical nonlinear convection. In addition, a linear stability analysis is performed to predict explicitly the thresholds for the onset of stationary, overstable and oscillatory convection, and the Hopf bifurcation as functions of the governing parameters. The combined effect of a magnetic field, Soret and Dufour parameters have a noticeable influence on the intensity of the convective flow, the heat and mass transfer rates, and the thresholds of linear convection. It is found that the imposition of a magnetic field delays the onset of convection and its intensification can lead to the total suppression of the convective currents. The heat transfer rate increases with the Dufour number and decreases with the Soret number and vice versa for the mass transfer rate.

During the transmission of heat and mass inside an annulus, the impacts of the thermal diffusion & diffusion-thermo should be considered. Then the target of this paper is solving the thermosolutal convection of a nanofluid inside an annulus amongst a square cavity and an inner prismatic shape with three circular cylinders. The ranges of the considered parameters are the solid volume fraction (0≤φ≤0.1), circular cylinder's radius (0.01≤Rc≤0.075), Hartmann number (0≤Ha≤40), Dufour number (0.03≤Du≤0.6), Rayleigh number (103≤Ra≤106), and Soret number (0.1≤Sr≤2). The results indicated that the radius of the circular cylinders is improving the nanofluid moments and strengths of convection flow in an annulus. The maximum of the streamlines is reducing according to an augmentation in Hartmann number or solid volume fraction. The extra buoyancy forces at higher Rayleigh numbers are improving the strengths of the temperature, concentration, and streamlines within an annulus. The mean Nusselt/Sherwood numbers are enhanced along with an expansion in the solid volume fraction or radius of the circular cylinders.

The present work introduces numerical simulations based on an incompressible scheme of smoothed particle hydrodynamics (ISPH) method for the thermosolutal convection from an inner I-shaped inside an infinite-shaped cavity embedded by nano-encapsulated phase change materials (NEPCMs). An infinite-shaped enclosure is occupied by a nanofluid and a porous medium. In this work, the heat capacity of a core and shell is used for the overall heat capacity of encapsulated nanoparticles. An inner I-shaped is embedded inside a center of an enclosure and it carries Th and Ch. The simulations are performed for different values of a length of an inner I-shaped L2(0.4≤L2≤1.5), a Stefan parameter Ste(0.2≤Ste≤0.9), a fusion temperature θf(0.05≤θf≤0.95), Darcy parameter Da(10−2≤Da≤10−5), an inclination angle γ (0≤γ≤π/2) and Rayleigh number Ra(103≤Ra≤106). The numerical simulations showed that a fusion temperature θf adjust the situations of a melting solidification zone. Further, the intensity of a melting solidification zone is adjusted by a Stefan parameter. Augmentations of an inner I-shaped length and Rayleigh number are powering buoyancy forces and thus the flow speed, and heat & mass transport are enhanced inside an infinite-shaped cavity. Mean Nusselt and Sherwood numbers are enhanced as I-shaped length and Rayleigh number are powered.