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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]

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]

In this paper, we study the problem of thermosolutal convection in a Navier–Stokes–Voigt fluid when the layer is heated from below and simultaneously salted from above or below. This problem is studied under the effects of Soret and slip boundary conditions. Both linear and nonlinear stability analyses are employed. When the layer is heated from below and salted from above, the boundaries exhibit great concordance, resulting in a very narrow region of probable subcritical instabilities. This proves that linear analysis is reliable enough to forecast the beginning of convective motion. The Chebyshev collocation technique and QZ algorithm have been used to solve systems of linear and nonlinear theories. For thermal convection in a dissolved salt field with a complex viscoelastic fluid of the Navier–Stokes–Voigt type, instability boundaries are computed. When the convection is of the oscillatory type, the Kelvin–Voigt parameter is observed to play a crucial role in functioning as a stabilizing agent. This effect's quantitative size is shown. [ABSTRACT FROM AUTHOR]

In the present paper, a numerical investigation was performed to assess the effect of the rheological behavior of non-Newtonian fluids on Rayleigh–Bénard thermosolutal convection instabilities within shallow and finite aspect ratio enclosures. Neumann and Dirichlet thermal and solutal boundary condition types were applied on the horizontal walls of the enclosure. Using the Boussinesq approximation, the momentum, energy, and species transport equations were numerically solved using a finite difference method. Performing a nonlinear asymptotic analysis, a bistability convective phenomenon was discovered, which was induced by the combined fluid shear-thinning and aiding thermosolutal convection effects. Therefore, bistability convection was the main focus in the current study using the more practical constitutive Carreau–Yasuda viscosity model, which is valid from zero to infinite shear rates. Also, the combined effects of the rheology parameters and double diffusive bistability convection were studied. For aiding flow, the shear-thinning and the slower diffusing solute effects were counteracting and, as a result, two steady-state finite amplitude solutions were found to exist for the same values of the governing parameters, which indicated and demonstrated evidence for the existence of bistability convective flows. For opposing flows, the shear-thinning effect strengthened subcritical flows, which sustained well below the threshold of Newtonian thermosolutal convection. Thus, bistability convection did not exist for opposing flows, as both the shear-thinning and the slower diffusing component effects favored subcritical convection. [ABSTRACT FROM AUTHOR]

We examine the nature of the thermosolutal convection with or without rotation in the infinite Prandtl number regime, which is applicable to magma chambers. The onset of bifurcation and the structure of the bifurcated solutions in this double diffusion problem are analyzed. The stress-free boundary condition is imposed at the top and bottom plates confining the fluid. For the rotation free case, two-dimensional Boussinesq equations are considered and we prove that there are bifurcating solutions from the basic solution and that the bifurcated solutions consist of only one cycle of steady state solutions that are homeomorphic to S1. By thoroughly investigating the structure and transitions of the solutions of the thermosolutal convection problem in physical space, we confirm that the bifurcated solutions are indeed structurally stable. In the presence of rotation, we consider three-dimensional Boussinesq equations and we can get similar results as of the rotation free case. We also see how intensively the rotation inhibits the onset of convective motion. In turn, this will corroborate and justify the suggested results with the physical findings about the presence of roll structure. [ABSTRACT FROM AUTHOR]

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

The effect of thermosolutal convection on the solute segregation in crystals grown by vertical directional solidification of binary metallic alloys or semiconductors is considered. Numerical results are obtained using finite differences in a two-dimensional, time-dependent model that assumes a planar crystal-melt interface. The configuration is assumed to be periodic in the horizontal direction with a given period, and the possibility of multiple flow states sharing the same period is examined. The results are summarized in bifurcation diagrams of the nonlinear states associated with the critical points of linear theory. The use of a time-dependent numerical scheme results in gaps in the bifurcation diagram where presumed unstable states exist that cannot be computed by this procedure. As the solutal Rayleigh number is varied, multiple steady states, time-periodic states, and quasiperiodic states may occur. This case is compared to the simpler case of thermosolutal convection with linear vertical gradients and stress-free boundaries, for which a rather complete numerical treatment is possible through the use of a simple spectral representation of the nonlinear solution, Retaining a finite number of terms in the expansion results in a set of coupled nonlinear algebraic equations for the Fourier coefficients, which is solved by a quasi-Newton method. The linear stability of the nonlinear solutions is also determined from a numerical computation of the eigenvalues of the Jacobian matrix. The resulting bifurcation diagram shows qualitative similarity to the bifurcation diagram computed for the solidification system. [ABSTRACT FROM AUTHOR]

