Vertical Throughflow Research Articles

Effects of vertical throughflow and variable gravity field on double diffusive convection in a fluid layer

Effects of vertical throughflow and variable gravity field on double diffusive convection in a fluid layer

Changes in the hydrodynamic stability of plane porous-Couette flow due to vertical throughflow

A detailed study on the linear stability of plane porous-Couette flow in the presence of a uniform vertical throughflow using the Brinkman–extended Darcy equation has been presented. The equivalent of the Orr–Sommerfeld eigenvalue problem is formulated and solved numerically using the Chebyshev collocation method. The throughflow introduces an asymmetry in the basic flow amounting to the existence of a different set of onset modes. The contributions of the throughflow dependent modified Reynolds number and the modified porous parameter on the critical values defining the threshold for the onset of instability are presented. It is found that the stability characteristics of plane Couette flow in a porous medium in the presence of throughflow are remarkably different from no throughflow and non-porous cases.

Benchmark solution for the stability of plane Couette flow with net throughflow

This paper investigates the stability of an incompressible viscous fluid flow between relatively moving horizontal parallel plates in the presence of a uniform vertical throughflow. A linear stability analysis has been performed by employing the method of normal modes and the resulting stability equation is solved numerically using the Chebyshev collocation method. Contrary to the stability of plane Couette flow (PCF) to small disturbances for all values of the Reynolds number in the absence of vertical throughflow, it is found that PCF becomes unstable owing to the change in the sign of growth rate depending on the magnitude of throughflow. The critical Reynolds number triggering the instability is computed for different values of throughflow dependent Reynolds number and it is shown that throughflow instills both stabilizing and destabilizing effect on the base flow. It is seen that the direction of throughflow has no influence on the stability of fluid flow. A comparative study between plane Poiseuille flow and PCF has also been carried out and the similarities and differences are highlighted.

Examination of the nanofluid convective instability of vertical constant throughflow in a porous medium layer with variable gravity

In the current article, the impact of varying gravitational field and flow on the beginning of nanofluid convective instability in a permeable medium layer is studied numerically utilizing Galerkin technique. The permeable layer is directed to a regular vertical throughflow and irregular descendent gravitational force which changes with the length from the layer. The influences of three types of gravitational force inconsistency: (a) linear, (b) parabolic, and (c) exponential are examined on the formation of nanofluid convective instability with vanish nanoparticle flux condition at the plates. Results proved that the throughflow factor $$Q$$ and gravity inconsistency factor $$\delta$$ suspend the start of convective instability, while the nanoparticle Rayleigh-Darcy number $$R_{{{\text{np}}}}$$ and the altered diffusivity ratio $${\text{NA}}_{{{\text{nf}}}}$$ quick the start of nanofluid convection. The measurement of the convective cells diminishes with $$R_{{{\text{np}}}}$$ and $${\text{NA}}_{{{\text{nf}}}}$$ , while $$Q$$ , $$\delta$$ and the altered nanofluid Lewis number $${\text{Le}}_{{{\text{nf}}}}$$ have duel effects on the measurement of convective cells.

THE VARIABLE GRAVITY FIELD AND VISCOUS DISSIPATION EFFECTS ON THE CONVECTIVE INSTABILITY IN A POROUS LAYER WITH THROUGHFLOW: BRINKMAN MODEL

