The effect of pulsating throughflow on the onset of magneto convection in a layer of nanofluid confined within a Hele-Shaw cell

2019 ◽  
Vol 233 (5) ◽  
pp. 1074-1085 ◽  
Author(s):  
Dhananjay Yadav
Keyword(s):  
Magnetic Field ◽  
Convective Motion ◽  
Lewis Number ◽  
Joint Effect ◽  
Linear Stability Theory ◽  
Number Formula ◽  
The Stability ◽  
The Impact ◽  
Profile Approach ◽  
Hele Shaw Cell

In this article, the joint effect of pulsating throughflow and magnetic field on the onset of convective instability in a nanofluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory and frozen profile approach. The model utilized for nanofluid combines the impacts of Brownian motion and thermophoresis, while for Hele-Shaw cell, Hele-Shaw model is considered. The Galerkin technique is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability framework is examined analytically. It is observed that the pulsating throughflow and magnetic field have both stabilizing effects. The impact of increasing the Hele-Shaw number [Formula: see text], the modified diffusive ratio [Formula: see text] and the nanoparticle Rayleigh number [Formula: see text] is to quicken the convective motion, while the Lewis number [Formula: see text] has dual impact on the stability framework in the existence of pulsating throughflow. It is also established that the oscillatory mode of convective motion is possible only when the value of the magnetic Prandtl number [Formula: see text] is not greater than unity.

scholarly journals Convective Instability in a Hele Shaw Cell with the Effect of Through Flow and Magnetic Field

2018 ◽  
Author(s):  
Dhananjay Yadav
Keyword(s):  
Magnetic Field ◽  
Convective Instability ◽  
Fluid Layer ◽  
Analytical Investigation ◽  
Linear Stability Theory ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Through Flow ◽  
The Stability ◽  
Hele Shaw Cell

In this paper, an analytical investigation of the combined effect of through flow and magnetic field on the convective instability in an electrically conducting fluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory. The Galarkin method is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability of the system is examined analytically as well as graphically. It is observed that the through flow and magnetic field have both stabilizing effects, while the Hele-Shaw number has destabilizing effect on the stability of system. It is also found that the oscillatory mode of convection possible only when the magnetic Prandtl number takes the values less than unity.

scholarly journals Effect of Vadasz Number on Magnetoconvection in a Darcy Porous Layer with Concentration Based Internal Heating

2019 ◽  
pp. 1-13
Author(s):  
C. Israel-Cookey ◽  
L. Ebiwareme ◽  
E. Amos
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Internal Heat ◽  
Lewis Number ◽  
Mode Analysis ◽  
Internal Heating ◽  
Vadasz Number ◽  
The Stability ◽  
Solutal Rayleigh Number

In this research article, the effect of Vadasz number on magnetoconvection in a Darcy Porous Layer with concentration based internal heating is studied. The flow is governed by the Oberbeck-Boussineq model for Newtonian fluid. The stability analysis method based on the perturbation of infinitesimal amplitude is carried out using the normal mode analysis. The onset criterion for both the stationary and oscillatory convection on the stability of system is obtained. The analysis examines the effects of pertinent parameters on the stability of the system: magnetic field parameter, solutal Rayleigh number, Lewis number and Vadasz number. The result show that, internal heat parameter,  and Lewis number, , hastens the onset of instability in the system, whereas magnetic field, , Vadasz number,  and solutal Rayleigh number,  delay the onset of instability.

Analysis of drivers' characteristics in car-following theory

2014 ◽  
Vol 28 (24) ◽  
pp. 1450191 ◽  
Author(s):  
Geng Zhang ◽  
Di-Hua Sun ◽  
Hui Liu ◽  
Min Zhao
Keyword(s):  
Numerical Simulation ◽  
Traffic Flow ◽  
Mkdv Equation ◽  
Reductive Perturbation Method ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Car Following ◽  
Car Following Model ◽  
The Stability ◽  
The Impact

In recent years, the influence of drivers' behaviors on traffic flow has attracted considerable attention according to Transportation Cyber Physical Systems. In this paper, an extended car-following model is presented by considering drivers' timid or aggressive characteristics. The impact of drivers' timid or aggressive characteristics on the stability of traffic flow has been analyzed through linear stability theory and nonlinear reductive perturbation method. Numerical simulation shows that the propagating behavior of traffic density waves near the critical point can be described by the kink–antikink soliton of the mKdV equation. The good agreement between the numerical simulation and the analytical results shows that drivers' characteristics play an important role in traffic jamming transition.

scholarly journals Linear stability of thermocapillary convection in cylindrical liquid bridges under axial magnetic fields