The influence of an externally enforced compositional gradient on the onset of convection of a mixture of two components in a rotating fluid spherical shell is studied for Ekman numbers E = 10-3 and E = 10-6, Prandtl numbers σ = 0.1, 0.001, Lewis numbers τ = 0.01, 0.1, 0.8, and radius ratio η = 0.35. The Boussinesq approximation of the governing equations is derived by taking the denser component of the mixture for the equation of the concentration. Differential and internal heating, an external compositional gradient, and the Soret and Dufour effects are included in the model. By neglecting these two last effects, and by considering only differential heating, it is found that the critical thermal Rayleigh number Rec depends strongly on the direction of the compositional gradient. The results are compared with those obtained previously for pure fluids of the same σ. The influence of the mixture becomes significant when the compositional Rayleigh number Rc is at least of the same order of magnitude as the known Rec computed without mixture. For positive and sufficiently large compositional gradients, Rec decreases and changes sign, indicating that the compositional convection becomes the main source of instability. Then the critical wave number mc decreases, and the drifting waves slow down drastically giving rise to an almost stationary pattern of convection. Negative gradients delay the onset of convection and determine a substantial increase of mc and ωc for Rc sufficiently high. Potential laws are obtained numerically from the dependence of Rec and of the critical frequency ωc on Rc, for the moderate and small Ekman numbers explored. [ABSTRACT FROM AUTHOR]

Studies the bifurcation phenomena confined in thermosolutal convection with lateral heating. Values of the salinity Rayleigh number fixed near the commencement of the double-diffusive region; Variety of multiple steady flows resulting from hysteresis points and isolas of asymmetric solutions.

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double-diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe. [ABSTRACT FROM AUTHOR]

In this paper, we study the effect of a homogeneous longitudinal through flow on the onset of convection in a horizontal porous layer saturated by a binary fluid and heated from below or above. The layer boundaries are subjected to a constant heat flux. The investigation is made by taking the Soret effect into account. It is found that in the case of positive separation ratio when the denser component moves toward the cooler wall, through flow has no effect on the stability threshold but exerts an orientating effect on the convective patterns. For negative separation ratio, a strong destabilization occurs of the spatially homogeneous state with respect to long-wave disturbances. The stability range for long-wavelength convective rolls is defined. [ABSTRACT FROM AUTHOR]

A layer of fluid lies between two parallel horizontal walls and the solute concentration and temperature are higher at the bottom wall. The onset of time-periodic instability in this double diffusion problem in three dimensions is analyzed. Periodicity with respect to the hexagonal lattice is assumed. The no-slip condition is imposed at the top and bottom boundaries. There are 11 bifurcating solutions, and their stability is presented. For relatively low solutal and thermal Rayleigh numbers, the solutions are found to be unstable. For the heating of salty water, situations are presented where the standing rolls, the standing patchwork quilt, and either the standing hexagons or the standing regular triangles, may be stable. [ABSTRACT FROM AUTHOR]

The study investigates the thermosolutal convection of a Casson fluid in a horizontal layer that is heated and salted from below. Both linear and non-linear analyses are performed using the method of normal modes to solve the governing equations. Interestingly, the study demonstrates that the linear and non-linear stability thresholds coincide. To solve the differential eigenvalue problem for linear theory, a one-term Galerkin approach is employed. Meanwhile, for the eigenvalue problem of non-linear instability, a numerical solution is obtained using the bvp4c routine in MATLAB. The results reveal some important findings. First, the Casson parameter is shown to destabilize the flow, leading to instability. However, the Darcy number and solutal Rayleigh number are found to have a stabilizing effect on the system. Furthermore, the study develops a weakly non-linear theory using multiple scale analysis to investigate heat and mass transport, offering valuable insight into these transport phenomena within the context of the system under consideration. [ABSTRACT FROM AUTHOR]

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

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

The convective instability that arises in a porous layer solely because of dissipative energy in the medium is studied. The thermal non-equilibrium model is considered for energy equation. The boundary at top is kept at constant temperature, and an adiabatic lower boundary is considered. The momentum equation is written according to the Brinkman model. A basic flow in the horizontal plane is considered, and the basic velocity and temperature profile have been derived. A comparison between the basic temperature profiles for solid and fluid of the porous medium is presented for Darcy and Brinkman models. Infinitesimal disturbance is introduced to the basic flow. A linear stability analysis has been carried out to study the stability of the basic flow. The parameters influencing the stability of the system are critical Rayleigh number (RaC), Gebhart number (Ge), ξ associated with the Darcy number (Da), and interphase heat transfer coefficient (H). The values of the critical Rayleigh number and wavenumber are compared by varying other variables. The flow is more stable when the Brinkman medium is considered. With the increase in interphase heat transfer coefficient, the critical Rayleigh number increases in both Darcy and Brinkman media. The longitudinal rolls appear as the most unstable rolls for all cases. The variation of convective rolls with respect to ξ and heat transfer coefficient is presented. [ABSTRACT FROM AUTHOR]

