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.

ONSET OF INSTABILITY IN HYDROMAGNETIC COUETTE FLOW

2004 ◽  
Vol 02 (02) ◽  
pp. 145-159 ◽  
Author(s):  
ISOM H. HERRON
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Couette Flow ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Rotating Cylinders ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of viscous flow between rotating cylinders in the presence of a constant axial magnetic field is considered. The boundary conditions for general conductivities are examined. It is proved that the Principle of Exchange of Stabilities holds at zero magnetic Prandtl number, for all Chandrasekhar numbers, when the cylinders rotate in the same direction, the circulation decreases outwards, and the cylinders have insulating walls. The result holds for both the finite gap and the narrow gap approximation.

scholarly journals A revised model of "Steady laminar natural convection of nanofluid under the impact of magnetic field on 2-D cavity with radiation" [AIP advances 9, 065008 (2019); https://doi.org/10.1063/1.5109192]

2020 ◽  
Vol 24 (1 Part A) ◽  
pp. 421-425
Author(s):  
Hossam Nabwey
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Natural Convection ◽  
Darcy Number ◽  
Porous Media Flow ◽  
Governing Equations ◽  
Laminar Natural Convection ◽  
The Impact ◽  
Published Paper ◽  
Steady Laminar

This discussion exhibits the major scientific errors on the recent published paper, entitled "Steady Laminar Natural Convection of Nanofluid Under the Impact of Magnetic Field on 2-D Cavity with Radiation" and their corrections indifferently. In Saleem et al. [1], the authors stated in both of abstract and problem assumptions that the non-Darcy model is used for the porous medium, while the porous terms are incompatible with this assumption. In addition, the authors used a non-inclined geometry in their investigation, but the governing equations are conflicting with this hypothesis. Further, the used range of the Darcy number is between 10?2-102 and this range is very large and did not represent the porous media flow. All of these observations make the mathematical formulations and the obtained results of Saleem et al. [1] are wrong. In the following sections, these scientific errors and their corrections will be presented minutely.

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 Jeffrey Fluid Flow through Porous Medium in the Presence of Magnetic Field in Narrow Tubes

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Santhosh Nallapu ◽  
G. Radhakrishnamacharya
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Fluid Flow ◽  
Effective Viscosity ◽  
Equations Of Motion ◽  
Flow Characteristics ◽  
Darcy Number ◽  
Jeffrey Fluid ◽  
Tube Radius ◽  
The Core

Jeffrey fluid flow in the presence of magnetic field through porous medium in tubes of small diameters is studied. It is assumed that the core region consists of a Jeffrey fluid and the peripheral region of a Newtonian fluid. Making the assumptions as in the work of Chaturani and Upadhya, the linearised equations of motion have been solved and analytical solution has been obtained. The influence of various pertinent parameters on the flow characteristics such as effective viscosity, core hematocrit, and mean hematocrit has been studied and discussed through graphs. It is found that the effective viscosity and mean hematocrit decrease with Jeffrey parameter and Darcy number but increase with tube hematocrit and tube radius. Also, the core hematocrit decreases with Jeffrey parameter, Darcy number, tube hematocrit, and tube radius. Further, it is noticed that the flow exhibits the anomalous Fahraeus-Lindquist effect.

Magnetic Field and Thermal Radiation Effects in Peristaltic Flow With Heat and Mass Convection

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
T. Hayat ◽  
Aneela Bibi ◽  
H. Yasmin ◽  
Fuad E. Alsaadi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Thermal Radiation ◽  
Transfer Coefficient ◽  
Radiation Effects ◽  
Schmidt Number ◽  
Oscillatory Behavior ◽  
Jeffrey Fluid ◽  
The Impact

This paper scrutinizes the impact of thermal radiation and applied magnetic field on Jeffrey fluid with peristalsis. The effects of Joule heating and viscous dissipation are retained. Convective conditions are imposed for the heat and mass transfer analysis. Lubrication approach is considered for the analysis. Expressions for pressure gradient, stream function, temperature, concentration, and heat transfer coefficient are developed and physically interpreted through illustrations. It is revealed that temperature enhances for higher estimation of Brinkman and Hartmann numbers, while it decays for larger Biot number. Furthermore, the concentration decreases for varying Schmidt number. Heat transfer coefficient has an oscillatory behavior for larger estimation of radiation parameter.

Linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles: application to controlled drug delivery

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Pascalin Tiam Kapen ◽  
Cédric Gervais Njingang Ketchate ◽  
Didier Fokwa ◽  
Ghislain Tchuen
Keyword(s):  
Magnetic Field ◽  
Drug Delivery ◽  
Stability Analysis ◽  
Magnetic Nanoparticles ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Controlled Drug Delivery ◽  
Darcy Number ◽  
Content Type ◽  
The Stability

Purpose For this purpose, a linear stability analysis based on the Navier–Stokes and Maxwell equations is made leading to an eigenvalue differential equation of the modified Orr–Sommerfeld type which is solved numerically by the spectral collocation method based on Chebyshev polynomials. Unlike previous studies, blood is considered as a non-Newtonian fluid. The effects of various parameters such as volume fraction of nanoparticles, Casson parameter, Darcy number, Hartmann number on flow stability were examined and presented. This paper aims to investigate a linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles with an application to controlled drug delivery. Design/methodology/approach Targeted delivery of therapeutic agents such as stem cells and drugs using magnetic nanoparticles with the help of external magnetic fields is an emerging treatment modality for many diseases. To this end, controlling the movement of nanoparticles in the human body is of great importance. This study investigates controlled drug delivery by using magnetic nanoparticles in a porous artery under the influence of a magnetic field. Findings It was found the following: the Casson parameter affects the stability of the flow by amplifying the amplitude of the disturbance which reflects its destabilizing effect. It emerges from this study that the taking into account of the non-Newtonian character is essential in the modeling of such a system, and that the results can be very different from those obtained by supposing that the blood is a Newtonian fluid. The presence of iron oxide nanoparticles in the blood increases the inertia of the fluid, which dampens the disturbances. The Strouhal number has a stabilizing effect on the flow which makes it possible to say that the oscillating circulation mechanisms dampen the disturbances. The Darcy number affects the stability of the flow and has a stabilizing effect, which makes it possible to increase the contact surface between the nanoparticles and the fluid allowing very high heat transfer rates to be obtained. It also emerges from this study that the presence of the porosity prevents the sedimentation of the nanoparticles. By studying the effect of the magnetic field on the stability of the flow, it is observed that the Hartmann number keeps the flow completely stable. This allows saying that the magnetic field makes the dissipations very important because the kinetic energy of the electrically conductive ferrofluid is absorbed by the Lorentz force. Originality/value The originality of this paper resides on the application of the linear stability analysis for controlled drug delivery.

Stability of a stratified partially ionized plasma in a vertical magnetic field

1978 ◽  
Vol 19 (1) ◽  
pp. 183-191 ◽  
Author(s):  
S. L. Maheshwari ◽  
P. K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Growth Rate ◽  
The Other ◽  
Conducting System ◽  
Vertical Magnetic Field ◽  
One Dimensional ◽  
Finite Electrical Conductivity ◽  
Partially Ionized ◽  
The Stability

The dynamic stability of a stratified layer of partially ionized compressible plasma is discussed to investigate the effects of finite electrical conductivity and ion viscosity. The prevailing magnetic field is assumed to be uniform and vertical. For a semi-infinite plasma having a one-dimensional exponential density gradient along the vertical, the dispersion relation has been obtained by variational methods. It is found that the ion viscosity and ion–neutral collisions, whether included jointly or separately, do not change the stability criterion of the perfectly conducting system. Their inclusion, however, has a tendency to reduce the growth rate of the unstable perturbations showing that they have a stabilizing influence. On the other hand the inclusion of the effects of finite resistivity and compressibility of the medium is found to be destabilizing as the wavenumber range over which the plasma would otherwise be stable, becomes unstable.

