Linear stability analysis of a Newtonian ferrofluid cylinder under a magnetic field

2021 ◽  
Vol 915 ◽  
Author(s):  
Romain Canu ◽  
Marie-Charlotte Renoult
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis

Abstract

Rayleigh–Bénard instability in a vertical cylinder with a vertical magnetic field

2002 ◽  
Vol 469 ◽  
pp. 189-207 ◽  
Author(s):  
B. C. HOUCHENS ◽  
L. MARTIN WITKOWSKI ◽  
J. S. WALKER
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Numerical Solution ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Hartmann Number ◽  
Critical Rayleigh Number ◽  
Vertical Wall ◽  
Vertical Cylinder ◽  
Vertical Magnetic Field

This paper presents two linear stability analyses for an electrically conducting liquid contained in a vertical cylinder with a thermally insulated vertical wall and with isothermal top and bottom walls. There is a steady uniform vertical magnetic field. The first linear stability analysis involves a hybrid approach which combines an analytical solution for the Hartmann layers adjacent to the top and bottom walls with a numerical solution for the rest of the liquid domain. The second linear stability analysis involves an asymptotic solution for large values of the Hartmann number. Numerically accurate predictions of the critical Rayleigh number can be obtained for Hartmann numbers from zero to infinity with the two solutions presented here and a previous numerical solution which gives accurate results for small values of the Hartmann number.

scholarly journals Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field

Fluids ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 177 ◽  
Author(s):  
Tagawa
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Liquid Metal ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Uniform Magnetic Field ◽  
Metal Flow ◽  
Rectangular Duct ◽  
Liquid Metal Flow ◽  
External Uniform Magnetic Field

Linear stability analysis of liquid metal flow driven by a constant pressure gradient in an insulating rectangular duct under an external uniform magnetic field was carried out. In the present analysis, since the Joule heating and induced magnetic field were neglected, the governing equations consisted of the continuity of mass, momentum equation, Ohm’s law, and conservation of electric charge. A set of linearized disturbance equations for the complex amplitude was decomposed into real and imaginary parts and solved numerically with a finite difference method using the highly simplified marker and cell (HSMAC) algorithm on a two-dimensional staggered mesh system. The difficulty of the complex eigenvalue problem was circumvented with a Newton—Raphson method during which its corresponding eigenfunction was simultaneously obtained by using an iterative procedure. The relation among the Reynolds number, the wavenumber, the growth rate, and the angular frequency was successfully obtained for a given value of the Hartmann number as well as for a direction of external uniform magnetic field.

Linear stability analysis of a Newtonian ferrofluid cylinder surrounded by a Newtonian fluid

2021 ◽  
Vol 927 ◽  
Author(s):  
Romain Canu ◽  
Marie-Charlotte Renoult
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Dispersion Relation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Density Ratio ◽  
Bond Number ◽  
Wire Radius ◽  
Azimuthal Magnetic Field ◽  
Relative Magnetic Permeability

We performed a linear stability analysis of a Newtonian ferrofluid cylinder surrounded by a Newtonian non-magnetic fluid in an azimuthal magnetic field. A wire is used at the centre of the ferrofluid cylinder to create this magnetic field. Isothermal conditions are considered and gravity is ignored. An axisymmetric perturbation is imposed at the interface between the two fluids and a dispersion relation is obtained allowing us to predict whether the flow is stable or unstable with respect to this perturbation. This relation is dependent on the Ohnesorge number of the ferrofluid, the dynamic viscosity ratio, the density ratio, the magnetic Bond number, the relative magnetic permeability and the dimensionless wire radius. Solutions to this dispersion relation are compared with experimental data from Arkhipenko et al. (Fluid Dyn., vol. 15, issue 4, 1981, pp. 477–481) and, more recently, Bourdin et al. (Phys. Rev. Lett., vol. 104, issue 9, 2010, 094502). A better agreement than the inviscid theory and the theory that only takes into account the viscosity of the ferrofluid is shown with the data of Arkhipenko et al. (Fluid Dyn., vol. 15, issue 4, 1981, pp. 477–481) and those of Bourdin et al. (Phys. Rev. Lett., vol. 104, issue 9, 2010, 094502) for small wavenumbers.

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.

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