Similarity Analyses of Boundary Value Problems in Engineering
Author: Arthur G. Hansen
Publisher:
Published: 1964
Total Pages: 136
ISBN-13:
DOWNLOAD EBOOKPosts
Introduction to Symmetry Analysis Paperback with CD-ROM
Author: Brian Cantwell
Publisher: Cambridge University Press
Published: 2002-09-23
Total Pages: 660
ISBN-13: 9780521777407
DOWNLOAD EBOOKAn introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.
Group Invariance in Engineering Boundary Value Problems
Author: R. Seshadri
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 232
ISBN-13: 1461251028
DOWNLOAD EBOOKREFEREN CES . 156 9 Transforma.tion of a Boundary Value Problem to an Initial Value Problem . 157 9.0 Introduction . 157 9.1 Blasius Equation in Boundary Layer Flow . 157 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods . 163 9.3 Summary . 168 REFERENCES . . . . . . . . . . . . . . . . . . 168 . 10 From Nonlinear to Linear Differential Equa.tions Using Transformation Groups. . . . . . . . . . . . . . 169 . 10.1 From Nonlinear to Linear Differential Equations . 170 10.2 Application to Ordinary Differential Equations -Bernoulli's Equation . . . . . . . . . . . 173 10.3 Application to Partial Differential Equations -A Nonlinear Chemical Exchange Process . 178 10.4 Limitations of the Inspectional Group Method . 187 10.5 Summary . 188 REFERENCES . . . . 188 11 Miscellaneous Topics . 190 11.1 Reduction of Differential Equations to Algebraic Equations 190 11.2 Reduction of Order of an Ordinary Differential Equation . 191 11.3 Transformat.ion From Ordinary to Partial Differential Equations-Search for First Integrals . . . . . . " 193 . 11.4 Reduction of Number of Variables by Multiparameter Groups of Transformations . . . . . . . . .. . . . 194 11.5 Self-Similar Solutions of the First and Second Kind . . 202 11.6 Normalized Representation and Dimensional Consideration 204 REFERENCES .206 Problems . 208 .220 Index .. Chapter 1 INTRODUCTION AND GENERAL OUTLINE Physical problems in engineering science are often described by dif ferential models either linear or nonlinear. There is also an abundance of transformations of various types that appear in the literature of engineer ing and mathematics that are generally aimed at obtaining some sort of simplification of a differential model.
Computational Methods in Engineering Boundary Value Problems
Author: T.Y. Na
Publisher: Academic Press
Published: 1980-01-18
Total Pages: 321
ISBN-13: 008095653X
DOWNLOAD EBOOKComputational Methods in Engineering Boundary Value Problems
Similarity and Modeling in Science and Engineering
Author: Josef Kuneš
Publisher: Springer Science & Business Media
Published: 2012-04-07
Total Pages: 451
ISBN-13: 1907343776
DOWNLOAD EBOOKThe present text sets itself in relief to other titles on the subject in that it addresses the means and methodologies versus a narrow specific-task oriented approach. Concepts and their developments which evolved to meet the changing needs of applications are addressed. This approach provides the reader with a general tool-box to apply to their specific needs. Two important tools are presented: dimensional analysis and the similarity analysis methods. The fundamental point of view, enabling one to sort all models, is that of information flux between a model and an original expressed by the similarity and abstraction Each chapter includes original examples and applications. In this respect, the models can be divided into several groups. The following models are dealt with separately by chapter; mathematical and physical models, physical analogues, deterministic, stochastic, and cybernetic computer models. The mathematical models are divided into asymptotic and phenomenological models. The phenomenological models, which can also be called experimental, are usually the result of an experiment on an complex object or process. The variable dimensionless quantities contain information about the real state of boundary conditions, parameter (non-linearity) changes, and other factors. With satisfactory measurement accuracy and experimental strategy, such models are highly credible and can be used, for example in control systems.
Similarity Solutions for the Boundary Layer Flow and Heat Transfer of Viscous Fluids, Nanofluids, Porous Media, and Micropolar Fluids
Author: John H. Merkin
Publisher: Academic Press
Published: 2021-09-09
Total Pages: 294
ISBN-13: 0128232056
DOWNLOAD EBOOKSimilarity Solutions for the Boundary Layer Flow and Heat Transfer of Viscous Fluids, Nanofluids, Porous Media, and Micropolar Fluids presents new similarity solutions for fluid mechanics problems, including heat transfer of viscous fluids, boundary layer flow, flow in porous media, and nanofluids due to continuous moving surfaces. After discussing several examples of these problems, similarity solutions are derived and solved using the latest proven methods, including bvp4c from MATLAB, the Keller-box method, singularity methods, and more. Numerical solutions and asymptotic results for limiting cases are also discussed in detail to investigate how flow develops at the leading edge and its end behavior. Detailed discussions of mathematical models for boundary layer flow and heat transfer of micro-polar fluid and hybrid nanofluid will help readers from a range of disciplinary backgrounds in their research. Relevant background theory will also be provided, thus helping readers solidify their computational work with a better understanding of physical phenomena. - Provides mathematical models that address important research themes, such as boundary layer flow and heat transfer of micro-polar fluid and hybrid nanofluid - Gives detailed numerical explanations of all solution procedures, including bvp4c from MATLAB, the Keller-box method, and singularity methods - Includes examples of computer code that will save readers time in their own work
Similarity Methods in Engineering Dynamics
Author: P.S. Westine
Publisher: Elsevier
Published: 2012-12-02
Total Pages: 397
ISBN-13: 0444598138
DOWNLOAD EBOOKHere is the second revised and updated edition of probably the most practical sourcebook on similarity methods and modeling techniques available. Written by leading authorities who incorporate many of the latest advances in the field, this new work maps out techniques for modeling as well as instrumentation and data analysis for an extremely wide array of problems in engineering dynamics. This practical reference uses experimental test data on various engineering problems demonstrating exactly how and why these similarity methods work. The problems involve spread of oil slicks, explosive cratering, car crashes, space vehicle heat exchange, explosive forming, and more. The spectrum of topics covered and number of examples are far greater than in other texts. Of particular importance are the dissimilar material modeling techniques which bring new versatility and freedom to the modeler in structural dynamics. The book also contains a clear, in-depth discussion of the theory underlying modeling and includes alternate methods for developing model laws. The work will undoubtedly prove invaluable to every professional involved in testing or design of dynamic experiments.
Nonlinear Boundary Value Problems in Science and Engineering
Author: C. Rogers
Publisher: Academic Press
Published: 1989-11-14
Total Pages: 433
ISBN-13: 0080958702
DOWNLOAD EBOOKOverall, our object has been to provide an applications-oriented text that is reasonably self-contained. It has been used as the basis for a graduate-level course both at the University of Waterloo and at the Centro Studie Applicazioni in Tecnologie Avante, Bari, Italy. The text is aimed, in the main, at applied mathematicians with a strong interest in physical applications or at engineers working in theoretical mechanics.
Momentum, Heat, and Mass Transfer Fundamentals
Author: Robert Greenkorn
Publisher: CRC Press
Published: 2018-10-03
Total Pages: 1066
ISBN-13: 1351989774
DOWNLOAD EBOOK"Presents the fundamentals of momentum, heat, and mass transfer from both a microscopic and a macroscopic perspective. Features a large number of idealized and real-world examples that we worked out in detail."
Symmetry and Integration Methods for Differential Equations
Author: George Bluman
Publisher: Springer Science & Business Media
Published: 2008-01-10
Total Pages: 425
ISBN-13: 0387216499
DOWNLOAD EBOOKThis text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.
