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deBoer, J. H.; Van den Heuvel, A.; Lonsen, B. G. Studies on Pore Systems in Catalysis 1% The Two Causes of Reversible Hysteresis. J. Catal. 1964,3,268. Ervin, G.; Osborn, E. F. The System A120,.H20. J. Geol. 1951,59, 381. Eyraud, C.; Goton, R. Etude Cinetique de la Dissociation Thermique d'Hydrates d'Alumine. J. Chem. Phys. 1954,51,430. Freund, F. The Dehydration of Gibbsite in the Formation of Boehmite. Ber. Dtsch. Keram. Ges. 1967,44 (4),141. Ginsberg, H.; Hutting, W.; Strunk-Lichtenberg, G. The Influence of the Starting Material on the Crystalline Forms Arising in the Thermal Decomposition and Conversion of Aluminum Hydroxides 11, Influence of the Starting Material on the Course of the Decomposition of the y-Hydroxide. 2.Anorg. Allg. Chem. 1957, 293,204. Hulbert, S.F. Models for Solid-state Reactions in Powdered Compacts. J. Br. Ceram. Soc. 1969,6,11. Oomes, L.E.; deBoer, J. H.; Lippens, B. C. Phase Transformations of Aluminum Hydroxides. In Reactiuity of Solids: Proceedings of the 4th International Symposium on the Reactivity of Solids; deBoer, J. H., Ed.; Elsevier: Amsterdam, 1961. Puchkov, L. V.; Chakhalyan, 0. K. Saturated Vapor Pressure over Solutions in the System: Na20.A1203.H20.J. Appl. Chem. USSR 1974,47,2206. Rouquerol, J.; Rouquerol, F.; Ganteaume, M. Thermal Decomposition of Gibbsite under Low Pressures I, Formation of the Boehmite Phase. J. Catal. 1975,50,99. Sanchez, M. G.; Herrera, J. E. Extruded Alumina Catalyst Supports Having Controlled Distribution of Pore Sizes. US. Patent
4,301,037,Nov 17,1981. Sanchez. M. G.: Ernest. M. V.: Laine. N. R. Soheroidal Particles and Catalysts Employing the Particles as a hpport. US. Patent 4,279,779,July 21,1981. Sato, T. The Dehydration of Alumina Trihydrate. J. Appl. Chem. 1959,9,331. Sato, T. Hydrothermal Reactions of Alumina Trihydrate. J. Appl. Chem. 1960,10,414. Sestak, J.; Berggren, G. Study of the Kinetics of the Mechanism of Solid-state Reactions at Increasing Temperatures. Thermochim. Acta 1971,3,1. Sing, K. S. W. Formation of Pore Structures. In Pore Structure and Properties of Materials; Modry, S., Ed.; Academia: Prague, 1974. Tertian, R.; Papee, D. Etude aux Rayons X des Produita Resultant de la Deshydration Menagee de 1"ydrargiUite et de la Bayerite. C. R. Acad. Sci. 1953,236, 1565. Tertian, R.; Papee, D.; Charrier, J. Etude aux Rayons X des Alumine Anhydres de Transition. C. R. Acad. Sci. 1954,238,98. Torkar, K.; Bertsch, L. Aluminum Hydroxide and Oxides VIII: Influence of Sodium Ions on the Formation and the Thermal Decomposition of Bayerite. Monatsh. Chem. 1961,92,525. Wefers, K.; Bell, G. M. 'Oxides and Hydroxide of Aluminum"; Technical Paper No. 19;Alcoa Research Laboratories, 1972. Yamaguchi, G.; Sakamoto, K. Hydrothermal Reactions of Aluminum Trihydroxides. Bull. Chem. SOC. Jpn. 1959,32,696. Received for review December 4,1990 Revised manuscript receiued May 17, 1991 Accepted June 24, 1991
Transient Responses of Natural Convection Heat Transfer with Liquid Gallium under an External Magnetic Field in either the x,y, or z Direction Kazuto Okada and Hiroyuki Ozoe* Institute of Advanced Material Study, Kyushu University, Kasuga Koen 6-1,Kasuga 816,J a p a n
The transient response of heat transfer of liquid gallium enclosed in a cubical 30 mm X 30 mm x 30 mm enclosure heated and cooled on opposing vertical walls was measured, and the effect of the direction of a magnetic field was studied. Under a very strong magnetic field such as 3700 G the transient response of system heat transfer was found to be in good agreement with that for pure conduction heated from above. The magnetic field was found to be most effective when it was perpendicular to the vertical heated wall or oriented vertically. 1. Introduction Recent rapid development of various electronic instruments has increased the demand for integrated circuits. Integrated circuits are constructed of semiconducting materials such as silicon crystals. Crystals with a purity of 99.999999999% or dopant-controlled crystals are required for reliable function as a semiconductor. Crystals are manufactured by growth from a seed crystal dipped in a melt with a pulling-up scheme. According to the Crystal Engineering Handbook? the pulling-up scheme has been called the Czochralski method5 in the field of metal growth or the Nacken methodlo in chemistry. When polycrystals are melted in a SiOz crucible, convection of molten silicon is induced. Oxygen molecules are dissolved in the molten silicon and are included in the crystal rod as an impurity. The suppression of convection would be expected to decrease the amount of oxygen. Brown' recently carried out an extensive survey of the literature on this topic, and only subsequent reports will be noted herein. 0888-5SS5/92/2631-07oo$o3.oo/o
