Numerical And Analytical Solutions For Solving Nonlinear Equations In Heat Transfer

Download or read book Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer written by Ganji, Davood Domiri and published by IGI Global. This book was released on 2017-07-26 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer written by Davood Domiri Ganji and published by Engineering Science Reference. This book was released on 2017-07-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Analytical Solution Methods for Boundary Value Problems written by A.S. Yakimov and published by Academic Press. This book was released on 2016-08-13 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Nonlinear Systems in Heat Transfer written by Davood Domairry Ganji and published by Elsevier. This book was released on 2017-09-15 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes written by Kuppalapalle Vajravelu and published by Academic Press. This book was released on 2015-09-08 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book The Optimal Homotopy Asymptotic Method written by Vasile Marinca and published by Springer. This book was released on 2015-04-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Advanced Numerical and Semi-Analytical Methods for Differential Equations written by Snehashish Chakraverty and published by John Wiley & Sons. This book was released on 2019-04-10 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.