Advances In The Homotopy Analysis Method

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Advances in the Homotopy Analysis Method

Shijun Liao
Advances in the Homotopy Analysis Method Book PDF

Author : Shijun Liao
Publisher : World Scientific
Page : 428 pages
File Size : 44,6 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9789814551267

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Advances in the Homotopy Analysis Method by Shijun Liao Pdf

Unlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness differentiates the HAM from all other analytic approximation methods. In addition, the HAM can be applied to solve some challenging problems with high nonlinearity. This book, edited by the pioneer and founder of the HAM, describes the current advances of this powerful analytic approximation method for highly nonlinear problems. Coming from different countries and fields of research, the authors of each chapter are top experts in the HAM and its applications. Contents:Chance and Challenge: A Brief Review of Homotopy Analysis Method (S-J Liao)Predictor Homotopy Analysis Method (PHAM) (S Abbasbandy and E Shivanian)Spectral Homotopy Analysis Method for Nonlinear Boundary Value Problems (S Motsa and P Sibanda)Stability of Auxiliary Linear Operator and Convergence-Control Parameter (R A Van Gorder)A Convergence Condition of the Homotopy Analysis Method (M Turkyilmazoglu)Homotopy Analysis Method for Some Boundary Layer Flows of Nanofluids (T Hayat and M Mustafa)Homotopy Analysis Method for Fractional Swift–Hohenberg Equation (S Das and K Vishal)HAM-Based Package NOPH for Periodic Oscillations of Nonlinear Dynamic Systems (Y-P Liu)HAM-Based Mathematica Package BVPh 2.0 for Nonlinear Boundary Value Problems (Y-L Zhao and S-J Liao) Readership: Graduate students and researchers in applied mathematics, physics, nonlinear mechanics, engineering and finance. Keywords:Analytic Approxiamtion Method;Nonlinear;Homotopy;Applied MathematicsKey Features:The method described in the book can overcome almost all restrictions of other analytic approximation method for nonlinear problemsThis book is the first in homotopy analysis method, covering the newest advances, contributed by many top experts in different fields

Homotopy Analysis Method in Nonlinear Differential Equations

Shijun Liao
Homotopy Analysis Method in Nonlinear Differential Equations Book PDF

Author : Shijun Liao
Publisher : Springer Science & Business Media
Page : 566 pages
File Size : 50,9 Mb
Release : 2012-06-22
Category : Mathematics
ISBN : 9783642251320

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Homotopy Analysis Method in Nonlinear Differential Equations by Shijun Liao Pdf

"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.

Advanced Numerical and Semi-Analytical Methods for Differential Equations

Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Advanced Numerical and Semi Analytical Methods for Differential Equations Book PDF

Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 55,9 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9781119423447

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Advanced Numerical and Semi-Analytical Methods for Differential Equations by Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao Pdf

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

Beyond Perturbation

Shijun Liao
Beyond Perturbation Book PDF

Author : Shijun Liao
Publisher : CRC Press
Page : 335 pages
File Size : 45,7 Mb
Release : 2003-10-27
Category : Mathematics
ISBN : 9781135438296

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Beyond Perturbation by Shijun Liao Pdf

Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.

The Optimal Homotopy Asymptotic Method

Vasile Marinca,Nicolae Herisanu
The Optimal Homotopy Asymptotic Method Book PDF

Author : Vasile Marinca,Nicolae Herisanu
Publisher : Springer
Page : 476 pages
File Size : 41,8 Mb
Release : 2015-04-02
Category : Technology & Engineering
ISBN : 9783319153742

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The Optimal Homotopy Asymptotic Method by Vasile Marinca,Nicolae Herisanu Pdf

This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.

Advanced Numerical and Semi-Analytical Methods for Differential Equations

Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Advanced Numerical and Semi Analytical Methods for Differential Equations Book PDF

Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 47,5 Mb
Release : 2019-04-16
Category : Mathematics
ISBN : 9781119423423

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Advanced Numerical and Semi-Analytical Methods for Differential Equations by Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao Pdf

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

Homotopy-Based Methods in Water Engineering

Manotosh Kumbhakar,Vijay P. Singh
Homotopy Based Methods in Water Engineering Book PDF

Author : Manotosh Kumbhakar,Vijay P. Singh
Publisher : CRC Press
Page : 471 pages
File Size : 47,8 Mb
Release : 2023-07-20
Category : Technology & Engineering
ISBN : 9781000893359

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Homotopy-Based Methods in Water Engineering by Manotosh Kumbhakar,Vijay P. Singh Pdf

