Nonlinear Flow Phenomena and Homotopy Analysis Fluid Flow and Heat T
Since most of the problems arising in science and engineering are nonlinear, they are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems, and often fail when used for problems with strong nonl
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Nonlinear Flow Phenomena and Homotopy Analysis Fluid Flow and Heat Transfer
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Kuppalapalle Vajravelu Robert A. Van Gorder
/POMJOFBS'MPX1IFOPNFOB BOE)PNPUPQZ"OBMZTJT Fluid Flow and Heat Transfer
Kuppalapalle Vajravelu Robert A. Van Gorder
Nonlinear Flow Phenomena and Homotopy Analysis Fluid Flow and Heat Transfer
With 71 figures
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Authors Kuppalapalle Vajravelu Department of Mathematics University of Central Florida Orlando Florida 32816 - 1364, USA E-mail: kvajravelu@cfl.rr.com
Robert A. van Gorder Department of Mathematics University of Central Florida Orlando Florida 32816 - 1364, USA E-mail: [email protected]
ISBN 978-7-04-035449-2 Higher Education Press, Beijing ISBN 978-3-642-32101-6
ISBN 978-3-642-32102-3 (eBook)
Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012943603 c Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publishers’ locations, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publishers can accept any legal responsibility for any errors or omissions that may be made. The publishers make no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword “The essence of mathematics lies entirely in its freedom” by Georg Cantor (1845—1918). Solving nonlinear problems is inherently difficult. Perturbation techniques are mostly used to gain analytic approximations of nonlinear equations. Unfortunately, perturbation methods depend too heavily on small physic
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