The linear instability and the nonlinear stability analyses have been performed to examine the combined impact of a uniform vertical throughflow and a depth-dependent viscosity on bidispersive porous convection using the Darcy theory with a single temperature field. The validity of the principle of exchange of stability is proved. The eigenvalue problems resulting from both linear instability and nonlinear stability analyses with variable coefficients are numerically solved using the Chebyshev pseudo-spectral method. The equivalence of linear instability and nonlinear stability boundaries is established in the absence of throughflow, while in its presence, the subcritical instability is shown to be evident. The stability of the system is independent of the direction of throughflow in the case of constant viscosity, whereas upflow is found to be more stabilizing than downflow when the viscosity is varying with depth. While the viscosity parameter offers a destabilizing influence on the onset of convection in the absence of throughflow, it imparts both stabilizing and destabilizing effects on the same in its presence. The influence of the ratio of permeabilities and the interphase momentum transfer parameter is to make the system more stable. The findings of a mono-disperse porous medium are presented as a specific case within the broader context of this investigation. [ABSTRACT FROM AUTHOR]

In this effort, the consequence of chemical reaction on the thermohaline convection in a permeable layer containing Casson fluid is inspected utilizing both linear and nonlinear stability procedures. To model the momentum equation, the Casson fluid version of Darcy's law is utilized. Applying the linear stability concept, the situation for the start of stationary and oscillatory pattern of convective motion is obtained, whereas the convective heat and mass transferences are determined using nonlinear stability theory. It is found that the oscillatory type of convective flow is probable only if the evaluation of the solutal Rayleigh–Darcy number is less than zero. The effect of the chemical reacting factor, the Casson factor, the Lewis number, and the solutal Rayleigh–Darcy number is to hurry the start of convection toward both stationary and oscillatory styles of convection and also surge the size of the convective cells. The convective heat and mass transfers enhance with increasing the Casson factor, the solutal and thermal Rayleigh–Darcy numbers while both decrease with enhancing the heat capacity quotient. The effect of chemical reacting factor is to increase the mass transmission in the system, while it has no effect on the heat transmission. It is also noted that the convective heat and mass transfers in the system enhance nearly 5.4% and 3.8%, respectively, with a 50% increase in the value of Casson factor. [ABSTRACT FROM AUTHOR]

A finite difference lattice Boltzmann approach is introduced to address the two-dimensional macroscopic equations of velocity–vorticity for generalized Newtonian fluids (GNFs). The study involves equations governing macroscopic momentum, energy, and concentration, along with constitutive models applicable to Newtonian, power-law, and viscoplastic fluids. Subsequently, the lattice Boltzmann method, which recovers these macroscopic equations, is detailed, along with proof of its capability to reproduce the aforementioned equations. In order to evaluate the effectiveness and time efficiency of the method, it is validated against various benchmarks. The results demonstrate the efficacy of the proposed method in successfully solving isothermal, thermal, and solutal problems of GNFs, while significantly reducing computational time compared to our previously suggested approach in this domain. [ABSTRACT FROM AUTHOR]

This study extensively examines double-diffusive natural convection of a water nanofluid containing Al2O3 nanoparticles in both horizontal and vertical rectangular enclosures subjected to uniform thermal and solutal fluxes along the horizontal direction. The key contribution of this research is to emphasize the significance of aspect ratio as a critical factor for enhancing heat transfer. Neglecting this factor could have substantial implications for the advancement and practical application of nanotechnology in heat transfer. The study also examines the impact of other relevant parameters namely nanoparticle concentration, thermal Rayleigh number, and three distinct models to calculate effective viscosity and thermal conductivity. A comparison among these models highlights a notable disparity between models based on experimental data (model II and III) and that based on theoretical assumptions (model I). It was revealed that the thermal Rayleigh number manifests a notable impact on both heat and mass transfers, especially for horizontal enclosures, and an augmentation in the aspect ratio improves the convective heat and mass transfers. However, for lower Rayleigh numbers, the aspect ratio effect diminishes. The incorporation of nanoparticles might deteriorate up to 21% or enhance up to 12% heat transfer according to the dominant transfer mode, we obtain the enhancement in conduction and deterioration in convection. Model I gives higher Nusselt and Sherwood numbers, followed by models II and III, but model I showed a peculiar behavior compared to models II and III. A critical aspect ratio is identified which defines the regions where nanofluid enhances heat transfer compared with clear water. [ABSTRACT FROM AUTHOR]

