Natural convection of magnetic fluid inside a cubical
enclosure under magnetic gravity compensation
Zuo-Sheng Lei, Sheng-Yang Song, Chun-Long Xu, Jia-Hong Guo
To cite this version:
Zuo-Sheng Lei, Sheng-Yang Song, Chun-Long Xu, Jia-Hong Guo. Natural convection of magnetic fluid inside a cubical enclosure under magnetic gravity compensation. 8th International
Conference on Electromagnetic Processing of Materials, Oct 2015, Cannes, France. EPM2015.
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Natural convection of magnetic fluid inside a cubical enclosure
under magnetic gravity compensation
Zuo-Sheng Lei1*, Sheng-Yang Song1, Chun-Long Xu1, Jia-hong Guo2
1
2
State Key Laboratory of Advanced Special Steel, Shanghai University, 200072, Shanghai, China
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 20072, Shanghai, China
*Corresponding author : [email protected]
Abstract
The experimental studies on natural convection of magnetic fluid inside a cubical enclosure under magnetic gravity
compensation are presented. The bottom wall of the enclosure was uniformly heated by a heating element from a DC
power supply while the top wall was cooled by ice water flowing from a container. The cubical enclosure was
positioned in the center of the Helmholtz-Maxwell coils, which can provide a uniform gradient magnetic field. The
magnetic force applied to the magnetic fluid was large enough to compensate gravitational force of the magnetic fluid,
which was the driven force of natural convection. The Nusselt number was calculated by measuring the heat flux on the
bottom wall and the temperature of both walls. Heat transfer efficiency of natural convection of magnetic fluid under
different effective gravitational accelerations was compared in this study.
Key words : natural convection, magnetic fluid, magnetic gravity compensation
Introduction
Experimental and numerical studies have been carried out on natural convection. Enhancements or suppressions of
natural convection heat transfer have been long-term research topics investigated by many researchers. The driving
force for natural convection is the buoyancy force caused by the density difference between hot and cold regions of the
fluid in terrestrial conditions. And controlling natural convection may be difficult as the gravitational acceleration is
constant and uniform on the earth.
In recent years, another option for flow control has appeared—the magnetic buoyancy force. One of the first works on
magnetic convection was carried out by Carruthers and Wolfe[1]. They found that when an insulating paramagnetic fluid
such as gaseous oxygen was subjected to combined thermal and magnetic field gradients, a magnetic body force was
shown to exist which was analogous to that of gravity. The possibility of magnetic control of thermal convection was
discussed for several instances. Braithwaite et al.[2] used a magnetic field both to enhance and suppress buoyancy-driven
convection in a solution of gadolinium nitrate, and showed that the effect depended on the relative orientation of
magnetic field and temperature gradient. Quantitative treatment of air convection under magnetic fields was initiated by
Bai et al.[3]. Huang et al.[4] studied the effect of a static, nonuniform magnetic field on a laterally unbounded
nonconducting paramagnetic fluid layer heated from below or above using a linear stability analysis of the NavierStokes equations supplemented by Maxwell’s equations and the appropriate magnetic body force. Tagawa et al.[5]
employed a procedure similar to the Boussinesq approximation and developed model equations for convection resulting
from a gradient magnetic field. Ozoe et al.[6] installed a four-poles magnet to apply the cusp-shaped magnetic field to air
in the cubic enclosure. A simple model equation was derived for magnetizing force and numerically computed for the
system. Bednarz et al.[7-10] investigated natural convection of paramagnetic fluids in a differentially heated cubic
enclosure under magnetic fields. It was shown in their works that by using a strong magnetic field they can enhance,
suppress or invert the usual gravitational convection with different combinations of the two main body forces
(gravitational and magnetic buoyancy forces) that act together to drive thermo-magnetic convection of paramagnetic
fluids.
In this present study, we develop an apparatus made of two pairs of Helmholtz-Maxwell coils, which can generate a
uniform magnetic gradient field for ferro-fluid filled inside a cubical enclosure, so as to produce a uniform magnetic
volume force to compensate the gravity. Then natural convection of water-based magnetic fluid inside the cubical
enclosure under magnetic gravity compensation is studied experimentally.