The present investigation aims to study the combined effect of viscous dissipation, vertical throughflow, and variable gravity field on the onset convective instability in a horizontal porous layer of finite thickness restricted between two permeable boundaries. The Brinkman extended Darcy model is accounted into the momentum equation of the governing flow through the porous layer. Also, linear, quadratic, and exponential gravity variation has been considered to study the present problem. The linear stability of the basic state is studied for the normal mode perturbations, and the corresponding eigenvalue problem is solved numerically using the bvp4c routine in MATLAB. The influence of throughflow parameter (Q), viscous dissipation (Ge), Darcy number (Da), and gravity variation parameter (λ) on the instability mechanism is discussed for the above three gravity field variations. The results indicate that the beginning of convection is postponed in the presence of Darcy number, throughflow, and gravity field parameter, while it is advanced in the presence of a significant viscous dissipation. Rac elevates to maximum at around 299% for linear variations of the gravity field, while it was 74% and 868% for quadratic and exponential varying gravity fields, respectively, when λ increases from 0 to 1.5. The value of Rac increased 6.5%, 5.4%, and 10.6%, respectively, for the linear, quadratic, and exponential gravity field variables, respectively, on changing the values of throughflow parameter from 0 to 1 and the increase in Rac is more for enhancing the value of the throughflow parameter from 1 to 2. Further, the system becomes more stable in the presence of an exponential gravity field.

WITHDRAWN: Linear stability analysis of Benard-Marangoni ferroconvection in presence of vertical throughflow

The stability analysis of throughflow effect on Bénard-Marangoni ferroconvection is investigated hypothetically. The bottom of the fluid layer is taken as rigid with temperature fixed, while the top of the fluid layer is assumed as free and, on the boundary, surface tension effect depending on temperature is taken as non-deformable and subjected to general thermal boundary condition. The Regular perturbation method is applied to solve the problem analytically. The results reveal that the direction of the throughflow doesn’t have any control on the characteristics of stability. Further, Peclet number Q is to delay the ferroconvection. The effect in increasing magnetic number Rm and Prandtl number Pr is to accelerate the convection. It is noticed that M 3 , representing non-linearity of fluid magnetization doesn’t affect the Bénard-Marangoni ferroconvection.

The variable gravity field and viscous dissipation effects on the double diffusive and Soret driven convective instability in a porous layer with throughflow

The influence of the Soret parameter, variable gravity field and viscous dissipation on the stability of convection with double-diffusion in a porous layer saturated by a viscous fluid is considered numerically. The impact of vertical throughflow on stability is also studied. Linear, quadratic, cubic and exponential functions are taken into consideration for gravity force variation. To solve the eigenvalue problem numerically, bvp4c method has been employed. The results show that Lewis number, gravity variation parameter, and Soret parameter are delaying the onset of convection, while solutal Rayleigh number and viscous dissipation parameter are enhancing the onset of convection in the flow field. It is distinguished that the system is becoming more stable for the exponential variation of the gravity field and more unstable for cubic variation of gravity variation.

Thermally unstable throughflow of a power–law fluid in a vertical porous cylinder with arbitrary cross–section

The present paper investigates how the cross–sectional shape of a vertical porous cylinder affects the onset of thermoconvective instability of the Rayleigh–Bénard type. The fluid saturating the porous medium is assumed to be a non–Newtonian power–law fluid. A linear stability analysis of the vertical thorughflow is carried out. Three special shapes of the cylinder cross–section are analysed: square, circular and elliptical. The effect of changing the power–law index is investigated. The stability of a steady base state with vertical throughflow is analysed. The resulting stability problem is a differential eigenvalue problem that is solved numerically through the shooting method. The dimensionless numbers here considered are the non–Newtonian version of the Darcy–Rayleigh number, Ra, the Péclet number, Pe, and the power–law index, n. Results are presented in the form of marginal stability curves with Ra plotted as a function of the cylinder aspect ratio, by assuming different values of Pe and n. The critical values of Ra are also computed. Results show that the critical Rayleigh number Rac for instability depends only on Pe and n, and is independent of the shape of the cylinder cross–section. The geometry of the sidewall just contributes the selection of the allowed wavenumbers.

