Laminar shear in a ferrofluid

Stability studies

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We consider steady solutions for a planar-Couette magnetic fluid flow under the influence of magnetic fields applied transverse to the flow direction. Keeping a small non-zero value for the spin viscosity, we solve the coupled system for the linear and angular momentum equations. The imposed magnetic fields are time-independent and have a dissipative effect on the flow. However, by considering spatially varying fields, the mid-plane symmetry of the planar Couette flow can be broken. Assuming periodic boundary conditions at the inflow and outflow boundaries of the planar Couette flow in two dimensions, we use COMSOL to solve the coupled equations for velocity and spin. A linear stability analysis shows that slow channel flows can be destabilized by a spatially varying magnetic field and this is corroborated by our numerical calculations. The instability criterion is correlated to the spatial gradient of the applied external field.

Original languageEnglish
Pages (from-to)505-511
Number of pages7
JournalMagnetohydrodynamics
Volume49
Issue number3-4
StatePublished - 18 Dec 2013

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Magnetic fluids
ferrofluids
Couette flow
Magnetic fields
shear
magnetic fields
Linear stability analysis
Angular momentum
channel flow
Channel flow
fluid flow
Flow of fluids
angular momentum
Boundary conditions
Viscosity
viscosity
boundary conditions
momentum
gradients
symmetry

Cite this

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title = "Laminar shear in a ferrofluid: Stability studies",
abstract = "We consider steady solutions for a planar-Couette magnetic fluid flow under the influence of magnetic fields applied transverse to the flow direction. Keeping a small non-zero value for the spin viscosity, we solve the coupled system for the linear and angular momentum equations. The imposed magnetic fields are time-independent and have a dissipative effect on the flow. However, by considering spatially varying fields, the mid-plane symmetry of the planar Couette flow can be broken. Assuming periodic boundary conditions at the inflow and outflow boundaries of the planar Couette flow in two dimensions, we use COMSOL to solve the coupled equations for velocity and spin. A linear stability analysis shows that slow channel flows can be destabilized by a spatially varying magnetic field and this is corroborated by our numerical calculations. The instability criterion is correlated to the spatial gradient of the applied external field.",
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Laminar shear in a ferrofluid : Stability studies. / Mukherjee, Arup; Vaidya, Ashuwin; Yecko, P.

In: Magnetohydrodynamics, Vol. 49, No. 3-4, 18.12.2013, p. 505-511.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Laminar shear in a ferrofluid

T2 - Stability studies

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AU - Vaidya, Ashuwin

AU - Yecko, P.

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N2 - We consider steady solutions for a planar-Couette magnetic fluid flow under the influence of magnetic fields applied transverse to the flow direction. Keeping a small non-zero value for the spin viscosity, we solve the coupled system for the linear and angular momentum equations. The imposed magnetic fields are time-independent and have a dissipative effect on the flow. However, by considering spatially varying fields, the mid-plane symmetry of the planar Couette flow can be broken. Assuming periodic boundary conditions at the inflow and outflow boundaries of the planar Couette flow in two dimensions, we use COMSOL to solve the coupled equations for velocity and spin. A linear stability analysis shows that slow channel flows can be destabilized by a spatially varying magnetic field and this is corroborated by our numerical calculations. The instability criterion is correlated to the spatial gradient of the applied external field.

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