The onset of double diffusive convection in a viscoelastic fluid layer

The onset of double-diffusive convection in a couple-stress fluid-saturated horizontal porous layer is studied using linear and weak nonlinear stability analyses. The modified Darcy equation that includes the time derivative term and the inertia term is used to model the momentum equation. The expressions for stationary, oscillatory and finite-amplitude Rayleigh number are obtained as a function of the governing parameters. The effect of couple-stress parameter, solute Rayleigh number, Vadasz number and diffusivity ratio on stationary, oscillatory and finite-amplitude convection is shown graphically. It is found that the couple-stress parameter and the solute Rayleigh number have a stabilizing effect on stationary, oscillatory and finite-amplitude convection. The diffusivity ratio has a destabilizing effect in the case of stationary and finite-amplitude modes, with a dual effect in the case of oscillatory convection. The Vadasz number advances the onset of oscillatory convection. The heat and mass transfer decreases with an increase in the values of couple-stress parameter and diffusivity ratio, while both increase with an increase in the value of the solute Rayleigh number.

Convective instabilities in the melt for solidifying mercury cadmium telluride

Linear stability analysis is performed for the onset of thermosolutal convection in a horizontal fluid layer with rigid-rigid boundaries. The temperature field between the walls of the fluid layer consists of two parts: a steady part and a time-dependent periodic part that oscillates with time. Only infinitesimal disturbances are considered. The effect of temperature modulation on the onset of thermosolutal convection has been studied using the Galerkin method and Floquet theory. The critical Rayleigh number is calculated as a function of frequency and amplitude of modulation, Prandtl number, diffusivity ratio and solute Rayleigh number. Stabilizing and destabilizing effects of modulation on the onset of double diffusive convection have been obtained. The effects of the diffusivity ratio and solute Rayleigh number on the stability of the system are also discussed.

The aim of the current study is to investigate the stability analysis in case of the linear as well as nonlinear of a thermo-solutal chemically reactive couple stress fluid under uniform magnetic field convection. Investigations have been conducted on the impact of chemical reaction and external vertical magnetic field on the commencement of double diffusive convection in couple stress fluid between infinite horizontal parallel plates. Darcy's modified law governs the flow in porous media and the Oberbeck-Boussinesq approximation is accurate. For modelling the momentum equation, the modified Darcy equation with the time derivative and inertia terms is utilized. Expressions for the Rayleigh numbers with finite amplitude, oscillatory, and stationary states are found in accordance with the regulating factors. Graphics are used to illustrate how the couple-stress parameter, solute Rayleigh number, Vadasz number and diffusivity ratio affect stationary, oscillatory and finite-amplitude convection. Stationary, oscillatory and finite-amplitude convection are found to be stabilized by the couple-stress parameter and the solute Rayleigh number. The normal mode analysis method is utilized to look into the linear stability of flow dynamics after the nonlinear mathematical problem has been linearized. When stationary and finite-amplitude modes are present, the diffusivity ratio has a destabilizing effect; when oscillatory convection is present, it has a dual effect. Oscillatory convection develops earlier when the Vadasz number is higher. The couple-stress parameter and diffusivity ratio both increase with increasing solute Rayleigh number values, but the heat and mass transfer decreases as these values rise. Using double Fourier series, a generalized weakly nonlinear stability analysis is done. The research illustrates how various regulating parameters support and destabilize the flow dynamics. The influence of finite-amplitude convection on stability is also examined. Furthermore, the best conditions for stationary and oscillatory convection are based on altering the couple stress flow stability by controlling the applied magnetic field.

Double-diffusive buoyancy convection in an open-top rectangular cavity with horizontal temperature and concentration gradients is considered. Attention is restricted to the case where the opposing thermal and solutal buoyancy effects are of equal magnitude (buoyancy ratio Rρ=−1). In this case, a quiescent equilibrium solution exists and can remain stable up to a critical thermal Grashof number Grc. Linear stability analysis and direct numerical simulation show that depending on the cavity aspect ratio A, the first primary instability can be oscillatory, while that in a closed cavity is always steady. Near a codimension-two point, the two leading real eigenvalues merge into a complex coalescence that later produces a supercritical Hopf bifurcation. As Gr further increases, this complex coalescence splits into two real eigenvalues again. The oscillatory flow consists of counter-rotating vortices traveling from right to left and there exists a critical aspect ratio below which the onset of convection is always oscillatory. Neutral stability curves showing the influences of A, Lewis number Le, and Prandtl number Pr are obtained. While the number of vortices increases as A decreases, the flow structure of the eigenfunction does not change qualitatively when Le or Pr is varied. The supercritical oscillatory flow later undergoes a period-doubling bifurcation and the new oscillatory flow soon becomes unstable at larger Gr. Random initial fields are used to start simulations and many different subcritical steady states are found. These steady states correspond to much stronger flows when compared to the oscillatory regime. The influence of Le on the onset of steady flows and the corresponding heat and mass transfer properties are also investigated.

It is well known that when a horizontal layer of fluid is heated from below, a thermal boundary layer of less dense and hot fluid rises up. When this boundary layer becomes unstable, convective motion in the fluid above sets in. Forecasting when instabilities take place is essential. When a salt dissolved in a fluid saturating a porous medium heated from below is considered, simultaneous mass diffusion and thermal diffusion occur. Unlike the diffusion of heat, the diffusion of salt can take place only through the fluid phase, so an additional physical effect has to be considered: the Soret effect, that is the mass flux created by a temperature gradient. In the present paper the onset of convection in a rotating layer of bi-disperse porous medium saturated by a binary fluid mixture, taking into account the Soret effect, is analysed. Linear stability analysis is performed in order to determine the instability thresholds for the onset of convection via a steady state (stationary convection) and via an oscillatory state (oscillatory convection). Nonlinear stability analysis is performed to obtain the global stability threshold with respect to the L^2-norm.

