Numerical And Analytical Solutions For Solving Nonlinear Equations In Heat Transfer

Author : Ganji, Davood Domiri,Talarposhti, Roghayeh Abbasi
Publisher : IGI Global
Page : 275 pages
File Size : 51,6 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.

Author : Davood Domairry Ganji,Yaser Sabzehmeidani,Amin Sedighiamiri
Publisher : Elsevier
Page : 288 pages
File Size : 54,7 Mb
Release : 2017-09-15
Category : Science
ISBN : 9780128120200

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Nonlinear Systems in Heat Transfer by Davood Domairry Ganji,Yaser Sabzehmeidani,Amin Sedighiamiri Pdf

Nonlinear Heat Transfer: Mathematical Modeling and Analytical Methods addresses recent progress and original research in nonlinear science and its application in the area of heat transfer, with a particular focus on the most important advances and challenging applications. The importance of understanding analytical methods for solving linear and nonlinear constitutive equations is essential in studying engineering problems. This book provides a comprehensive range of (partial) differential equations, applied in the field of heat transfer, tackling a comprehensive range of nonlinear mathematical problems in heat radiation, heat conduction, heat convection, heat diffusion and non-Newtonian fluid systems. Providing various innovative analytical techniques and their practical application in nonlinear engineering problems is the unique point of this book. Drawing a balance between theory and practice, the different chapters of the book focus not only on the broader linear and nonlinear problems, but also applied examples of practical solutions by the outlined methodologies. Demonstrates applied mathematical techniques in the engineering applications, especially in nonlinear phenomena Exhibits a complete understanding of analytical methods and nonlinear differential equations in heat transfer Provides the tools to model and interpret applicable methods in heat transfer processes or systems to solve related complexities

Author : Kuppalapalle Vajravelu,Robert A. Van Gorder
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 51,8 Mb
Release : 2013-07-22
Category : Mathematics
ISBN : 9783642321023

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Nonlinear Flow Phenomena and Homotopy Analysis by Kuppalapalle Vajravelu,Robert A. Van Gorder Pdf

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.

Author : Roland W. Lewis,Kenneth Morgan,B. A. Schrefler
Publisher : Unknown
Page : 580 pages
File Size : 53,6 Mb
Release : 1983-08-24
Category : Mathematics
ISBN : CORNELL:31924004631671

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Numerical Methods in Heat Transfer by Roland W. Lewis,Kenneth Morgan,B. A. Schrefler Pdf

Author : Bernhard Weigand
Publisher : Springer
Page : 310 pages
File Size : 42,7 Mb
Release : 2015-05-05
Category : Technology & Engineering
ISBN : 9783662465936

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Analytical Methods for Heat Transfer and Fluid Flow Problems by Bernhard Weigand Pdf

This book describes useful analytical methods by applying them to real-world problems rather than solving the usual over-simplified classroom problems. The book demonstrates the applicability of analytical methods even for complex problems and guides the reader to a more intuitive understanding of approaches and solutions. Although the solution of Partial Differential Equations by numerical methods is the standard practice in industries, analytical methods are still important for the critical assessment of results derived from advanced computer simulations and the improvement of the underlying numerical techniques. Literature devoted to analytical methods, however, often focuses on theoretical and mathematical aspects and is therefore useless to most engineers. Analytical Methods for Heat Transfer and Fluid Flow Problems addresses engineers and engineering students. The second edition has been updated, the chapters on non-linear problems and on axial heat conduction problems were extended. And worked out examples were included.

