This book unies the common tensor analytical aspects in engineering and physics. Using tensor analysis enables the reader to understand complex physical phenomena from the basic principles in continuum mechanics including the turbulence, its correlations and modeling to the complex Einstein' tensor equation. The development of General Theory of Relativity and the introduction of spacetime geometry would not have been possible without the use of tensor analysis. This textbook is primarily aimed at students of mechanical, electrical, aerospace, civil and other engineering disciplines as well as of theoretical physics. It also covers the special needs of practicing professionals who perform CFD-simulation on a routine basis and would like to know more about the underlying physics of the commercial codes they use. Furthermore, it is suitable for self-study, provided that the reader has a sufficient knowledge of differential and integral calculus. Particular attention was paid to selecting the application examples. The transformation of Cartesian coordinate system into curvilinear one and the subsequent applications to conservation laws of continuum mechanics and the turbulence physics prepares the reader for fully understanding the Einstein tensor equations, which exhibits one of the most complex tensor equation in theoretical physics.
Vectors and Tensors.- Transformation of Tensors.- Differential Operators
in Continuum Mechanics.- Tensors and Kinematics.- Differential Balances in
Continuum Mechanics.- Tensor Operations in Orthogonal Curvilinear.- Tensor
Application, Navier-Stokes Equation.- Curves, Curvature, Surfaces,
Geodesics.- Turbulent Flow, Modeling.- Special Theory of Relativity.- Tensors
In General Theory of Relativity.
Since 1987 Professor of Mechanical Engineering at Texas A\&M University, Meinhard T. Schobeiri received his entire engineering education and degrees from Technical University Darmstadt, Germany where he received the degree of Dr.-Ing. in 1979. From 1979 to 1987, he worked at Swiss Brown Boveri Company, Gas Turbine Division. During this time, he worked as R\&D group leader responsible for aero-thermodynamic design of High Temperature Nuclear Turbine, Compressed Air Energy Gas Turbines and High Efficiency Gas turbines. Dr. Schobeiri is the author of four books, covering turbomachinery aero-thermodynamics and heat transfer design, advanced fluid mechanics and applied fluid mechanics. He is the author of over hundred journal, conference and technical papers. He received the Alexander von Humboldt Prize in 2001, all Research awards at Texas A\&M university, and the Research Recognition Award of NASA Lewis Research Center, where he work for several years as a research faculty.
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