This study aims to numerically investigate the effect of surface radiation on double diffusion convection in a low Mach number compressible gaseous mixture, specifically focusing on the H2–air system in a square cavity. The cavity is subjected to low horizontal temperature and concentration gradients and isolated from its flat walls. The mathematical model's equations were discretized using the finite volume method based on the semi-implicit method for pressure-linked equations revised algorithm for the pressure–velocity coupling. The radiosity method is employed to calculate the radiative heat exchange between the internal walls of the cavity. This work addresses a significant research gap by exploring the interplay between surface radiation, compressibility effects, and double diffusion convection. It makes a novel contribution to the field and has implications for combustion, astrophysics, and industrial heat exchange processes. Comparing the results with those obtained for a light gaseous mixture, the findings demonstrate that the presence of radiation considerably modifies the thermal, dynamic, and mass fields, as well as the thermophysical properties of the gaseous mixture in the case of heavy gaseous mixtures. These modifications can reach up to 20%.The outcomes of this study provide a foundation for further research and experimentation, with applications ranging from engineering to astrophysics. [ABSTRACT FROM AUTHOR]

Uniform flow past side-by-side circular cylinders is a classical fluid dynamic model that triggers rich phenomena, from which asymmetric wakes usually emerge. Such asymmetry arising from a completely symmetric geometric setting is of theoretical interest when exploring the system bifurcations. Using direct numerical simulation, a detailed parametric map of the wakes behind two side-by-side circular cylinders is presented with several asymmetric wake patterns. These include asymmetric anti-phase (AAP), typical and special deflected (DF), and in-phase (IP) flows, for which AAP and special DF flows are discovered for the first time. Additionally, the IP flow is simulated by both two- and three-dimensional grids to explore the effect brought by three-dimensional vortical structures. The evolution of these asymmetric wakes is analyzed in different phases, with the aid of the wavelet transform, Hilbert–Huang transform, and dynamic mode decomposition, to reveal their temporal variations of developing features. Interestingly, although revealing with distinct fully developed flow fields, there are several common dynamics identified among these wake patterns: AP and IP vortex shedding, wake transition, and gap flow oscillation. The vicissitudes of dynamic flow evolution allow us to further differentiate several wake patterns and ultimately contribute to a deeper understanding of asymmetric flows. [ABSTRACT FROM AUTHOR]

Torsional flows are preferred at the onset of thermal convection in fluid spheres with stress-free and perfectly conducting boundary conditions, in a narrow region of the parameter space for Prandtl numbers Pr ≲ 0.9 and ratios Pr / Ek = O (10) , with Ek being the Ekman number. In this case, the transport of heat to the exterior is supposed instantaneous. When the thermal conductivity of the internal fluid is large, and the external convective heat transfer or radiative emissivity is low, the heat transmission is less efficient, and the thermal energy retained in the interior increases, enhancing the onset of convection. This study is devoted to analyzing the combined influence of the thermal conductivity and external conditions (temperature and resistance to heat transport) on the onset of the torsional convection by taking a Robin boundary condition for the temperature at the surface of the sphere. It is shown, by means of the numerical computation of the curves of simultaneous transitions to torsional flows and Rossby waves, that when the heat flux through the boundary decreases, the region where the axisymmetric flows are preferred shrinks, but it never strangles to an empty set. It has been found that with adequate scalings the curves delimiting the transition to torsional flows, and those of the critical Rayleigh number, Ra c , and the frequencies of the modes vs Ek become almost independent of the parameter of the Robin boundary condition. [ABSTRACT FROM AUTHOR]

The present paper deals with the investigation of the Soret-induced convection of a three-component mixture of hydrocarbons in a horizontal porous layer. This problem is important for geological applications. The first part of the paper is devoted to the linear stability of the conductive state. The longwave instability is studied analytically by the expansion into the power series with respect to the wave number. A new long-wave oscillatory instability mode existing at negative separation ratios is found out. It is shown that this mode is more dangerous than the long-wave monotonic instability mode in the entire range of its existence. The instability to the perturbations with nonzero wave numbers is studied numerically by the shooting method. Stability map is obtained. The results confirm the predictions of the longwave analysis. In the second part of the paper, the nonlinear convection regimes are studied by the finite difference method. The calculations give the results consistent with the linear stability analysis. It is found that the primary bifurcation as a result of which the conductive state losses its stability is supercritical. The transformations of the convective flow structure with the change in the Rayleigh–Darcy number are accompanied by the hysteresis phenomena. [ABSTRACT FROM AUTHOR]

