Modeling and Analysis of Modern Fluid Problems - 1st Edition - ISBN: 9780128117538, 9780128117590

Modeling and Analysis of Modern Fluid Problems

1st Edition

Authors: Liancun Zheng Xinxin Zhang
eBook ISBN: 9780128117590
Paperback ISBN: 9780128117538
Imprint: Academic Press
Published Date: 27th April 2017
Page Count: 480
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Table of Contents

Chapter 1. Introduction

  • 1.1. Basic Ideals of Analytical Methods
  • 1.2. Review of Analytical Methods
  • 1.3. Fractal Theory and Fractional Viscoelastic Fluid
  • 1.4. Numerical Methods
  • 1.5. Modeling and Analysis for Modern Fluid Problems
  • 1.6. Outline

Chapter 2. Embedding-Parameters Perturbation Method

  • 2.1. Basics of Perturbation Theory
  • 2.2. Embedding-Parameter Perturbation
  • 2.3. Marangoni Convection
  • 2.4. Marangoni Convection in a Power Law Non-Newtonian Fluid
  • 2.5. Marangoni Convection in Finite Thickness
  • 2.6. Summary

Chapter 3. Adomian Decomposition Method

  • 3.1. Introduction
  • 3.2. Nonlinear Boundary Layer of Power Law Fluid
  • 3.3. Power Law Magnetohydrodynamic Fluid Flow Over a Power Law Velocity Wall
  • 3.4. Marangoni Convection Over a Vapor–Liquid Surface
  • 3.5. Summary

Chapter 4. Homotopy Analytical Method

  • 4.1. Introduction
  • 4.2. Flow and Radiative Heat Transfer of Magnetohydrodynamic Fluid Over a Stretching Surface
  • 4.3. Flow and Heat Transfer of Nanofluids Over a Rotating Disk
  • 4.4. Mixed Convection in Power Law Fluids Over Moving Conveyor
  • 4.5. Magnetohydrodynamic Thermosolutal Marangoni Convection in Power Law Fluid
  • 4.6. Summary

Chapter 5. Differential Transform Method

  • 5.1. Introduction
  • 5.2. Magnetohydrodynamics Falkner–Skan Boundary Layer Flow Over Permeable Wall
  • 5.3. Unsteady Magnetohydrodynamics Mixed Flow and Heat Transfer Along a Vertical Sheet
  • 5.4. Magnetohydrodynamics Mixed Convective Heat Transfer With Thermal Radiation and Ohmic Heating
  • 5.5. Magnetohydrodynamic Nanofluid Radiation Heat Transfer With Variable Heat Flux and Chemical Reaction
  • 5.6. Summary

Chapter 6. Variational Iteration Method and Homotopy Perturbation Method

  • 6.1. Review of Variational Iteration Method
  • 6.2. Fractional Diffusion Problem
  • 6.3. Fractional Advection-Diffusion Equation
  • 6.4. Review of Homotopy Perturbation Method
  • 6.5. Unsteady Flow and Heat Transfer of a Power Law Fluid Over a Stretching Surface
  • 6.6. Summary

Chapter 7. Exact Analytical Solutions for Fractional Viscoelastic Fluids

  • 7.1. Introduction
  • 7.2. Fractional Maxwell Fluid Flow Due to Accelerating Plate
  • 7.3. Helical Flows of Fractional Oldroyd-B Fluid in Porous Medium
  • 7.4. Magnetohydrodynamic Flow and Heat Transfer of Generalized Burgers' Fluid
  • 7.5. Slip Effects on Magnetohydrodynamic Flow of Fractional Oldroyd-B Fluid
  • 7.6. The 3D Flow of Generalized Oldroyd-B Fluid
  • 7.7. Summary

Chapter 8. Numerical Methods

  • 8.1. Review of Numerical Methods
  • 8.2. Heat Transfer of Power Law Fluid in a Tube With Different Flux Models
  • 8.3. Heat Transfer of the Power Law Fluid Over a Rotating Disk
  • 8.4. Maxwell Fluid With Modified Fractional Fourier's Law and Darcy's Law
  • 8.5. Unsteady Natural Convection Heat Transfer of Fractional Maxwell Fluid
  • 8.6. Fractional Convection Diffusion With Cattaneo–Christov Flux
  • 8.7. Summary


Modeling and Analysis of Modern Fluids helps researchers solve physical problems observed in fluid dynamics and related fields, such as heat and mass transfer, boundary layer phenomena, and numerical heat transfer. These problems are characterized by nonlinearity and large system dimensionality, and ‘exact’ solutions are impossible to provide using the conventional mixture of theoretical and analytical analysis with purely numerical methods.

To solve these complex problems, this work provides a toolkit of established and novel methods drawn from the literature across nonlinear approximation theory. It covers Padé approximation theory, embedded-parameters perturbation, Adomian decomposition, homotopy analysis, modified differential transformation, fractal theory, fractional calculus, fractional differential equations, as well as classical numerical techniques for solving nonlinear partial differential equations. In addition, 3D modeling and analysis are also covered in-depth.

Key Features

  • Systematically describes powerful approximation methods to solve nonlinear equations in fluid problems
  • Includes novel developments in fractional order differential equations with fractal theory applied to fluids
  • Features new methods, including Homotypy Approximation, embedded-parameter perturbation, and 3D models and analysis


Graduate students and 1st year PhDs studying applied mathematics, mathematical aspects of fluid dynamics, and thermal science. The work will also appeal to a smaller number of mathematical-inclined engineers working in fluid dynamics


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© Academic Press 2017
Academic Press
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About the Authors

Liancun Zheng Author

Liancun Zheng (University of Science and Technology, Beijing), is a Professor in Applied mathematics with interest in partial/ordinary differential equations, fractional differential equations, non-Newtonian fluids, viscoelastic fluids, micropolar fluids, nanofluids, heat and mass transfer, radioactive heat transfer, nonlinear boundary value problems, and numerical heat transfer. He has published more than 260 papers in international journals and 5 books (in Chinese) and has served as Editor or Guest Editor of International Journals on 10 occasions.

Affiliations and Expertise

University of Science and Technology, Beijing, China

Xinxin Zhang Author

Xinxin Zhang is a Professor in the School of Engergy and Environmental Enginerring at the University of Science and Technology, Bejing.He is interested in thermal physical properties and thermal physics, mathematical modelling, system optimization and computer control, the numerical analysis of fluid flow, and heat transfer.

Affiliations and Expertise

University of Science and Technology, Beijing, China