Article

1998 ◽  
Vol 76 (12) ◽  
pp. 937-947
Author(s):  
M Takashima
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Transverse Magnetic Field ◽  
Wave Speed ◽  
Critical Reynolds Number ◽  
Maximum Velocity ◽  
Transverse Magnetic ◽  
Wave Number ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of combined plane Poiseuille and Couette flow of an electricallyconducting fluid under a transverse magnetic field is investigated using linear stability theory.In deriving the equations governing the stability, the so-called magnetic Stokes approximationis made using the fact that the magnetic Prandtl number Prm for most electrically conductingfluids is extremely small. The Chebyshev collocation method is adopted to obtain theeigenvalue equation, which is then solved numerically. The critical Reynolds number Rec,the critical wave number αc, and the critical wave speed cc are obtained for wide ranges ofthe Hartmann number Ha and the parameter k = U0 / (U0 + nu0), where U0 is the maximumvelocity of pure Couette flow and nu0 is the maximum velocity of pure Poiseuille flow. It isfound that a transverse magnetic field has both stabilizing and destabilizing effects on theflow depending on the value of k.PACS Nos. 47.20

scholarly journals Hydromagnetic Stability of Metallic Nanofluids (Cu-Water and Ag-Water) Using Darcy-Brinkman Model

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
J. Ahuja ◽  
U. Gupta ◽  
R. K. Wanchoo
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Darcy Number ◽  
Analytical Investigation ◽  
Brinkman Model ◽  
Free Boundaries ◽  
Weighted Residuals ◽  
Flow Through ◽  
The Stability ◽  
Chandrasekhar Number

Thermal convection of a nanofluid layer in the presence of imposed vertical magnetic field saturated by a porous medium is investigated for both-free, rigid-free, and both-rigid boundaries using Darcy-Brinkman model. The effects of Brownian motion and thermophoretic forces due to the presence of nanoparticles and Lorentz’s force term due to the presence of magnetic field have been considered in the momentum equations along with Maxwell’s equations. Keeping in mind applications of flow through porous medium in geophysics, especially in the study of Earth’s core, and the presence of nanoparticles therein, the hydromagnetic stability of a nanofluid layer in porous medium is considered in the present formulation. An analytical investigation is made by applying normal mode technique and Galerkin type weighted residuals method and the stability of Cu-water and Ag-water nanofluids is compared. Mode of heat transfer is through stationary convection without the occurrence of oscillatory motions. Stability of the system gets improved appreciably by raising the Chandrasekhar number as well as Darcy number whereas increase in porosity hastens the onset of instability. Further, stability of the system gets enhanced as we proceed from both-free boundaries to rigid-free and to both-rigid boundaries.

Numerical simulation for external magnetic field influence on Fe3O4-water nanofluid forced convection

2018 ◽  
Vol 35 (4) ◽  
pp. 1639-1654 ◽  
Author(s):  
Mohsen Sheikholeslami
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Volume Fraction ◽  
Control Volume ◽  
Darcy Number ◽  
Water Volume ◽  
Shape Effect ◽  
Content Type ◽  
Water Volume Fraction ◽  
The Impact

Purpose The purpose of this paper is to simulate nanofluid laminar steady flow in a lid-driven porous cavity under the impact of Lorentz forces. Design/methodology/approach Shape effect of nanoparticles and magnetic field impact on nanofluid properties are taken into consideration. The solutions of final equations are obtained by control volume based finite element method (CVFEM). Findings Graphs are depicted for different values of Darcy number, Fe3O4-water volume fraction, Reynolds and Hartmann numbers. Originality/value Results illustrated that using Platelet-shaped nanoparticles results in the highest Nusselt number. Nusselt number augments with rise of Darcy and Reynolds number.

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