1999 ◽  
Vol 394 ◽  
pp. 281-302 ◽  
Author(s):  
M. PRANGE ◽  
M. WANSCHURA ◽  
H. C. KUHLMANN ◽  
H. J. RATH
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Magnetic Fields ◽  
Prandtl Number ◽  
Linear Stability ◽  
Thermocapillary Convection ◽  
Axial Magnetic Field ◽  
Unstable Mode ◽  
Linear Stability Theory ◽  
The Stability

The stability of axisymmetric steady thermocapillary convection of electrically conducting fluids in half-zones under the influence of a static axial magnetic field is investigated numerically by linear stability theory. In addition, the energy transfer between the basic state and a disturbance is considered in order to elucidate the mechanics of the most unstable mode. Axial magnetic fields cause a concentration of the thermocapillary flow near the free surface of the liquid bridge. For the low Prandtl number fluids considered, the most dangerous disturbance is a non-axisymmetric steady mode. It is found that axial magnetic fields act to stabilize the basic state. The stabilizing effect increases with the Prandtl number and decreases with the zone height, the heat transfer rate at the free surface and buoyancy when the heating is from below. The magnetic field also influences the azimuthal symmetry of the most unstable mode.

scholarly journals Rayleigh-Bénard convection in an elastico-viscous Walters’ (model B’) nanofluid layer

2015 ◽  
Vol 63 (1) ◽  
pp. 235-244 ◽  
Author(s):  
G.C. Rana ◽  
R. Chand
Keyword(s):  
Fluid Model ◽  
Normal Mode Analysis ◽  
Sufficient Conditions ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Physical Parameters ◽  
Onset Of Convection ◽  
The Stability

Abstract In this study, the onset of convection in an elastico-viscous Walters’ (model B’) nanofluid horizontal layer heated from below is considered. The Walters’ (model B’) fluid model is employed to describe the rheological behavior of the nanofluid. By applying the linear stability theory and a normal mode analysis method, the dispersion relation has been derived. For the case of stationary convection, it is observed that the Walters’ (model B’) elastico-viscous nanofluid behaves like an ordinary Newtonian nanofluid. The effects of the various physical parameters of the system, namely, the concentration Rayleigh number, Prandtl number, capacity ratio, Lewis number and kinematics visco-elasticity coefficient on the stability of the system has been numerically investigated. In addition, sufficient conditions for the non-existence of oscillatory convection are also derived.

Assessing the impact of transmissibility on a cluster-based COVID-19 model in India

2021 ◽  
pp. 2141002
Author(s):  
Tanvi ◽  
Mohammad Sajid ◽  
Rajiv Aggarwal ◽  
Ashutosh Rajput
Keyword(s):  
Reproduction Number ◽  
Transmission Rate ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Nonlinear Mathematical Model ◽  
Globally Asymptotically Stable ◽  
Number Formula ◽  
The Stability ◽  
The Impact ◽  
Disease Free

In this paper, we have proposed a nonlinear mathematical model of different classes of individuals for coronavirus (COVID-19). The model incorporates the effect of transmission and treatment on the occurrence of new infections. For the model, the basic reproduction number [Formula: see text] has been computed. Corresponding to the threshold quantity [Formula: see text], the stability of endemic and disease-free equilibrium (DFE) points are determined. For [Formula: see text], if the endemic equilibrium point exists, then it is locally asymptotically stable, whereas the DFE point is globally asymptotically stable for [Formula: see text] which implies the eradication of the disease. The effects of various parameters on the spread of COVID-19 are discussed in the segment of sensitivity analysis. The model is numerically simulated to understand the effect of reproduction number on the transmission dynamics of the disease COVID-19. From the numerical simulations, it is concluded that if the reproduction number for the coronavirus disease is reduced below unity by decreasing the transmission rate and detecting more number of infectives, then the epidemic can be eradicated from the population.

On the stability of steady convective motion generated by internal heat sources in a magnetic field

1988 ◽  
Vol 66 (11) ◽  
pp. 990-993 ◽  
Author(s):  
A. A. Kolyshkin
Keyword(s):  
Magnetic Field ◽  
Internal Heat ◽  
Convective Motion ◽  
Transverse Magnetic ◽  
Heat Sources ◽  
Small Perturbations ◽  
Internal Heat Sources ◽  
Prandtl Numbers ◽  
The Stability

The stability of steady convective motion of a viscous incompressible fluid in a transverse magnetic field is investigated using the method of small perturbations. The motion is caused by internal heat sources uniformly distributed within the vertical layer of the fluid. The stability analysis shows that the critical Grasshof number increases with the growth of the magnetic field. The role of the Prandtl and Hartmann numbers on the stability characteristics are discussed. For high Prandtl numbers, instability occurs in the form of thermal running waves.