Most complex physical phenomena can be described by nonlinear equations, specifically, differential equations. In water engineering, nonlinear differential equations play a vital role in modeling physical processes. Analytical solutions to strong nonlinear problems are not easily tractable, and existing techniques are problem-specific and applicable for specific types of equations. Exploring the concept of homotopy from topology, different kinds of homotopy-based methods have been proposed for analytically solving nonlinear differential equations, given by approximate series solutions. Homotopy-Based Methods in Water Engineering attempts to present the wide applicability of these methods to water engineering problems. It solves all kinds of nonlinear equations, namely algebraic/transcendental equations, ordinary differential equations (ODEs), systems of ODEs, partial differential equations (PDEs), systems of PDEs, and integro-differential equations using the homotopy-based methods. The content of the book deals with some selected problems of hydraulics of open-channel flow (with or without sediment transport), groundwater hydrology, surface-water hydrology, general Burger’s equation, and water quality. Features: Provides analytical treatments to some key problems in water engineering Describes the applicability of homotopy-based methods for solving nonlinear equations, particularly differential equations Compares different approaches in dealing with issues of nonlinearity

Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer

Ganji, Davood Domiri,Talarposhti, Roghayeh Abbasi
Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer Book PDF

Author : Ganji, Davood Domiri,Talarposhti, Roghayeh Abbasi
Publisher : IGI Global
Page : 275 pages
File Size : 40,9 Mb
Release : 2017-07-26
Category : Technology & Engineering
ISBN : 9781522527145

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Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer by Ganji, Davood Domiri,Talarposhti, Roghayeh Abbasi Pdf

Engineering applications offer benefits and opportunities across a range of different industries and fields. By developing effective methods of analysis, results and solutions are produced with higher accuracy. Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer is an innovative source of academic research on the optimized techniques for analyzing heat transfer equations and the application of these methods across various fields. Highlighting pertinent topics such as the differential transformation method, industrial applications, and the homotopy perturbation method, this book is ideally designed for engineers, researchers, graduate students, professionals, and academics interested in applying new mathematical techniques in engineering sciences.

Computational Mathematics, Nanoelectronics, and Astrophysics

Shaibal Mukherjee,Abhirup Datta,Santanu Manna,Swadesh Kumar Sahoo
Computational Mathematics Nanoelectronics and Astrophysics Book PDF

Author : Shaibal Mukherjee,Abhirup Datta,Santanu Manna,Swadesh Kumar Sahoo
Publisher : Springer Nature
Page : 209 pages
File Size : 45,7 Mb
Release : 2021-03-23
Category : Mathematics
ISBN : 9789811597084

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Computational Mathematics, Nanoelectronics, and Astrophysics by Shaibal Mukherjee,Abhirup Datta,Santanu Manna,Swadesh Kumar Sahoo Pdf

This book is a collection of original papers presented at the International Conference on Computational Mathematics in Nanoelectronics and Astrophysics (CMNA 2018) held at the Indian Institute of Technology Indore, India, from 1 to 3 November 2018. It aims at presenting recent developments of computational mathematics in nanoelectronics, astrophysics and related areas of space sciences and engineering. These proceedings discuss the most advanced innovations, trends and real-world challenges encountered and their solutions with the application of computational mathematics in nanoelectronics, astrophysics and space sciences. From focusing on nano-enhanced smart technological developments to the research contributions of premier institutes in India and abroad on ISRO’s future space explorations—this book includes topics from highly interdisciplinary areas of research. The book is of interest to researchers, students and practising engineers working in diverse areas of science and engineering, ranging from applied and computational mathematics to nanoelectronics, nanofabrications and astrophysics.

Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy

Manoj Sahni,José M. Merigó,Walayat Hussain,Ernesto León-Castro,Raj Kumar Verma,Ritu Sahni
Mathematical Modeling Computational Intelligence Techniques and Renewable Energy Book PDF

Author : Manoj Sahni,José M. Merigó,Walayat Hussain,Ernesto León-Castro,Raj Kumar Verma,Ritu Sahni
Publisher : Springer Nature
Page : 474 pages
File Size : 40,5 Mb
Release : 2023-05-08
Category : Technology & Engineering
ISBN : 9789811999062

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Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy by Manoj Sahni,José M. Merigó,Walayat Hussain,Ernesto León-Castro,Raj Kumar Verma,Ritu Sahni Pdf

The book is a collection of best selected research papers presented at the Third International Conference on “Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy (MMCITRE 2022),” organized by the University of Technology Sydney, Australia, in association with the Department of Mathematics, Pandit Deendayal Energy University, India, and Forum for Interdisciplinary Mathematics. This book presents new knowledge and recent developments in all aspects of computational techniques, mathematical modeling, energy systems, applications of fuzzy sets and intelligent computing. The book provides innovative works of researchers, academicians and students in the area of interdisciplinary mathematics, statistics, computational intelligence and renewable energy.

