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FLOW OF WATER IN A VERTICAL CYLINDRICAL CONTAINER WITH AND WITHOUT ROTATION UNDER A VERTICAL MAGNETIC FIELD GRADIENT

Masato Akamatsu
Graduate School of Science and Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata 992-8510, Japan

Mitsuo Higano
Akita Prefectural University

Yoshio Takahashi
Faculty of Systems Science and Technology, Akita Prefectural University, 84-4 Tsuchiya-Ebinokuchi, Honjo, Akita 015-0055, JAPAN

Hiroyuki Ozoe
Institute of Advanced Material Study, Kyushu University, Kasuga, Japan; and Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an 710049, P. R. China

Abstract

Numerical computations were carried out in order to quantitatively estimate the heat transfer rate of water with the diamagnetic property in a vertical cylindrical container heated from below and cooled from above under a vertical magnetic field gradient. The effect of rotation of a container was also examined. Since the magnetizing force that is produced by the gradient of magnetic field is dependent on the location and the size of an electric coil, the electric coil was placed at either the hot or cold plates and the diameter of the electric coil was set 2.5 or 5 times that of the cylindrical container. The momentum equations including the magnetizing force term with the diamagnetic property were derived by the Boussinesq approximation. In a vertical cylindrical container without rotation, Nusselt number decreased with increase of magnetic strength when the electric coil was placed at the lower end plate and heated isothermally. On the other hand, Nusselt number increased with increase of magnetic strength when the electric coil was placed at the upper end plate and cooled isothermally. These different heat transfer phenomena in a gravitational field can be successfully explained by considering the gradient of the square of magnetic induction and the convection induced by the magnetizing force alone in a non-gravitational field. Furthermore, in a vertical cylindrical container with rotation, the convection induced by placing the electric coil at the cold plate was suppressed with increase of rotational Reynolds number. Under this convectional suppression, a complicated flow was observed at some strength of rotational Reynolds number. When rotational Reynolds number was further increased, this complicated flow was suppressed and the temperature field gradually changed to the conduction state.

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