Ferrofluid Ferrofluid is a liquid that is attracted to the poles of a magnet. It is a colloidal liquid made of nanoscale ferromagnetic or ferrimagnetic particles suspended in a carrier fluid (usually an organic solvent or water). Each magnetic particle ...

s can be used to transfer heat, since heat and

mass transport Public transport (also known as public transportation, public transit, mass transit, or simply transit) is a system of transport for passengers by group travel systems available for use by the general public unlike private transport, typica ...

in such magnetic fluids can be controlled using an external

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...

. B. A. Finlayson first explained in 1970 (in his paper "Convective instability of ferromagnetic fluids", ''

Journal of Fluid Mechanics The ''Journal of Fluid Mechanics'' is a peer-reviewed scientific journal in the field of fluid mechanics. It publishes original work on theoretical, computational, and experimental aspects of the subject. The journal is published by Cambridge Uni ...

'', 40:753-767) how an external magnetic field imposed on a ferrofluid with varying

magnetic susceptibility In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the ap ...

, 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 is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...

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 In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certai ...

. 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 non-isothermal 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.Phys. Fluids 16, 2228 (2004); doi:10.1063/1.1736691 (9 pages)
/ref> The ferrofluid

magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...

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 is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

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 cURL (pronounced like "curl", UK: , US: ) is a computer software project providing a library (libcurl) and command-line tool (curl) for transferring data using various network protocols. The name stands for "Client URL". History cURL was fi ...

-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 isotherms.

References

{{Reflist Convection Magnetism Continuum mechanics