Preface -- Contents -- CHAPTER 1 Application of a Magnetic Field for Material Processing -- References -- CHAPTER 2 Natural Convection of Liquid Metal Without a Magnetic Field -- 2.1 Two-Dimensional Computation of Oscillatory Natural Convection of Low-Prandtl-Number Fluid Heated from Below [1] -- 2.2 Experimental Heat Transfer Rates of Rayleigh-Benard Oscillatory Natural Convection of Liquid Gallium Heated from Below [10] -- 2.3 Three-Dimensional Computation of Natural Convection in a Shallow Rectangular Region Heated from Below [16] -- 2.4 Closing Remark -- References -- CHAPTER 3 Two-Dimensional Numerical Analyses for Natural Convection of Liquid Metal in a Magnetic Field -- 3.1 Two-Dimensional Numerical Computations in a Vertical Magnetic Field [1] -- 3.2 Two-Dimensional Analysis for a Lateral Magnetic Field [20] -- References -- CHAPTER 4 Three-Dimensional Natural Convection of Liquid Metal in a Cubical Enclosure with a Magnetic Field -- 4.1 The Effect of the Direction of the External Magnetic Field [1] -- 4.2 Experimental Results for Molten Gallium under an External Magnetic Field in the X, Y or Z Direction [15] -- 4.3 Summary -- Appendix A [15] Physical properties of gallium -- Appendix B [15] Uncertainty analysis -- References -- CHAPTER 5 Enhanced Heat Transfer Rate of Natural Convection Due to a Magnetic Field -- 5.1 Three-Dimensional Numerical Analyses [1,14] -- 5.2 Further Experimental Measurement for the Y-Directional Magnetic Field [10] -- APPENDIX -- References -- CHAPTER 6 Natural Convection of Liquid Metal in a Cube with the Seebeck Effect Under a Magnetic Field [1] -- 6.1 Introduction -- 6.2 Mathematical Model -- 6.3 Computed Results -- 6.4 Discussion -- 6.5 Conclusions -- References -- CHAPTER 7 Flow Visualization of Oscillatory Czochralski Convection [1] -- 7.1 Introduction -- 7.2 Experiments -- 7.3 Conclusions -- References.

CHAPTER 8 Liquid-Encapsulated Czochralski Bulk Flow with Flow Visualization [1] -- 8.1 Introduction -- 8.2 Mathematical Model Equations -- 8.3 Experimental Set-up and Conditions for Flow Visualization -- 8.4 Results and Discussion -- 8.5 Conclusions -- References -- CHAPTER 9 Effect of Radiation Cooling from a Free Surface in Czochralski Melt Flow [1] -- 9.1 Introduction -- 9.2 The System and Model Equations -- 9.3 Computational Schemes -- 9.4 Computed Results -- 9.5 Conclusions -- References -- CHAPTER 10 Effect of an Axial Magnetic Field on the Melt Convection of Czochralski Crystal Growth [6, 7, 10] -- 10.1 Introduction -- 10.2 Computed Results for a Static Crucible -- 10.3 Computed Results for a Rotating Crucible [9] -- 10.4 Summary of the Results in an Axial Magnetic Field -- References -- CHAPTER 11 Effect of a Transverse Magnetic Field on the Melt Convecton of Czochralski Crystal Growth [1, 2, 20] -- 11.1 Introduction -- 11.2 Model System -- 11.3 Computational Schemes -- 11.4 Computed Results -- 11.5 Experimental Measurement of Temperature -- 11.6 Elliptic Temperature Profile in a Transverse Magnetic Field -- 11.7 Conclusions -- References -- CHAPTER 12 Effect of a Cusp-Shaped Magnetic Field on the Melt Convection of Czochralski Crystal Growth [1, 2, 26] -- 12.1 Introduction -- 12.2 Numerical Analysis -- 12.3 Results and Discussion -- 12.4 Conclusion -- References -- CHAPTER 13 Effect of a Rotating Magnetic Field on the Melt Convection of Czochralski Crystal Growth [1] -- 13.1 Introduction -- 13.2 Model System -- 13.3 Computational Schemes -- 13.4 Computed Results -- 13.5 Conclusions -- References -- CHAPTER 14 Continuous Steel-Casting Systems with Various Magnetic Fields [10] -- 14.1 Introduction -- 14.2 Model Systems -- 14.3 Computed Results -- 14.4 Conclusions -- References.

CHAPTER 15 Convection Induced by a Cusp-Shaped Magnetic Field for Air in a Cube Heated from Above and Cooled from Below [1] -- 15.1 Introduction -- 15.2 Derivation of Magnetizing Force Model for Paramagnetic Gas -- 15.3 Computed Results -- 15.4 Experimental Flow Visualization -- 15.5 Conclusions -- References -- CHAPTER 16 Rayleigh-Benard Convection of Air in a Magnetic Field [1] -- 16.1 Introduction -- 16.2 Experiments -- 16.3 Numerical Analyses -- 16.4 Discussion -- 16.5 Conclusion -- References -- CHAPTER 17 Effects of Various Parameters on the Convection of Air in a Cubic Enclosure Under a Magnetic Field -- 17.1 Effect of the Direction of the Magnetic Field [1] -- 17.2 Effect of y and Ra [4] -- 17.3 Effect of the Number of Coils [5] -- References -- CHAPTER 18 Transient Characteristics of Convection and Diffusion of Oxygen Gas in an Open Vertical Cylinder Under Magnetizing Forces [1] -- 18.1 Experiments -- 18.2 Derivation of Model Equation -- 18.3 Computed Result -- 18.4 Conclusion -- References -- CHAPTER 19 Rayleigh-Benard Convection of Diamagnetic Fluid [19] -- 19.1 Introduction -- 19.2 Derivation of Model Equation -- 19.3 Model Systems and Computed Result -- 19.4 Discussion -- 19.5 Conclusion -- References -- CHAPTER 20 Magnetothermal Wind Tunnel [1] -- 20.1 Introduction -- 20.2 Numerical Methods -- 20.3 Results and Discussion -- 20.4 Conclusions -- References -- Appendix: How to compute a radial velocity component at a radial center -- Reference -- Nomenclature -- Greek letters -- Subscripts -- Acknowledgements -- Index -- About the author.