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The manufacture of silicon single crystals is one of the most important processes in the information technology industry. This book explains the details of liquid metal convection, providing a guide for the elegant operation and control of Czochralski crystal growth, including the effect of magnetic control. Also covered is the newly emerging research field of the application of strong magnetic field using a superconducting magnet. Model equations for the phenomena in the magnetic field are treated in detail, which will be of much use to researchers and engineers in the field. The coverage includes the effect of the Lorentz force in materials processing and the magnetic force of recently developed superconducting magnets. It examines heat, mass and momentum transfer in electro-conducting and non-conducting fluids under normal and very strong magnetic fields. The book also treats the Czochralski single crystal growth process and continuous steel casting process as the most important current applications of magnetic fields. Numerical approaches are compared with the corresponding experimental measurements.
Leading experts present the current state of knowledge of the subject of magnetoconvection from the viewpoint of applied mathematics.
This book presents a theoretical analysis of several problems in thermal and solutal convections in magneto-hydrodynamic (MHD) flows. It provides a systemic discussion on the development of fluid dynamics, continuum hypothesis, Newton’s law of viscosity, heat transfer, mass transfer, thermal diffusion, diffusion-thermo-MHD, gray and non-gray gases, Fourier’s law of conduction, and Fick’s law of diffusion in such a way that readers with little knowledge in physics will find it easier to understand the contents. Some physical principles, such as those governing fluid motion, fluid temperature, and fluid concentration, are presented in vector form, allowing the corresponding form to be derived in any orthogonal curvilinear coordinate system. Laplace transform technique in closed form is used to obtain exact solutions to unsteady one-dimensional flow problems, an implicit finite difference method of Crank–Nicholson type is used to solve unsteady two-dimensional flow problems, and an asymptotic series expansion method is used to solve the governing equations of the steady three-dimensional flow problem analytically. Flow and transport phenomena are thoroughly treated in each chapter separately. This book emphasizes the influence of an induced magnetic field. The outcomes of the works are graphically depicted so that readers can gain a tangible understanding of the problems. It also includes a list of inverse Laplace transforms (ILTs) for several specific functions, some of which are not found in the existing literature. The ILTs of special functions are given in brief form and can further be utilized as standard formulae in finding those as special cases. Some new special functions are introduced in the book, along with appropriate definitions. As a result, the formulations for velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number have been appeared in brief and convenient forms that are uncommon in other literature. This book addresses numerous areas of contemporary magneto-fluid dynamics research that have major implications in engineering. It is primarily intended for researchers working in the field of heat and mass transfer in hydromagnetic flows.
Solar and stellar photospheres constitute the layers most accessible to observations, forming the interface between the interior and the outside of the stars. The solar atmosphere is a rich physics laboratory, in which the whole spectrum of radiative, dynamical, and magnetic processes that tranfer energy into space can be observed. As the fundamental processes take place on very small spatial scales, we need high· resolution observations to explore them. On the other hand the small-scale processes act together to form global properties of the sun, which have their origins in the solar interior. The rapid advances in observational techniques and theoreticallllodelling over the past decade made it very timely to bring together scientists from east and west to the first lAU Symposium on this topic. The physics of the photosphere involves complicated interactions between magnetic fields, convection, waves, and radiation. During the past decade our understanding of these gener ally small-scale structures and processes has been dramatically advanced. New instrumen tations, on ground and in space, have given us new means to study the granular convection. Diagnostic methods in Stokes polarimetry have allowed us to go beyond the limitations of spatial resolution to explore the structure and dynamics of the subarcsec magnetic struc tures. Extensive numerical simulations of the interaction between convection and magnetic fields using powerful supercomputers are providing deepened physical insight. Granulation, magnetic fields, and dynamo processes are being explored in the photospheres of other stars, guided by our improved understanding of the solar photosphere.