scholarly journals Two-dimensional gyrotactic microorganisms flow of hydromagnetic power law nanofluid past an elongated sheet

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401988125 ◽  
Author(s):  
M Ferdows ◽  
M Gnaneswara Reddy ◽  
Shuyu Sun ◽  
Faris Alzahrani
Keyword(s):  
Prandtl Number ◽  
Power Law ◽  
Lewis Number ◽  
Stream Line ◽  
Two Dimensional ◽  
Gyrotactic Microorganisms ◽  
Non Linear ◽  
Number Formula ◽  
Power Law Nanofluid ◽  
The Impact

This article, describes two-dimensional magnetohydrodynamic steady incompressible viscous power law nanofluid comprising gyrotactic microorganisms adjacent to a vertical stretching sheet. The governing non-linear partial differential equations are lessened to a set of non-linear ordinary differential equation using similitude transformation. The non-dimensional boundary value problem is then solved under spectral relaxation method. The influences of different parameters such as buoyancy convection parameters [Formula: see text], magnetic field parameter M, power law parameter [Formula: see text], Prandtl number [Formula: see text], modified Prandtl number [Formula: see text], thermophoresis parameter [Formula: see text], Peclet number [Formula: see text], Lewis number [Formula: see text], Brownian motion parameter [Formula: see text], bioconvection Lewis number [Formula: see text], and bioconvection constant [Formula: see text] on flow convective characteristics phenomena are explored via plots and tables. The skin friction factor, rate of heat transfer, rate of mass transfer, and the density number of the motile microorganisms near the surface are also computed. Our results are compared with the existing results to support our model. Residual error analysis is determined for showing the convergence rate against iteration. Our result showed that the momentum thickness reduces as the value of [Formula: see text] induces and thermal boundary thickness increases as the value of [Formula: see text] induces. We also revealed that the density of the motile microorganisms [Formula: see text] is a reducing function of [Formula: see text] and concentration boundary layer induces with the increase of [Formula: see text], whereas its thickness close to the surface decreases with increasing of [Formula: see text]. Also, the stream line patterns are exhibited to the impact of physical sundry variables.

scholarly journals On Thermal Instability of Kuvshiniski Fluid with Suspended Particles Saturated in a Porous Medium in the Presence of a Magnetic Field June 13, 2017

2017 ◽  
Vol 22 (4) ◽  
pp. 981-994
Author(s):  
M. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Thermal Instability ◽  
Sufficient Conditions ◽  
Suspended Particles ◽  
Linear Stability Theory ◽  
Horizontal Magnetic Field ◽  
Medium Permeability ◽  
The Stability

Abstract The thermal instability of a Kuvshiniski viscoelastic fluid is considered to include the effects of a uniform horizontal magnetic field, suspended particles saturated in a porous medium. The analysis is carried out within the framework of the linear stability theory and normal mode technique. For the case of stationary convection, the Kuvshiniski viscoelastic fluid behaves like a Newtonian fluid and the magnetic field has a stabilizing effect, whereas medium permeability and suspended particles are found to have a destabilizing effect on the system, oscillatory modes are introduced in the system, in the absence of these the principle of exchange of stabilities is valid. Graphs in each case have been plotted by giving numerical values to the parameters, depicting the stability characteristics. Sufficient conditions for the avoidance of overstability are also obtained.

The Horton–Rogers–Lapwood problem in a Jeffrey fluid influenced by a vertical magnetic field

2021 ◽  
pp. 095440892110311
Author(s):  
Dhananjay Yadav ◽  
Abdul A Mohamad ◽  
Mukesh K Awasthi
Keyword(s):  
Magnetic Field ◽  
Darcy Number ◽  
Critical Conditions ◽  
Jeffrey Fluid ◽  
Vertical Magnetic Field ◽  
Magnetic Prandtl Number ◽  
Fluid Convection ◽  
The Stability ◽  
Convective Cells ◽  
The Impact

In this work, the impact of a magnetic field on the onset of the Jeffrey fluid convection through a porous medium is investigated theoretically. The layer of Jeffrey fluid is heated from below and is operated by a consistent upright magnetic field. Using the normal mode procedure, a dispersion equation is obtained analytically and this dispersion relation is utilized to derive the critical conditions for the onset of stationary and oscillatory patterns of convection. The results reveal that the stability of the system diminished with the augmentation of the Jeffrey parameter, while an opposite result is obtained with magnetic field parameters (magnetic Chandrasekhar–Darcy number and magnetic Prandtl number). The size of convective cells decreases with Jeffrey and magnetic field parameters. It is also found that the existence of a magnetic field indicates the possibility of the survival of the oscillatory mode of convection.

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