Experimental apparatus and the working fluid
The experimental setup is presented in Fig. 1, here the magnetic gravity compensation was realized by combining the
two pairs of Helmholtz-Maxwell coils and ferro-fluid[11]. The specifications of the coil system and the configuration of
the Helmholtz-Maxwell coil system is described in our other work[12]. The experimental cell consisted of a cubical
enclosure filled with magnetic fluid placed in the centre of the Helmholtz-Maxwell coils, a heater control system, a
cooling system, a heat flux meter and a portable data acquisition module connected to a personal computer. The details
of experimental cell is shown schematically in Fig. 2. Six separate elements were designed to assemble the final
experimental model. Those are: two copper plates (one for the cooling side and the other for the heating side) with one
hole in each to place two K-type thermocouples, a quartzose cubic cavity, the cooling chamber is made of stainless steel,
the base is made of polytetrafluoroethylene. There were a heat flux sensor and a heater between the heating plate and
the base. The heater was connected to a DC power supply (KXN-305D). The cooling copper plate was cooled by water
pumped from a container which is full of ice water. The cubic cavity had an internal dimension of 40mm on each side.
Fig. 1: Experimental setup
Fig. 2: Schematic view of the experimental apparatus
In the present experiment a water-based magnetic fluid which contains magnetic nanoparticles was used as the working
fluid. The major properties of the working fluid are listed in Table 1.
Table 1 Important properties of the working fluid at room temperature
Property
Value
α(thermal diffusivity)
1.2×10-7
β(thermal expansion coefficient)
5.2×10-4
λ(thermal conductivity)
0.59
ν(kinematic viscosity)
4.24×10-6
ρ(density at room temperature)
1.18×103
Unit
m2/s
1/K
W/(m∙K)
m2/s
kg/m3
When all parts of the experimental setup were assembled, it was possible to fill the enclosure with the working fluid.
This was done with a syringe and a thin needle. There was a hole through the cooling copper plate and the cooling
chamber. When the enclosure was filled, the hole was sealed by hot glue and the experimental apparatus was placed in
the center of the Helmholtz-Maxwell coils. The environmental temperature was kept constant. The electric current to
the Helmholtz coils was 130A while the electric current to the Maxwell coils increased from 0A to 93A in order to
modulate the gravity level. The heater power was set to 2W at the beginning of every group of experiments. The
temperature of heated and cooled side walls were monitored continuously. After about 1 hour, when the system had
reached a steady state, the temperatures and the heat flux were recorded. Then the heater power gradually increased by
2W until it reached 20W.
Results and Discussion
Fig. 3: The Nusselt number at different heating power under normal gravity and a uniform magnetic field
In Fig. 3, the natural convection Nusselt numbers are plotted against the heating power. As seen in Fig. 3, the Nusselt
number increases with the heating power no matter under normal gravity or under a uniform magnetic field. Because
the temperature gradient increases with the heating power, natural convection heat transfer is enhanced. The viscosity of
magnetic fluid increases under a uniform magnetic field, so the natural convection heat transfer efficiency under a
uniform magnetic field is lower than that under normal gravity consequently. As we can see in Fig. 3, the Nusselt
number is less under a uniform magnetic field at the same heating power.
Fig. 4: The Nusselt number at different heating power under different effective gravitational accelerations
Fig. 4 shows natural convection heat transfer of magnetic fluid under different effective gravitational accelerations. It is
clear in the figure that the Nusselt number decreases with the decrease of effective gravitational acceleration. In order to
figure out the effect of magnetic force to natural convection, we calculate the magnetic Grashof number. The Nusselt
numbers are plotted against the magnetic Grashof numbers in Fig. 5. The Nusselt number increases with the magnetic
Grashof number under the same effective gravitational acceleration but decreases with the increase of effective
gravitational acceleration. The magnetic force acting on the magnetic fluid applied by the gradient magnetic field causes
the magnetic acceleration. The magnetic force will suppress natural convection of magnetic fluid when the direction of
the magnetic acceleration is contrary to the direction of the gravitational acceleration. The magnetic acceleration
increases with the increase of magnetic force, so does the suppression of natural convection.
Fig. 5 The Nusselt number at different magnetic Grashof number under different effective gravitational accelerations
Conclusions
In this paper, natural convection of magnetic fluid under magnetic gravity compensation in a cubical enclosure has been
investigated experimentally. The enclosure is placed in the center of the Helmholtz-Maxwell coils. The heat transfer
measurements show that, as the magnetic field increases, the effective gravitational acceleration decreases, the Nusselt
number decreases, indicating that convection is suppressed.
Acknowledgment
This project financially supported by National Science Foundation of China (No.51274137 and NO.11372174).
References
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