This book covers the experimental and theoretical study of convection in non-isothermal ferro-nanofluids (FNFs). Since FNFs are not transparent and magnetic fields are very sensitive to the shape of the boundary between magnetic and nonmagnetic media, special flow visualization techniques based on the use of thermo-sensitive liquid crystal films, infrared cameras, as well as local and integral temperature sensors are discussed in the book. This book considers several major configurations of convective chambers and the applied magnetic field. For each of them, the stability boundaries are determined theoretically and experimentally. The physical types of dominant instabilities and the characteristics of their interactions are subsequently established using linear and weakly non-linear hydrodynamic stability analyses and elements of bifurcation theory. The book also discusses the potential of using magnetically controlled ferro-nanofluids as a heat carrier in situations where heat removal by natural convection is not possible due to the lack of gravity (orbital stations) or extreme confinement (microelectronics). Researchers and practitioners working in the areas of fluid mechanics, hydrodynamic stability, and heat and mass transfer will benefit from this book.
Thermal Convection - Patterns, Stages of Evolution and Stability Behavior provides the reader with an ensemble picture of the subject, illustrating the state-of-the-art and providing the researchers from universities and industry with a basis on which they are able to estimate the possible impact of a variety of parameters. Unlike earlier books on the subject, the heavy mathematical background underlying and governing the behaviors illustrated in the text are kept to a minimum. The text clarifies some still unresolved controversies pertaining to the physical nature of the dominating driving force responsible for asymmetric/oscillatory convection in various natural phenomena and/or technologically important processes and can help researchers in elaborating and validating new, more complex models, in accelerating the current trend towards predictable and reproducible natural phenomena and in establishing an adequate scientific foundation to industrial processes. Thermal Convection - Patterns, Stages of Evolution and Stability Behavior is intended as a useful reference guide for specialists in disciplines such as the metallurgy and foundry field and researchers and scientists who are now coordinating their efforts to improve the quality of semiconductor or macromolecular crystals. The text may also be of use to organic chemists and materials scientists, atmosphere and planetary physicists, as well as an advanced level text for students taking part in courses on the physics of fluids, fluid mechanics, the behavior and evolution of non-linear systems, environmental phenomena and materials engineering.
This new edition includes nearly 1000 new references.
The convection and conduction heat transfer, thermal conductivity, and phase transformations are significant issues in a design of wide range of industrial processes and devices. This book includes 18 advanced and revised contributions, and it covers mainly (1) heat convection, (2) heat conduction, and (3) heat transfer analysis. The first section introduces mixed convection studies on inclined channels, double diffusive coupling, and on lid driven trapezoidal cavity, forced natural convection through a roof, convection on non-isothermal jet oscillations, unsteady pulsed flow, and hydromagnetic flow with thermal radiation. The second section covers heat conduction in capillary porous bodies and in structures made of functionally graded materials, integral transforms for heat conduction problems, non-linear radiative-conductive heat transfer, thermal conductivity of gas diffusion layers and multi-component natural systems, thermal behavior of the ink, primer and paint, heating in biothermal systems, and RBF finite difference approach in heat conduction. The third section includes heat transfer analysis of reinforced concrete beam, modeling of heat transfer and phase transformations, boundary conditions-surface heat flux and temperature, simulation of phase change materials, and finite element methods of factorial design. The advanced idea and information described here will be fruitful for the readers to find a sustainable solution in an industrialized society.
Comprehensive and up-to-date synthesis of all aspects of mantle convection, for advanced students and researchers.
This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves, and magnetic field generation in the interiors and atmospheres of rotating planets and stars. Using a teaching method perfected in the classroom, Gary Glatzmaier begins by offering a step-by-step guide on how to design codes for simulating nonlinear time-dependent thermal convection in a two-dimensional box using Fourier expansions in the horizontal direction and finite differences in the vertical direction. He then describes how to implement more efficient and accurate numerical methods and more realistic geometries in two and three dimensions. In the third part of the book, Glatzmaier demonstrates how to incorporate more sophisticated physics, including the effects of magnetic field, density stratification, and rotation. Featuring numerous exercises throughout, this is an ideal textbook for students and an essential resource for researchers. Describes how to create codes that simulate the internal dynamics of planets and stars Builds on basic concepts and simple methods Shows how to improve the efficiency and accuracy of the numerical methods Describes more relevant geometries and boundary conditions Demonstrates how to incorporate more sophisticated physics