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RESEARCH PAPERS: Natural and Mixed Convection

Numerical and Experimental Analyses of Magnetic Convection of Paramagnetic Fluid in a Cylinder

[+] Author and Article Information
Piotr Filar, Toshio Tagawa, Hiroyuki Ozoe

Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga Koen 6-1, 816-8580 Fukuoka, Japan

Elzbieta Fornalik1

Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga Koen 6-1, 816-8580 Fukuoka, Japan and Department of Theoretical Metallurgy and Metallurgical Engineering, AGH University of Science and Technology, 30 Mickiewicz Avenue, 30-059 Krakow, Poland

Janusz S. Szmyd

Department of Theoretical Metallurgy and Metallurgical Engineering, AGH University of Science and Technology, 30 Mickiewicz Avenue, 30-059 Krakow, Poland

1

Corresponding author; e-mail: elaf@agh.edu.pl

J. Heat Transfer 128(2), 183-191 (Jul 26, 2005) (9 pages) doi:10.1115/1.2142334 History: Received February 09, 2005; Revised July 26, 2005

The magnetic convection of paramagnetic fluid in a cylindrical enclosure is studied experimentally and numerically. The upper side wall of the cylinder is cooled and the lower side wall heated, an unstable configuration. The whole system is placed coaxially in a bore of a superconducting magnet in the position of the minimum radial component of magnetic buoyancy force at the middle cross section of the enclosure. The stable configuration— when the whole system is placed inversely and the horizontal axial case are also considered. As a paramagnetic fluid an aqueous solution of glycerol with the gadolinium nitrate hexahydrate is used. The isotherms in the middle-height cross section are visualized by thermochromic liquid crystal slurry. For the unstable configuration the magnetic buoyancy force acts to assist the gravitational buoyancy force to give multiple spoke patterns at the mid cross section. The stable configuration gives an almost stagnant state without the magnetic field. Application of the magnetic field induces the convective flow similar to the unstable configuration. For the horizontal configuration a large roll convective flow (without the magnetic field) is changed under the magnetic field to the spoke pattern. The numerical results correspond to the experimental results.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematical view of the experimental apparatus

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Figure 2

The configurations of modeled system; (a) unstable, (b) stable, and (c) horizontal

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Figure 3

Photographs of the isotherms at the midheight of the cylinder: (a) at Ra=1.69×105 and b=0T, unstable configuration, (b) at Ra=1.67×105 and b=1T, unstable configuration, (c) at Ra=2.57×105 and b=0T, stable configuration, (d) at Ra=1.89×105 and b=2T, stable configuration, (e) at Ra=1.70×105 and b=0T, horizontal configuration, and (f) at Ra=1.51×105 and b=2T, horizontal configuration

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Figure 4

(a) Modeled system in the unstable configuration, (b) distribution of magnetic induction b, (c) distribution of gradient of square magnetic induction ∇b2

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Figure 5

The results for the unstable system at Ra=1.69×105 and b=0T: (a) computed isothermal contours with velocity vectors; (b) computed isotherms at cylinder midheight and three-dimensional demonstration of long time streak lines; and (c) isothermal contours at T=±0.05 and the gravitational buoyancy force vectors

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Figure 6

The results for the unstable system at Ra=1.67×105 and b=1T: (a) computed isothermal contours with velocity vectors; (b) computed isotherms at cylinder midheight and three-dimensional demonstration of long time streak lines; and (c) isothermal contours at T=0.01 and T=0.08 and the total force vectors

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Figure 7

The isotherms for the stable system at Ra=2.57×105 and b=0T: (a) computed isothermal contours with velocity vectors; (b) computed isotherms at cylinder midheight and three-dimensional demonstration of long time streak lines; and (c) isothermal contours at T=±0.4 and gravitational buoyancy force vectors

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Figure 8

The results for the stable system at Ra=1.89×105 and b=2T: (a) computed isothermal contours with velocity vectors at Z=1.68; (b) computed isotherms at Z=1.68 and three-dimensional demonstration of long time streak lines; and (c) isothermal contours at T=0.04 and T=0.1 and total force vectors

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Figure 9

The isotherms for the horizontal system at Ra=1.70×105 and b=0T: (a) computed isothermal contours with velocity vectors at the midheight; (b) computed isotherms at the cylinder midheight and three-dimensional demonstration of long time streak lines; and (c) isothermal contours and the gravitational buoyancy force vectors. Isothermal contours are at T=0 and T=±0.1

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Figure 10

The isotherms for the horizontal system at Ra=1.51×105 and b=2T: (a) computed isothermal contours with velocity vectors at the midheight; (b) computed isotherms at cylinder midheight and three-dimensional demonstration of long time streak lines; and (c) isothermal contours and total force vectors. Isothermal contours are at T=−0.04 and T=0.08

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