Thermomagnetic convection
Encyclopedia
Ferrofluid
s can be used to transfer heat
, since heat and mass
transport in such magnetic fluids can be controlled using an external magnetic field
.
B. A. Finlayson
first explained in 1970 (in his paper "Convective instability of ferromagnetic fluids", Journal of Fluid Mechanics
40:753-767) how an external magnetic field imposed on a ferrofluid with varying magnetic susceptibility
, e.g., due to a temperature gradient, results in a nonuniform magnetic body force, which leads to thermomagnetic convection. This form of heat transfer can be useful for cases where conventional convection
fails to provide adequate heat transfer, e.g., in miniature microscale devices or under reduced gravity conditions.
Ozoe group has studied thermomagnetic convection both experimentally and numerically. They showed how to enhance, suppress and invert the convection modes. . They have also carried out scaling analysis for paramagnetic fluids in microgravity conditions .
A comprehensive review of thermomagnetic convection (in A. Mukhopadhyay, R. Ganguly, S. Sen, and I. K. Puri
, "Scaling analysis to characterize thermomagnetic convection", International Journal of Heat and Mass Transfer 48:3485-3492, (2005)) also shows that this form of convection can be correlated with a dimensionless magnetic Rayleigh number
. Subsequently, this group explained that fluid motion occurs due to the presence of a Kelvin body force that has two terms. The first term can be treated as a magnetostatic pressure, while the second is important only if there is a spatial gradient of the fluid susceptibility, e.g., in a nonisothermal system. Colder fluid that has a larger magnetic susceptibility is attracted towards regions with larger field strength during thermomagnetic convection, which displaces warmer fluid of lower susceptibility. They showed that thermomagnetic convection can be correlated with a dimensionless magnetic Rayleigh number. Heat transfer due to this form of convection can be much more effective than buoyancy-induced convection for systems with small dimensions.
The ferrofluid magnetization
depends on the local value of the applied magnetic field H as well as on the fluid magnetic susceptibility. In a ferrofluid flow encompassing varying temperature
s, the susceptibility is a function of the temperature. This produces a force that can be expressed in the Navier–Stokes or momentum equation governing fluid flow as the "Kelvin body force (KBF)".
The KBF creates a static pressure field that is symmetric about a magnet, e.g., a line dipole, that produces a curl-free force field, i.e., curl(ℑ) = 0 for constant temperature flow. Such a symmetric field does not alter the velocity. However, if the temperature distribution about the imposed magnetic field is asymmetric so is the KBF in which case curl(ℑ) ≠ 0. Such an asymmetric body force leads to ferrofluid motion across isotherm
s.
Ferrofluid
A ferrofluid is a liquid which becomes strongly magnetized in the presence of a magnetic field.Ferrofluids are colloidal liquids made of nanoscale ferromagnetic, or ferrimagnetic, particles suspended in a carrier fluid . Each tiny particle is thoroughly coated with a surfactant to inhibit clumping...
s can be used to transfer heat
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...
, since heat and mass
Mass transfer
Mass transfer is the net movement of mass from one location, usually meaning a stream, phase, fraction or component, to another. Mass transfer occurs in many processes, such as absorption, evaporation, adsorption, drying, precipitation, membrane filtration, and distillation. Mass transfer is used...
transport in such magnetic fluids can be controlled using an external magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
.
B. A. Finlayson
Bruce A. Finlayson
Bruce A. Finlayson is an American chemical engineer and applied mathematician. He is currently the Professor Emeritus of Chemical Engineering at the University of Washington, USA. He is a member of the National Academy of Engineering...
first explained in 1970 (in his paper "Convective instability of ferromagnetic fluids", Journal of Fluid Mechanics
Journal of Fluid Mechanics
The Journal of Fluid Mechanics is the leading scientific journal in the field of fluid mechanics. It publishes original work on theoretical, computational and experimental aspects of the subject. The journal is usually referred to by its initials JFM by academics in the field. Within citations,...
40:753-767) how an external magnetic field imposed on a ferrofluid with varying magnetic susceptibility
Magnetic susceptibility
In electromagnetism, the magnetic susceptibility \chi_m is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field...
, e.g., due to a temperature gradient, results in a nonuniform magnetic body force, which leads to thermomagnetic convection. This form of heat transfer can be useful for cases where conventional convection
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....
fails to provide adequate heat transfer, e.g., in miniature microscale devices or under reduced gravity conditions.
Ozoe group has studied thermomagnetic convection both experimentally and numerically. They showed how to enhance, suppress and invert the convection modes. . They have also carried out scaling analysis for paramagnetic fluids in microgravity conditions .
A comprehensive review of thermomagnetic convection (in A. Mukhopadhyay, R. Ganguly, S. Sen, and I. K. Puri
Ishwar K. Puri
Ishwar K. Puri is N. Waldo Harrison Professor and Head of the Department of Engineering Science and Mechanics at Virginia Tech. There, he also directs and mentors the Multiphysics Research Group .-Early years:...
, "Scaling analysis to characterize thermomagnetic convection", International Journal of Heat and Mass Transfer 48:3485-3492, (2005)) also shows that this form of convection can be correlated with a dimensionless magnetic Rayleigh number
Rayleigh number
In fluid mechanics, the Rayleigh number for a fluid is a dimensionless number associated with buoyancy driven flow...
. Subsequently, this group explained that fluid motion occurs due to the presence of a Kelvin body force that has two terms. The first term can be treated as a magnetostatic pressure, while the second is important only if there is a spatial gradient of the fluid susceptibility, e.g., in a nonisothermal system. Colder fluid that has a larger magnetic susceptibility is attracted towards regions with larger field strength during thermomagnetic convection, which displaces warmer fluid of lower susceptibility. They showed that thermomagnetic convection can be correlated with a dimensionless magnetic Rayleigh number. Heat transfer due to this form of convection can be much more effective than buoyancy-induced convection for systems with small dimensions.
The ferrofluid magnetization
Magnetization
In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material...
depends on the local value of the applied magnetic field H as well as on the fluid magnetic susceptibility. In a ferrofluid flow encompassing varying temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
s, the susceptibility is a function of the temperature. This produces a force that can be expressed in the Navier–Stokes or momentum equation governing fluid flow as the "Kelvin body force (KBF)".
The KBF creates a static pressure field that is symmetric about a magnet, e.g., a line dipole, that produces a curl-free force field, i.e., curl(ℑ) = 0 for constant temperature flow. Such a symmetric field does not alter the velocity. However, if the temperature distribution about the imposed magnetic field is asymmetric so is the KBF in which case curl(ℑ) ≠ 0. Such an asymmetric body force leads to ferrofluid motion across isotherm
Isotherm
Isotherm may refer to:* Isotherm a type of contour line that connects points of equal temperature at a given date or time on a geographic map* Isotherm in thermodynamics, a curve on a p-V diagram for an isothermal process...
s.