Linear stability and weakly nonlinear stability analyses are developed for Rayleigh–Bénard convection in water near 3.98 °C subject to isothermal boundary conditions. The density–temperature relationship (equation of state) is approximated by a cubic polynomial, including linear, quadratic, and cubic terms. The continuity equation, the Navier–Stokes momentum equation, the equation of state, and the energy equation constitute the governing system. Linear stability analysis is used to investigate how the maximum density property of water affects the onset of convective instability and the choice of unstable wave number for four different types of boundary conditions. Then, a weakly nonlinear stability study is done using the spectral Fourier method for isothermal tangential stress-free boundary conditions to quantify the heat transport of the system and demonstrate the transition from regular/periodic convection to chaotic convection. A Stuart-Ginzburg–Landau equation is obtained using the multiscale expansion method. Streamlines and isotherms are presented and analyzed. The influence of maximum density has been shown to delay the onset of instability and is, therefore, a stabilizing mechanism for thermal instability. Due to the maximum density, the onset of chaotic convection is also delayed. Among four different boundaries, the impermeable rigid boundaries require the highest Rayleigh number for instability to begin. Increasing boundary temperatures advance the onset of chaotic convection and improve the heat transport situation. [ABSTRACT FROM AUTHOR]

Previously, the double-diffusive convection (or the DDC) generated through the interaction between horizontal temperature and concentration gradients had been investigated by both experimental and computational studies. In the present study, we employ a theoretical approach by performing linear stability analysis to examine the stability characteristics of the DDC under a wide range of physical parameters. Results show that, under the competition between the two gradients, the stability can be discerned into thermal, salt-finger, and diffusive types, where all are influenced by both the Prandtl number Pr and Lewis number Le. The onset of instability can be the stationary shear mode (or the SSM) or the oscillatory buoyant mode (or the OBM), depending on both Pr and Le. Specifically, for the solute Grashof number Gs < 10, the onset of instability changes from SSM to OBM at the transition boundary Pr = 12.5; for the thermal Grashof number Gt < 10, the transition boundary is governed by the relation Pr = 12.5Le−1.11 + 0.46. We compare the present results with those of previous studies to justify the linear stability analysis's correctness and infer that the DDCs observed by previous experiments and nonlinear computations are nonlinear salt-finger convection. [ABSTRACT FROM AUTHOR]

A finite difference lattice Boltzmann method (FDLBM) for the simulation of mud and debris flows for one-dimensional cases has been introduced. The proposed FDLBM recovers the generalized equations of mud and debris flows, that is, an unsteady one-dimensional Saint-Venant equation, including the effects of the non-Newtonian behavior of the mixture of water and soil, contraction–expansion losses (or large eddy loss), wind force, various geometries, and lateral inflow or outflow. The proposed FDLBM can be implemented for various non-Newtonian viscoplastic constitutive models of the studied mud and debris flows. The method is validated against previous studies for several benchmark cases, including steady-state problems, hydraulic jump tests, dam breaks with dry and wet beds, and slope dam break floods. Finally, the Anhui debris dam failure flood was investigated by this approach, and the results demonstrated a good agreement with the observed computational and field tests. [ABSTRACT FROM AUTHOR]

We investigate thermal convection instability in a system of two horizontal miscible liquid layers confined in an annular Hele–Shaw cell rotating uniformly about its axis and subjected to a radial temperature gradient. We first determine the Hele–Shaw averaged velocity field in each fluid layer by taking into account the Coriolis force. Thereafter, the linear stability analysis leads to an eigenvalue problem solved numerically by the spectral collocation method. Depending on the buoyancy number, the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly, the centrifugal force gives rise to two convection regimes: the oscillating regime corresponding to single-cell convection over the entire width of the Hele–Shaw cell and the stratified regime with separate convection in each of the two layers. In the stratified regime, it turns out that the cells rotate in the same direction and, thus, only thermal coupling is dominant in the Hele–Shaw cell geometry, regardless of the value of the viscosity ratio. We show that increasing the curvature parameter of the cell has a stabilizing effect and decreases the critical Buoyancy number corresponding to the transition from the oscillatory to the stratified regime. At a low Ekman number, the Coriolis force is strongly stabilizing and has little effect on the critical buoyancy number. Moreover, the increase in the curvature parameter and the decrease in the Ekman number together cause the transition from the oscillating regime to a nearly stratified regime. The effects of fluid layer thicknesses and the ratio of kinematic viscosities on the active or passive character of a layer are also examined. [ABSTRACT FROM AUTHOR]