Significances of blowing and suction processes on the occurrence of thermo-magneto-convection phenomenon in a narrow nanofluidic medium: A revised Buongiorno's nanofluid model

In this numerical examination, the thermal stability of an electrically conducting nanofluid is deliberated comprehensively by considering the presence of an externally applied magnetic field along with an imposed vertical throughflow. Additionally, this thin nanofluidic layer is supposed to have a Newtonian rheological behavior, heated from below, and confined horizontally between two permeable rigid plates of infinite extension. Herein, the governing conservation equations are strengthened realistically by the revised version of the Buongiorno's mathematical model, in which the vertical component of the mass flux of solid nanoparticles is presumed to vanish entirely at the horizontal permeable boundaries. After specifying the basic state of the present nanofluid problem, the linear stability theory and normal mode analysis technique are applied properly to obtain the principal stability equations. Finally, the eigenvalue problem derived analytically is tackled thereafter numerically via the Chebyshev-Gauss-Lobatto Spectral Method (CGLSM), in which the thermal Rayleigh number is chosen as an eigenvalue. As a main result, it was demonstrated that the throughflow effect exhibits a dual behavior on the complex dynamics of the system. However, the excreted magnetic field has always a stabilizing impact on the nanofluidic medium.

Throughflow and G-Jitter Effects on Oscillatory Convection in a Rotating Porous Medium

The impact of vertical throughflow and g-jitter effect on rotating porous medium is investigated. A feeble nonlinear stability analysis associate to complex Ginzburg-Landau equation (CGLE) has been studied. This weakly nonlinear analysis performed for a periodic mode of convection and quantified heat transport in terms of the Nusselt number, which is governed by the non-autonomous advanced CGLE. Each idea, rotation and throughflow is used as an external mechanism to the system either to extend or decrease the heat transfer. The results of amplitude and frequency of modulation on heat transport are analyzed and portrayed graphically. Throughflow has dual impact on heat transfer either to increase or decrease heat transfer in the system. Particularly the outflow enhances and inflow diminishes the heat transfer. High centrifugal rates promote heat transfer and low centrifugal rates diminish heat transfer. The streamlines and isotherms area portrayed graphically, the results of rotation and throughflow on isotherms shows convective development.

The onset of Darcy‐Brinkman convection in a porous medium layer with vertical throughflow and variable gravity field effects

AbstractIn this study, the influence of constant throughflow and varying downward gravity field on the onset of Darcy‐Brinkman convection in a porous medium layer is examined numerically. We considered two cases of gravity field variations: (a) linear and (b) parabolic. A higher‐order Galerkin‐weighted residual technique and QZ procedure are used to get the numerical solution for the entire Darcy numbers amid (Horton‐Rogers‐Lapwood convection) and (Rayleigh Bénard Convection). It is obtained that the throughflow, the downward gravity field and the Darcy number are to holdup the beginning of convection. It is also obtained that the system is more stable for linear variation of gravity field in comparison to the parabolic variation.

Stability of porous-Poiseuille flow with uniform vertical throughflow: High accurate solution

This paper investigates the influence of a uniform vertical throughflow on the stability of Poiseuille flow in a Newtonian fluid-saturated Brinkman porous medium. The solution to the stability eigenvalue problem is obtained numerically using the Chebyshev collocation and the Galerkin methods. The vertical throughflow, irrespective of its direction, imparts an identical stabilizing/destabilizing effect on the fluid flow. The throughflow dependent Reynolds number RT instills both stabilizing and destabilizing effects in a fluid saturated channel of porous medium and the range of RT up to which the system gets destabilized increases with increasing porous parameter. The results for the clear fluid case are also obtained as a particular case from the present study, and contrary to the porous case, throughflow always displays a stabilizing effect. Moreover, the numerical solutions presented will be useful for checking the performance and accuracy of any numerical methodologies.