The effect of local thermal non-equilibrium on the onset of double-diffusive convection in a porous medium consisting of two horizontal layers, each internally heated, is studied analytically. Linear stability theory is applied. Variations of permeability, fluid thermal conductivity, solid thermal conductivity, heat source strength in the solid and fluid phases, concentration source strength, interphase heat transfer coefficient and porosity are considered. In addition to the major effects from heterogeneity of permeability, fluid thermal conductivity and heat source strength in the fluid phase as with single-diffusive convection, it is now found that major effects arise from heterogeneity of solutal source strength and porosity. We used two different methods to obtain our results. Analytical results that readily show the effects of parameter variations were obtained by using a low-term Galerkin approximation, which was validated by using a highly accurate numerical solver. Since for a problem with large number of parameters simple analytical results are highly desirable, the quantification of the accuracy of a low-term Galerkin approximation presented in our paper is quite important.

Exploration of anisotropy on nonlinear stability of thermohaline viscoelastic porous convection

CO2 storage in porous media unsteady thermosolutal natural convection -Application in deep saline aquifer reservoirs

We used linear stability theory based on the normal mode decomposition technique and nonlinear stability theory based on the minimum representation of double Fourier series to study the criterion of appearance of the stationary convection and the oscillatory convection; and the rate of heat and mass transfer in a binary viscoelastic fluid mixture in a rotating porous medium under the effect of helical force. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. Expressions for heat and mass transfer rates are determined as a function of Nusselt and Sherwood number, respectively. The transient behaviors of the Nusselt number and the Sherwood number are studied by solving the finite amplitude equations using the Runge‐Kutta method. Then, the effect of each dimensionless parameter on the system is studied pointed out interesting results. According to the analysis of the different results obtained, it appears that in a porous medium saturated by a binary mixture of viscoelastic fluid in rotation, the Taylor‐Darcy number , the delay time parameter λ2 and the mass Rayleigh‐Darcy number delay the onset of stationary and oscillatory convection. On the other hand, the helical force , the relaxation time parameter λ1, the ratio of diffusivities τ and the number of Vadasz accelerate the onset of stationary and oscillatory convection. In the case of the nonlinear stability study, at steady state, the helical force accelerates the rate of heat and mass transfer. On the other hand, the Taylor‐Darcy number , the diffusivity ratio τ and the mass Rayleigh‐Darcy number retard the rate of heat and mass transfer. In the unsteady state, the helical force , the relaxation time parameter λ1 and the mass Rayleigh‐Darcy number accelerate the rate of heat and mass transfer. This is not the case for the Taylor‐Darcy number and the delay time parameter λ2.

Hydromagnetic double-diffusive mixed convection in trapezoidal enclosure due to uniform and nonuniform heating at the bottom side: Effect of Lewis number

This research focuses on convection driven by a thermal gradient and a concentration gradient in an Oldroyd-B hybrid nanofluid saturated by a highly permeable layer with cross-diffusion effects. The Buongiorno model is implemented with the diversity of thermophoresis and Brownian diffusion. Using linear stability theory, an analytical expression for thermal Rayleigh number is obtained at the onset of binary liquid convection. For the nonlinear analysis, the governing PDEs are altered into ODEs by making use of similarity transformations. The rate of heat and mass transfer are calculated with the help of the built-in function NDSolve in computational tool MATHEMATICA 12.0. The numerical results are offered for the base fluid as ethylene glycol with hybrid copper and silver nanoparticles. The graphical illustrations are described to understand the impact of all the emerging parameters on the onset of convective phenomenon. Hybrid nanofluid is found to be more stable in comparison with single particle nanofluid. As far as technological applications are concerned, mono nanofluid could be replaced by hybrid nanofluid and this can be stated as a novelty of the article. We have observed that the heat and mass transfer profile is boosted up for increasing viscoelastic parameters i.e. stress relaxation and strain retardation parameters, solutal Rayleigh number and Prandtl number. In addition, the heat transfer displays an increasing nature toward the higher amounts of nanoparticle volume fraction.

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth‐order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.

This study considers the effects of concentration based internal heat and vertical magnetic field on the onset of double diffusive convection in a horizontal porous layer using normal mode analysis. The normal mode analysis is used to find solutions for the fluid variables, the critical wave number and the critical Rayleigh number for the onset of convection with free-free boundaries. The results obtained are displayed graphically and in tables. The results show that the concentration based internal heat, , hastens the onset of instability while the magnetic field, , and solutal Rayleigh number, , delays the onset of instability in the system for stationary and oscillatory convections. The influence of Lewis number, , and porosity, , is also presented.

In this paper, the effect of magnetic field dependent (MFD) viscosity on the onset of thermomagnetic convection is examined for a horizontal layer of magnetic nanofluid (or ferrofluid) saturated porous layer. A model that comprises the effect of Brownian diffusion, thermophoresis, magnetophoresis, and Darcy's law is considered. We employed the Chebyshev pseudospectral QZ-method to solve the developed mathematical model and the results are derived for water-based and ester-based magnetic nanofluids. The effects of significant parameters are analysed at the onset of convection in the gravity as well as in the microgravity environment. The influence of MFD viscosity, permeability parameter, the width of the fluid layer, Lewis number, Langevin parameter, particle concentration, and the concentration Rayleigh number at the onset of thermomagnetic convection are graphically illustrated.