Variational Analysis and Approximate Solutions for Transport Phenomena PDF Download
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Author: George A. Keramidas
Publisher:
ISBN:
Category :
Languages : en
Pages : 83
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Book Description
Certain concepts of classical mechanics are utilized to derive the variational formulation for a field partial differential equation. By introducing suitable parameters, it is demonstrated that the concepts of virtual work and generalized coordinates can be extended to the general transport equation and this equation can be translated into Lagrange's equations of mechanics. The system of equations may represent a large number of physical processes and it is not restricted by any means to a particular problem. The Lagrangian system of equations is most suitable for deriving approximate solutions and this is demonstrated by assuming a linear series expansion in terms of the generalized coordinates. Furthermore, it is shown that approximate methods, such as the finite element method, can be directly derived as a special application of the generalized approach. Examples of approximate solutions are given for some typical problems encountered in transport processes. (Author).
Author: George A. Keramidas
Publisher:
ISBN:
Category :
Languages : en
Pages : 83
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Book Description
Certain concepts of classical mechanics are utilized to derive the variational formulation for a field partial differential equation. By introducing suitable parameters, it is demonstrated that the concepts of virtual work and generalized coordinates can be extended to the general transport equation and this equation can be translated into Lagrange's equations of mechanics. The system of equations may represent a large number of physical processes and it is not restricted by any means to a particular problem. The Lagrangian system of equations is most suitable for deriving approximate solutions and this is demonstrated by assuming a linear series expansion in terms of the generalized coordinates. Furthermore, it is shown that approximate methods, such as the finite element method, can be directly derived as a special application of the generalized approach. Examples of approximate solutions are given for some typical problems encountered in transport processes. (Author).
Author: Marcio L. de Souza-Santos
Publisher: CRC Press
ISBN: 1420016539
Category : Mathematics
Languages : en
Pages : 592
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Book Description
On the job or in the field, when facing a problem with differential equations and boundary conditions, most likely you don't have time to read through several publications in search of a method that may or may not solve your problem. Organized for quick and easy access to practical solutions, Analytical and Approximate Methods in Transport Pheno
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1126
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Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author: B. D. Vujanovic
Publisher: Academic Press
ISBN: 0080926428
Category : Mathematics
Languages : en
Pages : 383
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Book Description
This book provides a comprehensive survey of analytic and approximate solutions of problems of applied mechanics, with particular emphasis on nonconservative phenomena. Include
Author: C. A. Brebbia
Publisher: Springer Science & Business Media
ISBN: 3662063751
Category : Technology & Engineering
Languages : en
Pages : 638
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Book Description
Author: Richard C. Farmer
Publisher: CRC Press
ISBN: 1439882053
Category : Science
Languages : en
Pages : 530
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Book Description
Although computer technology has dramatically improved the analysis of complex transport phenomena, the methodology has yet to be effectively integrated into engineering curricula. The huge volume of literature associated with the wide variety of transport processes cannot be appreciated or mastered without using innovative tools to allow comprehen
Author: P. A. Ramachandran
Publisher: Cambridge University Press
ISBN: 1139991566
Category : Technology & Engineering
Languages : en
Pages : 805
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Book Description
An integrated, modern approach to transport phenomena for graduate students, featuring traditional and contemporary examples to demonstrate the diverse practical applications of the theory. Written in an easy to follow style, the basic principles of transport phenomena, and model building are recapped in Chapters 1 and 2 before progressing logically through more advanced topics including physicochemical principles behind transport models. Treatments of numerical, analytical, and computational solutions are presented side by side, often with sample code in MATLAB, to aid students' understanding and develop their confidence in using computational skills to solve real-world problems. Learning objectives and mathematical prerequisites at the beginning of chapters orient students to what is required in the chapter, and summaries and over 400 end-of-chapter problems help them retain the key points and check their understanding. Online supplementary material including solutions to problems for instructors, supplementary reading material, sample computer codes, and case studies complete the package.
Author: Estéban Saatdjian
Publisher: John Wiley & Sons
ISBN:
Category : Science
Languages : en
Pages : 440
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Book Description
This invaluable text, provides a much-needed overview of both the theoretical development, as well as appropriate numerical solutions, for all aspects of transport phenomena. It contains a basic introduction to many aspects of fluid mechanics, heat transfer and mass transfer, and the conservation equations for mass, energy and momentum are discussed with reference to engineering applications. Heat transfer by conduction, radiation, natural and forced convection is studied, as well as mass transfer and incompressible fluid mechanics. The second part of the book deals with numerical methods used to solve the problems encountered earlier. The basic concepts of finite difference and finite volume methods are presented. Other subjects usually covered in mathematical textbooks such as vector and tensor analysis, Laplace transforms, and Runge-Kutta methods are discussed in the Appendices. * Offers comprehensive coverage of both transport phenomena and numerical and analytical solutions to the problems. * Includes comprehensive coverage of numerical techniques. * Provides real-life problems and solutions, which are vital to the understanding and implementation of applications. This work will be welcomed not only by senior and graduate students in mechanical, aeronautical and chemical engineering, but also for engineers practising in these fields.
Author: Bruce A. Finlayson
Publisher: SIAM
ISBN: 1611973236
Category : Mathematics
Languages : en
Pages : 429
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Book Description
This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.
Author: Hans Petter Langtangen
Publisher: Springer Nature
ISBN: 3030237885
Category : Mathematics
Languages : en
Pages : 395
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Book Description
This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
