Schematic illustration of the model. A long, cylindrical vessel filled with water is installed at or near the center of a solenoidal magnet, and can be tilted together with the magnet. This vessel is in height and in diameter. The vessel bottom is isothermally heated and the top cooled. The electric current to generate magnetic force is approximated with 65 independent coils regularly arranged with in the innermost diameter, in the outermost diameter, and in height. The magnetic force acting on a diamagnetic substance is schematically shown by arrows. The size of the vessel and coils does not scale. The gravity vector is also shown.
Vessel positions in Cases A, B, and C studied in Secs. IV A–IV C, respectively. In Case A, the vessel is set up vertical at or near the magnet center. The position of the vessel center is (i) (0, 0, 0); (ii) (0, 0, ); or (III) (0, 0, ). In Case B, the vessel at the magnet center is tilted. In Case C, the vessel center is a little moved to (i) or to (ii) .
The decomposition of the gravitational force. (a) The angle (rad) is defined between the axis and the vertical line (the axis). Uc and Bc are the representative points at the center of the vessel top and bottom surfaces. (b) represents the decomposition of the gravity vector at an arbitrary point in the magnet bore into the radial and the circumferential components of a cylindrical coordinate system. The bore is seen downward from the axis. is the circumferential coordinate.
(Color online) The streak lines and isothermal contours of convections in a vertical vessel (Case A). The thermal properties are and . The cross sections of isothermal contours are taken from the plane so that the details become clearer than that at the plane. (a)–(d) represent the vessel center located at the magnet center with (a), (b), (c), and (d); (e) represents the vessel whose center is moved to with ; (f) represents the vessel whose center is moved to with .
The distributions of the magnetic force and resultant force in Case A. (a) shows the distributions of the magnetic force; (b)–(f) show the distributions of the resultant force. In (a) and (b) , (c) , and (d) . (e) with a vessel whose center is moved to , and (f) with the vessel center at . Note that the point is at the vessel top in (b) and within the vessel in (c)–(e).
(Color online) The computed streak lines projected over the plane, and isothermal contours cut in the plane for Case B at and .
(Color online) The computed streak lines projected over the plane, and isothermal contours cut in the plane [except for (a)] for Case C at , , and . The vessel center is at or at . The cross section of (a) is taken from the plane (since this section gives a more typical result than that in the plane).
(Color online) The computed streak lines projected over the plane, and isothermal contours cut in the plane at , , , and (rad). The vessel center is located either at the magnet center as shown in Fig. 2(B) or at as shown in Fig. 2(C) (ii).
The magnetic force distributions [(a) and (b)] and the resultant force distributions [(c) and (d)]. Case C (i) with vessel center at and Case C (ii) at . (rad) and .
Summary of the computed results to evaluate the number of meshes. .
Summary of the computed results in a vertical vessel (Case A). .
Summary of the computed results in an inclined vessel (Case B). .
Summary of the computed results in an inclined and off-centered vessel (Case C). .
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