Nonlinear Systems in Heat Transfer

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

Engineers and researchers in nonlinear differential equations and analytical methods in nonlinear engineering problems. Design and research engineers, PhD students, and researchers in engineering and applied sciences

Chapter 1: An introduction to analytical methods for solving nonlinear problems

• Perturbation Method (PM)

• Homotopy-Perturbation Method (HPM)

• Variational-Iteration Method (VIM)

• Parameterized Perturbation Method (PPM)

Chapter 2 : Convection in Heat Transfer

• Lumped System

• Boundary Layer Flow

• Unsteady Nonlinear Equations

Chapter 3 : Heat Diffusion

• Nonlinear equations

Chapter 4 : Heat Radiation

• Epidemic Model

• Porous Media Equations

Chapter 5 : Heat Conduction

• Cubic Nonlinearity

• Unsteady Nonlinear Equations

Chapter 6 : Review of Fin problems

• Fin Radiation

• Rectangular Fin

• Temperature Distribution

• Efficiency of Fins

Chapter 7 : Non-Newtonian Fluids

• Axisymmetric Channel