Inspired by the applications in electromagnetic nanomaterials processing in enclosures and hybrid fuel cell technologies, a mathematical model is presented to analyze the mixed convective flow of electrically conducting nanofluids (γ - A l 2 O 3 − H 2 O and γ - A l 2 O 3 − C 2 H 6 O 2 ) inside a square enclosure saturated with porous medium under an inclined magnetic field. The Tiwari–Das model, along with the viscosity, thermal conductivity, and effective Prandtl number correlations, is considered in this study. The impacts of Joule heating, viscous dissipation, and internal heat absorption/generation are taken into consideration. Strongly nonlinear conservation equations, which govern the heat transfer and momentum inside the cavity with associated initial and boundary conditions, are rendered dimensionless with appropriate transformations. The marker-and-cell technique is deployed to solve the non-dimensional initial-boundary value problem. Validations with a previous study are included. A detailed parametric study is carried out to evaluate the influences of the emerging parameters on the transport phenomena. When 5 % γ - A l 2 O 3 nanoparticles are suspended into H 2 O base-fluid, the average heat transfer rate of γ - A l 2 O 3 − H 2 O nanoliquid is increased by 25.63 % compared with the case where nanoparticles are absent. When 5 % γ - A l 2 O 3 nanoparticles are suspended into C 2 H 6 O 2 base-fluid, the average heat transfer rate of γ - A l 2 O 3 − C 2 H 6 O 2 nanofluid is increased by 43.20 % compared with the case where nanoparticles are absent. Furthermore, when the heat source is present, the average heat transfer rate of γ - A l 2 O 3 − C 2 H 6 O 2 nanofluid is 194.92 % higher than that in the case of γ - A l 2 O 3 − H 2 O nanofluid. [ABSTRACT FROM AUTHOR]

The direction of coupled buoyancy and electric forces has a significant effect on both the fluid flow and heat transfer in an electro-thermo-convection (ETC) system. Here, we theoretically and numerically investigate the instability and bifurcations of ETC inside a tilted square cavity. A linear stability analysis is conducted using a unified linearized-lattice Boltzmann model by solving the coupled linear Navier–Stokes equation, linear Poisson equation, linear Nernst–Planck equation, and the linear energy equation. The numerical simulation is performed by integrating our code with the Palabos library. Results show that the interactions between the stabilizing buoyancy force and electric force lead to a Hopf bifurcation for Rayleigh number Ra = 1 × 105. The steady flow transitions to a traveling-wave flow by a subcritical bifurcation when tilted angles are less than δc ∈ [48°,49°]. For tilted angles above δc, the flow loses its stability through a local oscillation caused by a supercritical bifurcation. Finally, the chaotic behavior is quantitatively analyzed through the calculation of the Lyapunov exponent, which increases linearly with the electric Rayleigh number and is weakly dependent on the tilted angle. [ABSTRACT FROM AUTHOR]

Controlling the flow and heat transfer characteristics of conductive gases in circular tubes by means of applied magnetic fields is of great significance in various applications. However, the specific effects of magnetic fields with different orientations on these flow and heat transfer characteristics remain poorly understood. This paper addresses this issue by applying numerical calculations for evaluating the effect of magnetic fields (MFs) with different magnitudes defined according to the Hartmann number (Ha) ranging from 0 to 740 and orientation, including transverse (TMFs), axial (AMFs), and radial (RMFs) on the flow and heat transfer characteristics of high-temperature conductive gas flows with Reynolds numbers (Re) ranging from 9612 to 32 040. The results demonstrate that applied TMFs have anisotropic effects on the flow and heat transfer of conductive gases, while the effects of applied AMFs and RMFs are isotropic. Applied AMFs have little effect on the heat transfer characteristics of conductive gases, while applied TMF and RMF conditions suppress heat transfer at the tube wall, and the suppression effect of RMFs is stronger. Moreover, the heat transfer suppression effect of applied TMFs and RMFs first increases and then decreases with increasing Ha for a constant Re, and the value of Ha required to achieve the optimal heat transfer suppression effect increases with increasing Re. In addition, the transition gradient of the magnetic field directly outside of the applied magnetic field region causes the accumulation of Joule heat and therefore detracts significantly from the heat transfer suppression effect of TMFs and RMFs. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of two-dimensional double-diffusive convection is numerically investigated using a high-accuracy numerical method. The process of flow transition in the presence of buoyancy is studied in detail, and the effects of the fluid properties and geometric parameters on the flow characteristics and heat and mass transfer are discussed. The results show that, as the buoyancy ratio increases from 0 to 2, the flow undergoes a complex series of transitions, from a steady, temperature-dominated state to periodic motion, then chaotic motion, back to periodic motion, and finally back to a steady, concentration-dominated state. At a fixed buoyancy ratio, when the Prandtl number Pr is less than 1, the flow changes from periodic or chaotic to steady with increasing Pr, and the heat and mass transfer efficiencies oscillate with an increasing trend. When P r ≥ 1 , the flow is steady, and the heat and mass transfer remain nearly constant. For low Rayleigh numbers, the heat and mass transfer efficiencies increase monotonically with increasing Lewis number, but the flow is always in a steady state. For high Rayleigh numbers, the flow transitions from steady to periodic or chaotic via a supercritical Hopf bifurcation with increasing Lewis number, and the heat and mass transfer efficiencies oscillate with an increasing trend. In the range of aspect ratios considered in this study, the heat and mass transfer efficiencies exhibit an overall decay with increasing aspect ratio. [ABSTRACT FROM AUTHOR]