Author : Kuppalapalle Vajravelu,Swati Mukhopadhyay
Publisher : Academic Press
Page : 202 pages
File Size : 51,6 Mb
Release : 2015-09-08
Category : Mathematics
ISBN : 9780128037850

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Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes by Kuppalapalle Vajravelu,Swati Mukhopadhyay Pdf

Most of the equations governing the problems related to science and engineering are nonlinear in nature. As a result, they are inherently difficult to solve. Analytical solutions are available only for some special cases. For other cases, one has no easy means but to solve the problem must depend on numerical solutions. Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes: Numerical Solutions presents the current theoretical developments of boundary layer theory, a branch of transport phenomena. Also, the book addresses the theoretical developments in the area and presents a number of physical problems that have been solved by analytical or numerical method. It is focused particularly on fluid flow problems governed by nonlinear differential equations. The book is intended for researchers in applied mathematics, physics, mechanics and engineering. Addresses basic concepts to understand the theoretical framework for the method Provides examples of nonlinear problems that have been solved through the use of numerical method Focuses on fluid flow problems governed by nonlinear equations

Author : A.S. Yakimov
Publisher : Academic Press
Page : 200 pages
File Size : 51,5 Mb
Release : 2016-08-13
Category : Mathematics
ISBN : 9780128043639

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Analytical Solution Methods for Boundary Value Problems by A.S. Yakimov Pdf

Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods. Discusses the theory and analytical methods for many differential equations appropriate for applied and computational mechanics researchers Addresses pertinent boundary problems in mathematical physics achieved without using the theory of series Includes results that can be used to address nonlinear equations in heat conductivity for the solution of conjugate heat transfer problems and the equations of telegraph and nonlinear transport equation Covers select method solutions for applied mathematicians interested in transport equations methods and thermal protection studies Features extensive revisions from the Russian original, with 115+ new pages of new textual content

Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Publisher : John Wiley & Sons
Page : 265 pages
File Size : 41,7 Mb
Release : 2019-04-10
Category : Mathematics
ISBN : 9781119423430

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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.

Author : Jan Taler,Piotr Duda
Publisher : Springer Science & Business Media
Page : 890 pages
File Size : 44,5 Mb
Release : 2010-04-16
Category : Science
ISBN : 9783540334712

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Solving Direct and Inverse Heat Conduction Problems by Jan Taler,Piotr Duda Pdf

This book presents a solution for direct and inverse heat conduction problems, discussing the theoretical basis for the heat transfer process and presenting selected theoretical and numerical problems in the form of exercises with solutions. The book covers one-, two- and three dimensional problems which are solved by using exact and approximate analytical methods and numerical methods. An accompanying CD-Rom includes computational solutions of the examples and extensive FORTRAN code.

Author : M. Necati Özişik,Helcio R. B. Orlande,Marcelo J. Colaço,Renato M. Cotta
Publisher : CRC Press
Page : 580 pages
File Size : 42,9 Mb
Release : 2017-07-20
Category : Science
ISBN : 9781482243468

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Finite Difference Methods in Heat Transfer by M. Necati Özişik,Helcio R. B. Orlande,Marcelo J. Colaço,Renato M. Cotta Pdf

Finite Difference Methods in Heat Transfer, Second Edition focuses on finite difference methods and their application to the solution of heat transfer problems. Such methods are based on the discretization of governing equations, initial and boundary conditions, which then replace a continuous partial differential problem by a system of algebraic equations. Finite difference methods are a versatile tool for scientists and for engineers. This updated book serves university students taking graduate-level coursework in heat transfer, as well as being an important reference for researchers and engineering. Features Provides a self-contained approach in finite difference methods for students and professionals Covers the use of finite difference methods in convective, conductive, and radiative heat transfer Presents numerical solution techniques to elliptic, parabolic, and hyperbolic problems Includes hybrid analytical–numerical approaches

Author : Geeta Arora,Mangey Ram
Publisher : CRC Press
Page : 177 pages
File Size : 52,9 Mb
Release : 2024-01-23
Category : Mathematics
ISBN : 9781003811022

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Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations by Geeta Arora,Mangey Ram Pdf

Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. Models guided by differential equations with intuitive solutions can be used throughout engineering and the sciences. Almost any changing system may be described by a set of differential equations. They may be found just about anywhere you look in fields including physics, engineering, economics, sociology, biology, business, healthcare, etc. The nature of these equations has been investigated by several mathematicians over the course of hundreds of years and, consequently, numerous effective methods for solving them have been created. It is often impractical to find a purely analytical solution to a system described by a differential equation because either the system itself is too complex or the system being described is too vast. Numerical approaches and computer simulations are especially helpful in such systems. The content provided in this book involves real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems. Theories and practical applications in the sciences and engineering are also discussed. Students of engineering and applied mathematics, as well as researchers and engineers who use computers to solve problems numerically or oversee those who do, will find this book focusing on advance numerical techniques to solve linear and nonlinear differential equations useful.

