Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer

ISBN-13: 9783642541766 / Angielski / Miękka / 2014 / 190 str.

Kuppalapalle Vajravelu; Robert A. Van Gorder

Opis

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 nonlinearity. Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer presents the current theoretical developments of the analytical method of homotopy analysis. This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis method. The particular focus lies on fluid flow problems governed by nonlinear differential equations. This book is intended for researchers in applied mathematics, physics, mechanics and engineering.Both Kuppalapalle Vajravelu and Robert A. Van Gorder work at the University of Central Florida, USA."

Recenzje

From the reviews:

"This book has many facets: the Homotopy Analysis Method (HAM) is applied to various fluid flow problems, but it also includes some theory, useful mini-summaries of previous research, nice physical interpretations, lots of graphs, and much hyperbole. ... The book gives a readable introduction. ... In summary, this book is a useful basic introduction to the Homotopy Analysis Method, especially for those with a fluid mechanics background." (Anthony John Roberts, Mathematical Reviews, March, 2014)

"The book is devoted to the presentation of the homotopy analysis method (HAM) applied to the resolution of nonlinear differential equations. ... The book will be useful for researchers or engineers which are faced to the resolution of nonlinear differential equations. Besides the presentation of the HAM, the description of the application of this powerful method to the many examples contained in the book will help them when they will try to apply this tool to their own problems." (Alain Brillard, zbMATH, Vol. 1277, 2014)

Spis treści

Part I: Theoretical Considerations.- Principles of the Homotopy Analysis Method.- Methods for the Control of Convergence in Obtained Solutions.- Additional Techniques. Part II: Applications to Physical Problems.- Application of the Homotopy Analysis Method to Fluid Flow Problems.- Application of the Homotopy Analysis Method to Heat Transfer Problems.- Application of the Homotopy Analysis Method to More Advanced Problems.