Analytical study of linear and weakly nonlinear stability analyses of Rayleigh–Bénard convection in a chemically reactive two-component fluid system is reported by considering physically realistic and idealistic boundaries. Analytical expression for the eigenvalue as functions of the chemical potential and the relaxation parameter is reported in the cases of stationary, oscillatory, and subcritical instabilities. The preferred stationary mode at onset is attributed to the assumption of a chemical reaction. The possibility of subcritical motion in a specific range of values of the relaxation parameter is reported and the threshold value of this parameter at which the transition from the subcritical to the critical motion takes place is documented for different values of the chemical reaction rate. The higher-order generalized Lorenz model leads to the reduced-order cubic–quintic, Ginzburg–Landau equation (GLE), and using its solution, the heat transport is quantified in steady and unsteady convective regimes. The drawback of the cubic GLE and the need for the cubic–quintic GLE for studying the heat transfer in the case of subcritical regime is explained. The possibility of having pitchfork and inverted bifurcations at various values of the relaxation parameter is highlighted. The steady Nusselt number plots clearly show that in the case of a supercritical bifurcation, a smooth transition takes place from unity in the conduction state to a higher value as the Rayleigh number exceeds its critical value predicted by linear theory. In the case of subcritical bifurcation, however, a discontinuous transition is observed. [ABSTRACT FROM AUTHOR]

The impact of chemical reactions on the double-diffusive convective motion in a non-Newtonian viscoelastic fluid (Kuvshiniski type) saturated porous layer is examined applying both linear and nonlinear stability techniques. The Darcy model that includes the Kuvshiniski type viscoelastic effect of viscoelastic fluid and the Boussinesq estimation is employed as the momentum equation. The conditions for the occurrence of the stationary and oscillatory style of convective motions are determined by applying linear stability theory in terms of a critical thermal Rayleigh–Darcy number. Using the weakly nonlinear stability analysis, the convective heat and mass transfers are calculated. It is observed that the occurrence of oscillatory convection is possible only if the value of the solute Rayleigh–Darcy number is negative and also depends on other involved physical parameters. With rising values of the Kuvshiniski parameter and the heat capacity ratio, the range of the solute Rayleigh–Darcy number in which oscillatory convection is privileged diminishes, whereas it grows with the chemical reacting parameter and the Lewis number. The critical thermal Rayleigh–Darcy number at which the convective motion occurs increased nearly 3% with a 15% increase in the value of the Kuvshiniski parameter. Furthermore, the convective heat and mass transfers are reduced by growing the Kuvshiniski parameter and the heat capacity ratio, while both are enhanced by increasing the thermal Rayleigh–Darcy number and the solute Rayleigh–Darcy number. [ABSTRACT FROM AUTHOR]

Thermal-viscous fingering instability in porous media is a common phenomenon in nature as well as in many scientific problems and industrial applications. Despite the importance, however, thermal transport in flow of a non-Newtonian fluid in porous media and the resulting fingering has not been studied extensively, especially if the pore space is heterogeneous. In this paper, we propose a pore network model with full graphics processing unit-parallelized acceleration to simulate thermal transport in flow through three-dimensional unstructured pore networks at centimeter scale, containing millions of pores. A thermal Meter equation is proposed to model temperature- and shear stress-dependent rheology of the non-Newtonian fluids. After comparing the simulation results with an analytical solution for the location of the thermal front in a spatially uncorrelated pore network, thermal transport in flow of both Newtonian and non-Newtonian fluids is studied in the spatially uncorrelated and correlated pore networks over a range of injection flow rates. The simulations indicate that the injection flow rate, the shear-thinning rheology, and the morphological heterogeneity of the pore space all enhance thermal-viscous fingering instability in porous media, but with distinct patterns. In spatially correlated networks, the average temperature and apparent viscosity at the breakthrough point in flow of a shear-thinning fluid exhibit non-monotonic dependence on the injection flow rate. An analysis of the fractal dimension of thermal patterns at the breakthrough point supports the conclusion. The results highlight the importance of designing optimal flow conditions for application purposes. [ABSTRACT FROM AUTHOR]

