Dynamical Theory Of Dendritic Growth In Convective Flow (advances In Mechanics And Mathematics)

Convective flow in the liquid phase is always present in a realistic process of freezing and melting and may significantly affect the dynamics and results of the process. The study of the interplay of growth and convection flow during the solidification has been an important subject in the broad fields of materials science, condensed matter physics, fluid physics, micro-gravity science, etc. The present book is concerned with the dynamics of free dendritic growth with convective flow in the melt. It systematically presents the results obtained in terms of a unified asymptotic approach in the framework of the interfacial wave (IFW) theory. In particular, the book explores the effect of the various types of convection flow on the selection and pattern formation of dendritic growth based on the global stability analysis. Content: Front Matter....Pages i-xii Introduction....Pages 1-9 Interfacial Wave Theory of Dendritic Growth from Pure Melt with No Convection....Pages 11-62 Steady Dendritic Growth from Melt with Convective Flow....Pages 63-67 Steady Viscous Flow Past a Paraboloid of Revolution....Pages 69-111 Asymptotic Solution of Dendritic Growth in External Flow (I): The Case of Rapid Growth U ≫ U ∞ ....Pages 113-129 Asymptotic Solution of Dendritic Growth in External Flow (II): The Case of PR → ∞....Pages 131-155 Steady Dendritic Growth with Natural Convection (I): The Case of PR = O(1) and � ≪ 1....Pages 157-176 Steady Dendritic Growth with Natural Convection (II): The Case of PR ≫ 1 and � = O(1)....Pages 177-195 Stability and Selection of Dendritic Growth with Convective Flow....Pages 197-231 Concluding Remark....Pages 233-233 Back Matter....Pages 235-240 Preface 1: Introduction 2: Interfacial Wave Theory of Dendritic Growth with No Convection 3: Steady Dendritic Growth from Melt with Convective Flow 4: Steady Viscous Flow Past a Slender Paraboloid of Revolution 5: Asymptotic Solution of Dendritic Growth in External Flow (I) 6: Asymptotic Solution of Dendritic Growth in External Flow (II) 7: Steady Dendritic Growth with Natural Convection (I) 8: Steady Dendritic Growth with Natural Convection (II) 9: Stability and Selection of Dendritic Growth with Convective Flow 10: Concluding Remark References.