Transient characteristics of convection and diffusion of oxygen gas in an open vertical cylinder under magnetizing and gravitational forces☆
Introduction
The recent development of a superconducting magnet appears to have marked the start of a new era of magnet applications in industrial processes. Typical developments in this area were reported at the 3rd International Symposium on Electro-magnetic Processing of Materials. In the plenary lecture of this meeting, Kitazawa, Hirota, Ikezoe, and Uetake (2000) described various phenomena of a steep gradient of magnetic field, i.e., magnetizing force effects, which the group had discovered (Ikezoe, Hirota, Nakagawa, & Kitazawa, 1998; Ikezoe et al., 1998a; Uetake, Nakagawa, Hirota, & Kitazawa, 1999; Nakagawa, Hirota, Kitazawa, & Shoda, 1999). Magnetizing force becomes dominant in a steep gradient of magnetic field expressed by the square of magnetic induction for a fluid with a high magnetic susceptibility. This force induces various interesting phenomena, such as lifting (or lowering) of a part of a liquid surface (Moses effect), microgravity effects, levitation of a liquid droplet in a gravity field, etc. Wakayama and coworkers (Wakayama 1991, Wakayama 1991a, Wakayama 1993; Wakayama, Ito, Kuroda, Fujita, & Ito, 1996; Bai, Yabe, Qi, & Wakayama, 1999) have also been actively experimenting with magnetizing force fields. Their findings include a jet-like nitrogen gas flow in a decreasing magnetic gradient in air, the so-called Wakayama jet, and the magnetic promotion of combustion in diffusion flames. Braithwaite, Beaugnon, and Tournier (1991) reported the enhancing effects of natural convection of paramagnetic fluid on Rayleigh–Benard convection. They reported enhanced or decreased heat transfer rates of natural convection. Ohgaki and Matsumura (1995) measured the effect of magnetic gradient on the diffusion and mixing of oxygen-containing gas.
All the above reports concern the magnetizing force induced by a steep gradient of a strong magnetic field. This force acts selectively on materials, such as oxygen gas, with a high magnetic susceptibility. This phenomenon was discovered by Faraday (1847), who reported that a bubble of oxygen gas is attracted to the center of a strong magnetic field. Pauling, Wood, and Sturdivant (1946) developed a paramagnetic oxygen analyzer based on this phenomenon. Knowledge of this magnetizing force thus has a long history, but its application has been rather neglected until the recent development of the superconducting magnet. A strong magnetic field allows diamagnetic material to be floated in a gravity field, and this is expected to be employed for processing new materials.
The present report aims to develop a model equation for the transient flow and diffusion characteristics of oxygen gas in a vertical open cylinder under a steep gradient of a magnetic field, i.e., magnetizing force. The transient decrease in the oxygen concentration in a pipe was computed and compared with the measured concentration in a similar experimental set-up.
Section snippets
The experimental results
To study the flow and diffusion characteristics of oxygen gas under a magnetizing force, the following simple system was adopted. A vertical pipe was filled with oxygen gas. At time zero the top and bottom caps are removed, and at intervals thereafter the transient concentration of oxygen gas was measured. Fig. 1 shows the schematics of the experimental apparatus. A glass pipe of inner length was placed in the bore of a superconducting magnet , and a small amount
Derivation of model equation
The above system was subsequently studied numerically. There appear to be no simple model equations for such a system, and we therefore developed the following model equations for a magnetizing force field in a similar way to those for natural convection. Wakayama, Ito, Kuroda, Fujita, and Ito (1996) derived an equation for the magnetizing force of oxygen gas, which can be rewritten in terms of magnetic induction aswhere the relationship was
Computed result
The model equations in Section 3 were numerically solved by a standard finite difference method (Hirt, Nichols, & Pomeco, 1975) for the system described in Fig. 3. The system considered for the computation is rather small in comparison with the experimental one of Fig. 1, since the experimental domain is extremely large and would require enormous amounts of time for computation. The system was assumed to be axially symmetrical. The system has a radius rp and an axial length ℓp, and ℓp/rp=10.
Conclusion
Based on the model for magnetizing force proposed by the Wakayama group, a magnetizing force term was included in a Navier–Stokes equation. The model equation was derived and numerically solved for the transient convection and diffusion of pure oxygen gas in a vertical pipe outward through the top and bottom openings. The transient characteristics of the oxygen concentration at the middle level agreed quite well with those of experimental measurements in a similar system. These results suggest
References (17)
Effect of a decreasing magnetic field on the flow of nitrogen gas
Chemical Physics Letters
(1991)Magnetic promotion of combustion in diffusion flames
Combustion and Flame
(1993)- et al.
Magnetic support of combustion in diffusion flames under microgravity
Combustion and Flame
(1996) - et al.
Quantitative analysis of air convection caused by magnetic-fluid coupling
AIAA Journal
(1999) - Bird, R.B., Stewart, W.E., & Lightfoot, E.N. (1960). Transport phenomena (p. 511). New York:...
- et al.
Magnetically controlled convection in a paramagnetic fluid
Nature
(1991) Philosophical Magazine S.
(1847)- et al.
Simplification of the mathematical description of boundary and initial value problem
A.I.Ch.E. Journal
(1964)
Cited by (35)
Influence of the shape of the inner boundary on thermomagnetic convection in the annulus between horizontal cylinders: Heat transfer enhancement
2020, International Journal of Thermal SciencesHeat transfer rate characteristics of the magnetothermal Rayleigh-Benard convection of paramagnetic air
2015, International Journal of Thermal SciencesCitation Excerpt :In contrast, control of the thermal convection of non-electro-conducting fluids such as paramagnetic and diamagnetic fluids has become possible with the recent development of a superconducting magnet with strong magnetic induction (10 T or more). For paramagnetic and diamagnetic fluids, the force called a magnetic force [5,6] or magnetizing force [7,8] generated by applying an inhomogeneous magnetic field was used. In addition, the control of ferromagnetic fluid [9,10] has also been extensively studied from the basics to the application.
On the air enrichment by polymer magnetic membranes
2009, Journal of Membrane ScienceFlow regimes in trickle beds using magnetic emulation of micro/macrogravity
2009, Chemical Engineering ScienceCitation Excerpt :Despite life support research strives to establish reliable and predictive models to be used as a basis for design of life support hardware for microgravity applications, a major obstacle in developing adapted multiphase reactor concepts for life support in reduced gravity is an insufficient knowledge concerning the interrelations between fluid flows and fluid/fluid interactions once in space. Following the work by Beaugnon and Tournier (1991) on magnetic levitation, strong inhomogeneous magnetic fields generated in superconducting magnets have been used to emulate a variety of phenomena in artificial gravity conditions (Lin et al., 2000; Wakayama et al., 2001; Tagawa et al., 2001; Wang and Wakayama, 2002). It was established that strong inhomogeneous magnetic fields allow diamagnetic materials to be levitated by compensating their weights.
Numerical computation of magnetothermal convection of water in a vertical cylindrical enclosure
2005, International Journal of Heat and Fluid FlowTransient buoyant convection of air in an enclosure under strong magnetic effect
2005, International Journal of Heat and Mass Transfer
- ☆
Invited contribution to celebrate 50 years of Chemical Engineering Science.