#### Title

A study of ferromagnetic fluids.

#### Date of Award

2000

#### Degree Type

Dissertation

#### Degree Name

Ph.D.

#### Department

Mathematics and Statistics

#### Keywords

Mathematics.

#### Rights

CC BY-NC-ND 4.0

#### Abstract

This dissertation deals with a study of ferromagnetic fluids as a polarizable media with couple stress. Ferromagnetic fluids are artificially synthesized for their applications and can be thought of as liquid magnets. They are stable suspensions of very small mono-domain magnetic particles in a liquid medium. They display very strong magnetic response while retaining their fluid structure. The purpose of this dissertation is to provide a mathematical description of ferromagnetic fluids and study some flow and stability problems. This dissertation contains two parts. The first part takes a theoretical look by modeling ferromagnetic fluids as a continuum and by studying uniqueness and stability of ferrohydrodynamic motions. As the suspended particles rotate independently of the medium under an applied magnetic field, the stress is not symmetric and the medium is anisotropic through magnetization. It is shown that under appropriate limiting cases of this model one can obtain some popular models used in the literature. The various models that describe the magnetization relaxation phenomenon are analyzed. Asymptotic stability and uniqueness of ferrohydrodynamic motion are studied using an energy method. Sufficiency conditions for the system to be asymptotically stable under an arbitrary disturbance are obtained in terms of bounds for the Reynolds number. Conditions on uniqueness of solutions for ferromagnetic fluid flows are also derived. Rheological properties and heat transfer properties of ferromagnetic fluids are studied in the latter part of this dissertation. Using the model derived earlier, exact solutions are obtained for some traditional viscometric flows and the difference in the flow structure of a ferromagnetic fluid with that of a classical fluid is described. Effective viscosities of two parallel flows, two axisymmetric flows and a flow between eccentric disks are studied in order to illustrate the rheological characteristics of magnetic fluid flows. The results are then compared with the polar fluids in the appropriate limits. Transformation techniques for ferrohydrodynamics are introduced and the effectiveness of these techniques are illustrated by an example. The heat transfer problem is studied as an onset of Benard - Marangoni instability in a layer of ferromagnetic fluid between a free and flat upper boundary and a solid lower boundary. The complexity is enhanced due to the temperature dependence of the magnetization. A uniform vertical magnetic field is applied normal to the boundary. The combined effects of surface tension, gravity and magnetization on the system are studied, when a vertical temperature gradient is present. The effect of the magnetic properties of boundary plate material used is critically analyzed. A paramagnetic and a strongly ferromagnetic boundary are considered. Results are analyzed in order to find the conditions for which a specific force dominates the system. The physical properties of the various fluids that are studied are included as parameters which affect the system. These include: the Biot number, Rayleigh number, Marangoni number, magnetic Rayleigh number, magnetic susceptibility of the fluid and non-linearity of the material magnetization. The three mechanisms of surface tension, magnetization and buoyancy are seen to strongly depend on one another. A tight coupling, between these three mechanisms, is observed for low Biot numbers. It is seen that magnetic forces inhibit stability.Dept. of Economics, Mathematics, and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2000 .V36. Source: Dissertation Abstracts International, Volume: 67-02, Section: B, page: 0931. Thesis (Ph.D.)--University of Windsor (Canada), 2000.

#### Recommended Citation

Venkatasubramanian, Somasundhar., "A study of ferromagnetic fluids." (2000). *Electronic Theses and Dissertations*. 775.

http://scholar.uwindsor.ca/etd/775

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