Nonlinear Systems in Heat Transfer

Mathematical Modeling and Analytical Methods

Davood Domairry Ganji,Yaser Sabzehmeidani,Amin Sedighiamiri

• Publisher: Elsevier Science
• Year: 2017
• ISBN:
  9780128120200
• Topic: Physical Sciences
• Subtopic: Energy

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

Chapter 1

Introduction to Nonlinear Systems and Solution Methods

Abstract

Nonlinear differential or partial differential equations are widely employed in a wide range of applied science and engineering fields to model and understand the underlying mechanism of phenomena deeply. Along with the rapid advancement in nonlinear science, an increasing interest among scientists and researchers has emerged to solve the nonlinear problems and to find either the exact or the approximate solutions. Since differential or partial differential equations governing complex real world phenomena consist of different dependent and independent variables and parameters related to the physics of the system, it is preferred to solve those equations analytically as a function of those parameters. Some of the newly developed techniques to approximate the solution of the nonlinear equations are: homotopy perturbation method, variational iteration method, and the Adomian decomposition method. This chapter gives a thorough explan...