The Effect of Throughflow on Weakly Nonlinear Convection in a Viscoelastic Saturated Porous Medium

In this paper we have investigated the effect of throughflow on thermal convection in a viscoelastic fluid saturated porous media. The governing equations are modelled in the presence of throughflow. These equations are made dimensionless and the obtained nonlinear problem solved numerically. There are two types of throughflow effects on thermal instability inflow and outflow investigated by finite amplitude analysis. This finite amplitude equation is obtained using the complex Ginzburg-Landau amplitude equation (CGLE) for a weak nonlinear oscillatory convection. The heat transport analysis is given by complex Ginzburg-Landau amplitude equation (CGLE). The numerical results indicate that due to the non-uniform throughflow there is instability at the bottom plate and influence the heat transfer in the system. The vertical throughflow is having both stable and unstable modes depending on flow direction. The nature of viscoelastic fluid is having both effects either stabilize or destabilize. Further, it is found that the nonlinear throughflow effects have dual role on heat transport. The solutions of the present problem are obtained numerically by using Runge-Kutta fourth order method.

Two- and Three-Dimensional Absolute Instabilities in a Porous Medium with Inclined Temperature Gradient and Vertical Throughflow

A linear stability analysis for the onset of mixed convection in a saturated porous medium through an absolute instability of both two- and three-dimensional disturbances is performed. Relevant control parameters associated with the inclined temperature gradient and the vertical throughflow are the vertical and horizontal Rayleigh numbers, $$R_{\mathrm{v}}$$ and $$R_{\mathrm{h}}$$, and the vertical Peclet number, $$Q_{\mathrm{v}}$$, respectively. This work extends previous studies on the very same problem in two fronts. For two-dimensional disturbances, the present results do not agree with the literature for a few of the parametric conditions reported. This is caused by the collision of the convectively unstable downstream propagating branch with multiple upstream propagating branches, which generates several saddle points and, hence, makes the identification of the correct pinching point more difficult. In other words, literature results are all saddle points but not always pinching points. For three-dimensional disturbances, this issue is not present and the current results agree with the literature. On the other hand, due to the inherent difficulties associated with a three-dimensional absolute instability analysis, literature results have only been able to report the group velocities at the onset of convective instability. When their real parts are zero, transition occurs directly from stable to absolutely unstable. Otherwise, transition occurs from stable to convectively unstable first and nothing can be said about the onset of absolute instability. In this work, a novel technique recently developed by the authors allowed the identification of the onset of absolute instability under all parametric conditions investigated in the literature, extending earlier results. Doing so confirmed the dichotomy already observed in these earlier studies, i.e., the onset of absolute instability for two- and three-dimensional longitudinal modes indeed differs.

Convection in a Horizontal Porous Layer with Vertical Pressure Gradient Saturated by a Power-Law Fluid

The onset of convection in a porous layer saturated by a power-law fluid is here investigated. The walls are considered to be isothermal, isobaric and permeable in such a way that a vertical throughflow is described. The threshold for a buoyancy-driven cellular flow is investigated by means of a linear stability analysis. This study consists in introducing disturbances with small amplitude. The disturbances are plane waves, i.e. a normal modes stability analysis of the basic stationary solution is performed. The resulting problem is an ordinary differential equation eigenvalue problem which is solved numerically by coupling the Runge–Kutta method with the shooting method. Results are presented in the form of marginal stability curves and their critical points representing the values of the control parameters such that the growth rate of the disturbances is zero. It is found that, among roll disturbances, the most unstable modes are stationary and uniform with infinite wavelength. For this reason, an asymptotic analysis for vanishing wave numbers is carried out. The results of this asymptotic analysis are obtained analytically displaying a very good agreement with the numerical solution. It is found that vertical throughflow plays a destabilising role for pseudoplastic fluids and a stabilising role for dilatant fluids.

Numerical investigation of the combined impact of variable gravity field and throughflow on the onset of convective motion in a porous medium layer

The present article is to examine the joint influence of variable gravity filed and throughflow on the onset of convective motion in a porous medium layer using higher order Galerkin method. The porous layer subjected to a constant upward vertical throughflow and variable downward gravity field which differs with distance across the layer. We discussed the four cases of gravity field variation: (i) G(z) = − z, (ii) G(z) = − z2, (iii) G(z) = − z3 and (iv) G(z) = − (ez − 1). Results indicate that both the throughflow and gravity variation parameters are to postpone the onset of convective motion. The system is observed to be more stable for case (iv), while more unstable for case (iii).