Author : Moghtada Mobedi,Gamze Gediz Ilis
Publisher : Springer Nature
Page : 209 pages
File Size : 52,8 Mb
Release : 2023-07-05
Category : Science
ISBN : 9789819909575

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Fundamentals of Heat Transfer by Moghtada Mobedi,Gamze Gediz Ilis Pdf

This book demonstrates the analytical solution of fundamental problems in heat transfer which covers conduction, convection, and radiation heat transfer. The analytical solution of heat transfer problems is described in a simple way which is easy to understand. This book also provides competence of solving fundamental heat transfer problems by analytical method which is particularly important to gain a strong background on heat transfer. The book is an interdisciplinary heat transfer book which is useful for all academicians and students from different disciplines with different levels of mathematical knowledge. The book can be used as a core or supplementary textbook in undergraduate and graduate bridge courses. Furthermore, it is suitable for professional and vocational coursework for technology and engineering professionals.

Author : C. Y. Wang
Publisher : Springer Nature
Page : 163 pages
File Size : 54,5 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9783031590870

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Essential Analytic Heat Transfer by C. Y. Wang Pdf

Author : Grigoruants
Publisher : CRC Press
Page : 316 pages
File Size : 42,6 Mb
Release : 1994-04-04
Category : Technology & Engineering
ISBN : 0849375347

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Basics of Laser Material Processing by Grigoruants Pdf

The chapters present the problems of stresses and strains induced in metals and nonmetals in the processes of laser heating, analyze the results, offer the ways of laser treatment that dispense with subsequent machining operations, and describe the basic approaches to increase the strength of materials during laser heating. Other topics include the practical methods of implementing the processes of laser welding, cutting, hardening, alloying, and cladding (hardfacing). Basics of Laser Material Processing is designed for scientific workers and for those students in senior- and graduate-level courses.

Author : Je-Chin Han,Lesley M. Wright
Publisher : CRC Press
Page : 595 pages
File Size : 48,6 Mb
Release : 2022-06-24
Category : Science
ISBN : 9781000597295

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Analytical Heat Transfer by Je-Chin Han,Lesley M. Wright Pdf

Analytical Heat Transfer explains how to analyze and solve conduction, convection, and radiation heat transfer problems. It enables students to tackle complex engineering heat transfer problems prevalent in practice. Covering heat transfer in high-speed flows and unsteady highly turbulent flows, the book also discusses enhanced heat transfer in channels, heat transfer in rotating channels, numerical modeling for turbulent flow heat transfer, and thermally developing heat transfer in a circular tube. The second edition features new content on Duhamel’s superposition method, Green’s function method for transient heat conduction, finite-difference method for steady state and transient heat conduction in cylindrical coordinates, and laminar mixed convection. It includes two new chapters on laminar-to-turbulent transitional heat transfer and turbulent flow heat transfer enhancement, in addition to end-of-chapter problems. The book bridges the gap between basic heat transfer undergraduate courses and advanced heat transfer graduate courses for a single semester of intermediate heat transfer, advanced conduction/radiation heat transfer, or convection heat transfer. Features: Focuses on analyzing and solving classic heat transfer problems in conduction, convection, and radiation Covers 2-D and 3-D view factor evaluation, combined radiation with conduction and/or convection, and gas radiation optically thin and optically thick limits Features updated content and new chapters on mass and heat transfer analogy, thermally developing heat transfer in a circular tube, laminar-turbulent transitional heat transfer, unsteady highly turbulent flows, enhanced heat transfer in channels, heat transfer in rotating channels, and numerical modeling for turbulent flow heat transfer Provides step-by-step mathematical formula derivations, analytical solution procedures, and demonstration examples Includes end-of-chapter problems with an accompanying Solutions Manual for instructors This book is ideal for undergraduate and graduate students studying basic heat transfer and advanced heat transfer.