Our present work focuses on the coupling between thermal diffusion and convection in order to improve the thermal gravitational separation of mixture components. The separation phenomenon was studied in a porous medium contained in vertical columns. We performed analytical and numerical simulations to corroborate the experimental measurements of the thermal diffusion coefficients of ternary mixture n-dodecane, isobutylbenzene, and tetralin obtained in microgravity in the international space station. Our approach corroborates the existing data published in the literature. The authors show that it is possible to quantify and to optimize the species separation for ternary mixtures. The authors checked, for ternary mixtures, the validity of the "forgotten effect hypothesis" established for binary mixtures by Furry, Jones, and Onsager. Two complete and different analytical resolution methods were used in order to describe the separation in terms of Lewis numbers, the separation ratios, the cross-diffusion coefficients, and the Rayleigh number. The analytical model is based on the parallel flow approximation. In order to validate this model, a numerical simulation was performed using the finite element method. From our new approach to vertical separation columns, new relations for mass fraction gradients and the optimal Rayleigh number for each component of the ternary mixture were obtained. [ABSTRACT FROM AUTHOR]

The Gill stability problem encompasses the investigation of stability of natural convection flow in a vertical porous layer governed by Darcy's law under a local thermal equilibrium (LTE) perspective and was proved analytically by Gill [Gill, J. Fluid Mech. 35, 545–547 (1969)] that the flow is always stable. The present study deals with the simultaneous influence of the Darcy–Prandtl number and the density maximum property on Gill's stability problem subject to a lack of thermal equilibrium. The density variation with fluid temperature is assumed to be pure quadratic, and it is established that the linear stability of the basic state for a three-dimensional problem can be Squire-transformed. It is observed that Gill's proof of linear stability cannot be extended to the present model and hence we approached numerically by evaluating the growth rate of normal mode perturbations. The neutral stability curves are obtained, and the critical parameters at the onset of instability are determined. Even though the isolation presence of time-dependent velocity term and the density maximum property evidence the basic flow to be stable for all infinitesimal perturbations, their simultaneous occurrence induces instability under certain parametric conditions. The finite range of values of the scaled interphase heat transfer coefficient within which the flow is stable is found to increase with increasing Darcy–Prandtl number but vanishes with increasing porosity-modified conductivity ratio. Moreover, the basic state becomes stable when the Darcy–Prandtl number is larger than 7.08. The results of LTE model are delineated as a particular case from the present study. [ABSTRACT FROM AUTHOR]

The stability of basic buoyant flow in a vertical fluid layer induced by temperature and solute concentration differences between the vertical boundaries is investigated. The linear dynamics of the perturbed flow is formulated as an eigenvalue problem and solved numerically by employing the Chebyshev collocation method. The validity of Squire's theorem is proved, and therefore, two-dimensional motions are considered. The neutral stability curves defining the threshold of linear instability and the critical values of the thermal Grashof number and wave number at the onset of instability are determined for various values of the Prandtl number P r , the solute Grashof number G S , and the Lewis number L e. The magnitude of the Prandtl number at which the transition from stationary to travelling-wave mode occurs can be either increased or decreased by tuning the values of G S and L e. For certain combinations of the parameters, there exist one or two closed disconnected travelling-wave neutral curves emphasizing the necessity of multiple thermal Grashof numbers to embark upon the stability of fluid flow, a result of contrast to that of the single-diffusive fluid layer. The mechanism of modal instability is deciphered by using the method of energy budget and four different modes of instability are identified, one of which is new and due entirely to the presence of solutal buoyancy. [ABSTRACT FROM AUTHOR]

In order to better understand the influence of the physical conditions, such as high temperature, high humidity, and high speed, on porous media in coastal engineering, a compressible, viscous, unsteady flow around and through a hygroscopic porous circular cylinder was discussed in this paper. The effects of the hygroscopicity, the Mach number, and the Darcy number on the flow structure, temperature field, and water content of the porous cylinder are evaluated in detail. The results of numerical simulations show significant effects of compressibility of moist air on the lift and drag of the cylinder. With an increase in the Mach number, the frequency of vortex shedding argument and dimensionless lift and drag of the porous cylindrical surface decrease. Nevertheless, the effect of the Mach number on the magnitude of the vorticity and distribution of temperature is negligible. In our simulation, we also found that an increase in the Darcy number significantly weakens the magnitude of the vorticity and the amplitude of lift and drag of the cylinder. Moreover, the absorption of the porous cylinder may also have a weak effect on accelerating vortex shedding. Considering the high temperature, high humidity, and high speed of the coastal environment, this paper has some significance for the study of wind erosion. [ABSTRACT FROM AUTHOR]