Molten silicon is electroconducting and this characteristic induces a Lorentz force under an external magnetic field. The application of an external m.agnetic field enables control of convection and hence of the concentration of oxygen in the crystal rod. An application of the magnetic field on thermal convection was apparently first studied by Nakagawa," who took streak photographs on the surface of mercury. Chandrasekhar2 summarized the early works. Hurle' reported a temperature oscillation of liquid gallium and reported the suppression of the oscillation by an application of a magnetic field. Uteck and Fleming18 employed an external vertical magnetic field for the solidification process of tellurium-doped indium antimonide in a horizontal boat and reported the elimination of solute banding in the crystals. Witt et al.lg applied a transverse horizontal magnetic field in the crystal growth of InSb in the Czochralski method and reported the damping of the temperature fluctuation. These are the only representative works in the early days. Hoshi et alS6applied this scheme for molten silicon and reported various good effects. However, there appears to be no definitive answer on the 0 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 701
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In the present paper, the transient response of the rate of heat transfer under a step change either in the heat input or in the strength of an external magnetic field is reported for liquid gallium in a cubic enclosure. The effect of the direction of the magnetic field was also studied.
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best orientation of the external magnetic field. Recently Ozoe and Okada14studied the effect of an external magnetic field on natural convection in liquid metals in a cubic enclosure, using a three-dimensional numerical analysis, and found a significant difference of orientation on suppression. Okada and Ozoe13 subsequently carried out heat-transfer experiments with liquid gallium in an enclosure and verified the effect of the direction of the magnetic field qualitatively. Their experiment was for heating with a uniform flux. Ozoe and M ~ t s u o on , ~ ~the other hand, carried out transient numerical simulations of natural convection under an external magnetic field. Their work was motivated by the possible application of an external magnetic field to suppress the motion and therefore allow the measurement of the thermal conductivity of molten materials. Their idea was subsequently niaterialized by Nakamura et al.12for the measurement of the thermal conductivity of mercury. For this purpose, it is necessary to know the transient characteristics of heat conduction in a real liquid metal.
2. Experimental Apparatus The experimental setup is shown in Figure 1. An experimental apparatus (7) was placed inside an electromagnet (61, and both were kept in a temperature-controlled compact room (8). The experimental apparatus was a Plexiglas cubic enclosure whose one vertical side wall was a 1-mm-thickcopper plate and heated electrically from ita rear side. An opposing side wall was cooled isothermally. Four other walls were thermally insulated by fiber glass. Temperatures were measured with 0.05-mm-diameter copper-constantan thermocouples. One junction of the thermocouple was inserted into a hole in a cold copper plate, and another junction on the liquid-side surface of the hot copper plate was attached with instant glue. This is schematically shown in Figure 2. Three junctions on the hot plate are located at z = 5,15, and 25 mm from the top of the enclosure. The coordinate of the enclosure is shown in Figure 3. The net heat flux through a layer of fluid by thermal conduction and/or natural convection is very difficult to measure. Ozoe and Churchill16invented a simple method, and their scheme was employed herein. At the beginning, an experiment was carried out with air (known thermal conductivity) heated from above and cooled from below. The temperature differences between the hot and cold plate were measured for various rates of electrical heating Qbt. In Figure 4 the computed rate of heat transfer by pure conduction in air and the measured heat input are both plotted versus the temperature on the hot wall. The difference between them is considered to be the heat loss, Q1., This heat loss to the surroundings is expected to be the same for the same value of the hot wall temperature 6, even when convection occurs inside the cavity under the total heating rate of several wattage. This is currently the best way for authors to estimate the net heat flux due to natural convection without using special devices. 3. Experimental Results 3.1. Measurements of Thermal Conductivity of Liquid Gallium. According to the Metals Handbook? the thermal conductivity of liquid gallium at 350.15 K (77 O C ) is as follows. k~~ = 28.68, 34.04, or 38.31 [W/(mK)]
702 Ind. Eng. Chem. Res., Vol. 31, No. 3, 1992 1
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