Homotopy Methods and Global Convergence

B. Curtis Eaves
Homotopy Methods and Global Convergence Book PDF

Author : B. Curtis Eaves
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461335726

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Homotopy Methods and Global Convergence by B. Curtis Eaves Pdf

This Proceedings presents refereed versions of most of the papers presented at the NATO Advanced Research Institute on Homotopy Methods and Global Convergence held in Porto Cervo, Sardinia, June 3-6, 1981. This represents the fourth recent occurrence of an international conference addressing the common theme of fixed point computation. The first such conference, ti tled "Computing Fixed Points with Applications," was held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina, June 26-28, 1974 and was sponsored by the Office of Naval Research and the Office of the Army Research Center. The second conference, "Symposium on Analysis and Computation of Fixed Points," was held at the University of Wisconsin, Madison, May 7-8, 1979, under the sponsorship of the National Science Foundation, the U. S. Army, and the Mathematics Research Center of the University of Wisconsin, Madison. The third conference, titled "Symposium on Fixed Point Algorithms and Complementarity," was held at the University of Southampton, Southampton, UK, July 3-5, 1979 and was sponsored by U. N. E. S. C. O. , European Research Office (London), Department of Mathematics (University of Southampton), I. B. M. U. K. , Ltd. , Lloyds Bank, Ltd. , and the Office of Naval Research (London). The Advanced Research Institute held in Sardinia was devoted to the theory and application of modern homotopy methods. The following topics were stressed: Path-Following Techniques; Bottom-Line Applications; Global vs. Classical Methods; and Sta- v vi PREFACE of-the-Art, Perspectives and Potential.

Advanced Numerical Methods for Differential Equations

Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
Advanced Numerical Methods for Differential Equations Book PDF

Author : Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
Publisher : CRC Press
Page : 336 pages
File Size : 54,9 Mb
Release : 2021-07-29
Category : Mathematics
ISBN : 9781000381085

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Advanced Numerical Methods for Differential Equations by Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar Pdf

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Advances in Mechatronics and Control Engineering

Yun Hae Kim,Prasad Yarlagadda
Advances in Mechatronics and Control Engineering Book PDF

Author : Yun Hae Kim,Prasad Yarlagadda
Publisher : Trans Tech Publications Ltd
Page : 2500 pages
File Size : 49,8 Mb
Release : 2013-01-11
Category : Technology & Engineering
ISBN : 9783038139768

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Advances in Mechatronics and Control Engineering by Yun Hae Kim,Prasad Yarlagadda Pdf

Mechatronics is the synergistic combination of precision mechanical engineering, electronic control and systems thinking in the design of products and manufacturing processes. It relates to the design of systems, devices and products aimed at achieving an optimal balance between basic mechanical structure and its overall control. Volume is indexed by Thomson Reuters CPCI-S (WoS). The peer reviewed papers are grouped as follows: Chapter 1: Engineering Design of Machines and Equipment for Manufacturing; Chapter 2: Materials and Processing Technologies; Chapter 3: Robotics and its Motor System; Chapter 4: Sensors, Measurement, Monitoring and Detection; Chapter 5: Electronics and Microelectronics; Chapter 6: Data Acquisition and Data Processing, Computational Techniques; Chapter 7: Control and Automation, Theory and Applications; Chapter 8: Software, Communication and Computer Applications in Industry and Engineering; Chapter 9: Engineering Education, Engineering Management, Products Design and Manufacture Management; Chapter 10: Other Related Topics.

Advanced Computing in Industrial Mathematics

Krassimir Georgiev,Michail Todorov,Ivan Georgiev
Advanced Computing in Industrial Mathematics Book PDF

Author : Krassimir Georgiev,Michail Todorov,Ivan Georgiev
Publisher : Springer
Page : 446 pages
File Size : 40,9 Mb
Release : 2018-09-27
Category : Technology & Engineering
ISBN : 9783319972770

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Advanced Computing in Industrial Mathematics by Krassimir Georgiev,Michail Todorov,Ivan Georgiev Pdf

This book gathers the peer-reviewed proceedings of the 12th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM’17, held in Sofia, Bulgaria, in December 2017. The general theme of BGSIAM’17 was industrial and applied mathematics, with a particular focus on: high-performance computing, numerical methods and algorithms, analysis of partial differential equations and their applications, mathematical biology, control and uncertain systems, stochastic models, molecular dynamics, neural networks, genetic algorithms, metaheuristics for optimization problems, generalized nets, and Big Data.

Advanced Topics in Mass Transfer

Mohamed El-Amin
Advanced Topics in Mass Transfer Book PDF

Author : Mohamed El-Amin
Publisher : BoD – Books on Demand
Page : 642 pages
File Size : 50,8 Mb
Release : 2011-02-21
Category : Science
ISBN : 9789533073330

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Advanced Topics in Mass Transfer by Mohamed El-Amin Pdf

This book introduces a number of selected advanced topics in mass transfer phenomenon and covers its theoretical, numerical, modeling and experimental aspects. The 26 chapters of this book are divided into five parts. The first is devoted to the study of some problems of mass transfer in microchannels, turbulence, waves and plasma, while chapters regarding mass transfer with hydro-, magnetohydro- and electro- dynamics are collected in the second part. The third part deals with mass transfer in food, such as rice, cheese, fruits and vegetables, and the fourth focuses on mass transfer in some large-scale applications such as geomorphologic studies. The last part introduces several issues of combined heat and mass transfer phenomena. The book can be considered as a rich reference for researchers and engineers working in the field of mass transfer and its related topics.