Numerical study of nanofluid thermo-bioconvection containing gravitactic microorganisms in porous media: Effect of vertical throughflow

An analytical investigation of the onset of nanofluid thermo-bioconvection in a fluid saturated by porous media containing gravitactic and nanoparticles microorganisms subjected to a vertical throughflow is presented. The heat conservation equation is formulated by introducing the convective term of nanoparticle flux. The fluid is stimulated with modified Brinkman model, normal mode analysis and six-term Galerkin methods are used to solve the governing equations. The combined effects of vertical throughflow, nanoparticles, gravitactic microorganisms, and porosity have been taken into account. The effects of bioconvection Rayleigh number, bioconvection Péclet number, nanoparticle Rayleigh number, Péclet number, bioconvection Lewis number, and porosity on critical thermal Rayleigh number have been examined. The analysis leads that critical wave number is the function of bioconvection parameters, nanofluid parameters and throughflow parameters. It is also found that vertical throughflow disturbs the formation of bioconvection pattern which are necessary for the development of bioconvection.

A Bio-Thermal Convection in Water-Based Nanofluid Containing Gyrotactic Microorganisms: Effect of Vertical Throughflow

The effect of vertical throughflow on the onset of bio-thermal convection in a water-based nanofluid containing gyrotactic microorganisms is investigated using more realistic boundary conditions. The Galerkin weighted residual method is used to obtain numerical solutions of the mathematical model. The effects of bioconvection Rayleigh number, gyrotaxis number, bioconvection Péclet number, Lewis number, Péclet number, particle density increment number, modified diffusitivity ratio, and nanoparticle Rayleigh number on thermal Rayleigh number are examined.The combined effect of Brownian motion and thermophoresis of nanoparticles, vertical throughflow, and gyrotactic microorganisms on the thermal Rayleigh number is found to be destabilizing and its value is decreased by first to third orders of magnitude as compared to regular fluids. Critical wave number is dependent on bioconvection parameters, nanofluid parameters as well as throughflow parameter. The results obtained using passive boundary conditions are compared with those of active boundary conditions. The present study may find applications in seawater convection at the ocean crust.

Stability of Vertical Throughflow of a Power Law Fluid in Double Diffusive Convection in a Porous Channel

Stability of Vertical Throughflow of a Power Law Fluid in Double Diffusive Convection in a Porous Channel

Convective Stability of Vertical Throughflow of a Non-Newtonian Fluid in a Porous Channel with Soret Effect

The linear stability analysis of vertical throughflow of power law fluid for double-diffusive convection with Soret effect in a porous channel is investigated in this study. The upper and lower boundaries are assumed to be permeable, isothermal and isosolutal. The linear stability of vertical through flow is influenced by the interactions among the non-Newtonian Rayleigh number (Ra), Buoyancy ratio (N), Lewis number (Le), Peclet number (Pe), Soret parameter (Sr) and power law index (n). The results indicate that the Soret parameter has a significant influence on convective instability of power law fluid. It has also been noticed that buoyancy ratio has a dual effect on the instability of fluid flow. Further, it is noticed that the basic temperature and concentration profiles have singularities at \(Pe = 0\) and \(Le = 1\), the convective instability is looked into for the limiting case of \(Pe\rightarrow 0\) and \(Le \rightarrow 1\). For the case of pure thermal convection with no vertical throughflow, the present numerical results coincide with the solution of standard Horton–Rogers–Lapwood problem. The present results for critical Rayleigh number obtained using bvp4c and two-term Galerkin approximation are compared with those available in the literature and are tabulated.