Perspectives in Magnetohydrodynamics Research (Earth Sciences in the 21st Century: Space Science, Exploration and Policies)

This book presents and discusses current research in the study of magnetohydrodynamics. Topics discussed include MHD free convection in a porous medium bounded by a vertical wavy wall and a parallel flat wall; the immersed boundary method; transient hydromagnetic natural convection between two vertical walls heated/cooled asymmetrically; the effect of suction/injection on MHD flat plate thermometer and flute and ballooning modes in the inner magnetosphere of the earth PERSPECTIVES IN MAGNETOHYDRODYNAMICS RESEARCH......Page 2 PERSPECTIVES IN MAGNETOHYDRODYNAMICS RESEARCH......Page 4 Contents......Page 6 Preface......Page 8 Abstract......Page 12 1. Introduction......Page 13 2. Mathematical Analysis......Page 15 2.b. Solution Procedure for Perturbed Part......Page 18 3. Skin Friction and Nusselt Number at the Walls......Page 20 4. Results and Discussion......Page 21 4.a. Presentation of First Order Solution......Page 28 Nomenclature......Page 34 Subscript......Page 35 Appendix......Page 36 References......Page 39 Immersed Boundary Method: The Existence of Approximate Solution in Two-Dimensional Case......Page 42 Abstract......Page 68 1. Introduction......Page 69 2. Mathematical Formulation......Page 70 Steady State Solution......Page 75 Results and Discussion......Page 76 Conclusion......Page 82 Greek Symbols......Page 83 References......Page 84 Abstract......Page 86 Introduction......Page 87 Problem Formulation......Page 88 Results and Discussion......Page 90 Conclusion......Page 94 Subscripts......Page 95 References......Page 96 Abstract......Page 98 Introduction......Page 99 1. Main Equations......Page 102 1.1. Initial Equations......Page 103 1.2. Magnetic Label......Page 105 1.3. Equations of Small Oscillations......Page 106 1.4. Ballooning Approximation......Page 108 2. Dipole Model of the Geomagnetic Field......Page 113 2.1. Magnetic Field......Page 114 2.2. Equilibrium......Page 116 2.3. Equations of Small Oscillations in Dipole Geometry......Page 119 2.4. Polarization of Ballooning Modes......Page 122 3. Ionospheric Boundary Conditions......Page 124 3.1. Boundary Conditions......Page 125 3.2. Expression for......Page 128 3.3. Derivation of......Page 130 3.4. Boundary Conditions for Ballooning Modes in Dipole Geometry......Page 131 4.1. Energetic Analysis......Page 134 4.2. Boundary Problem for the Stability Threshold......Page 137 4.3. Stability Threshold......Page 140 4.3.1. Flute Perturbations......Page 141 4.3.3. Numerical Analysis......Page 143 4.4. Stability Criterion of Ballooning Modes with Perfectly Conductive Boundary......Page 144 References......Page 146 Index......Page 150