Weighted Residual Methods

Weighted Residual Methods

Principles, Modifications and Applications

1st Edition - October 30, 2017

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  • Author: Mohammad Hatami
  • eBook ISBN: 9780128132197
  • Paperback ISBN: 9780128132180

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Weighted Residual Methods: Principles, Modifications and Applications introduces a range of WRMs, providing examples that show how they can be used to solve complex engineering problems with greater accuracy and computational efficiency. Examples focus on non-linear problems, including the motion of a spherical particle, nanofluid flow and heat transfer, magnetohydrodynamic flow and heat transfer, and micropolar fluid flow and heat transfer. These are important factors in understanding processes, such as filtration, combustion, air and water pollution and micro contamination. In addition to the applications, the reader is provided with full derivations of equations and summaries of important field research.

Key Features

  • Includes the basic code for each method, giving readers a head start in using WRMs for computational modeling
  • Provides full derivations of important governing equations in a number of emerging fields of study
  • Offers numerous, detailed examples of a range of applications in heat transfer, nanotechnology, medicine, and more


Researchers/MScs working on projects involving heat transfer, nanotechnology, nanofluid flow, or particle mechanics.

Table of Contents

  • Chapter 1: Introduction to analytical methods

    1.1 Introduction

    1.2 Adomian Decomposition Method (ADM)

    1.3 Variational Iteration Method (VIM)

    1.4 Differential Transformation Method (DTM)

    1.5 Homotopy Perturbation Method (HPM)

    1.6 Homotopy Analysis Method (HAM)

    1.7 Weighted Residual Methods (WRMs)

    1.8 Differential Quadrature Method (DQM)

    1.9 Optimal Homotopy Asymptotic Method (OHAM)

    1.10 References

    Chapter 2: Weighted Residual Methods (WRMs) principles and modifications

    2.1 Introduction

    2.2 Weighted Residual Methods (WRMs) principles

    2.2.1 Collocation Method (CM)

    2.2.2 Least Square Method (LSM)

    2.2.3 Galerkin Method (GM)

    2.2.4 Rayleigh–Ritz Method (RRM)

    2.3 WRMs for coupled equations

    2.4 Optimal WRMs for infinite boundary conditions

    2.5 Combined WRMs with other analytical methods

    2.6 Modified WRMs for Combined Boundary Conditions

    2.7 Hybrid WRMs for partial differential equations

    2.8 Multi-step Polynomial WRMs for fractional order differential equations

    2.9 Padé Approximation and Other Analytical Methods

    2.10 References

    Chapter 3: WRMs in Fluid Mechanic Applications

    3.1 Introduction

    3.2 Nanofluid flow in porous channel

    3.3 Nanofluid flow between parallel disks

    3.4 Jeffery-Hamel flow

    3.5 Condensation flow over inclined disks

    3.6 Electro-hydrodynamic (EHD) flow

    3.7 Magneto-hydrodynamic (MHD) flow in divergent/convergent channels

    3.8 Nanofluid flow in Micro-channel Heat Sink (MCHS)

    3.9 Nanofluid flow in expanding and contracting gaps

    3.10 References

    Chapter 4: WRMs in Heat Transfer and Energy Conversion Applications

    4.1 Introduction

    4.2 Heat Transfer of Longitudinal Convective-Radiative Porous Fins

    4.3 Heat Transfer of Circular Convective-Radiative Porous Fins

    4.4 Heat Transfer of Convective–Radiative Semi-Spherical Fins

    4.5 Refrigeration of Fully Wet Circular Porous Fins

    4.6 Refrigeration of Fully Wet Semi-spherical Porous Fins

    4.7 Nanofluids Condensation and Heat transfer

    4.8 Nanofluids Heat Transfer in Circular Concentric Heat Pipes

    4.9 Nanofluids Heat Transfer in Microchannel Heat Sink (MCHS)

    4.10 References

    Chapter 5: WRMs in Nano-Engineering Applications

    5.1 Introduction

    5.2 Natural Convection of Non-Newtonian Nanofluid

    5.3 MHD Jeffery–Hamel Nanofluid Flow

    5.4 MHD Nanofluids over a Cylindrical Tube

    5.5 Forced convection for MHD nanofluid flow over a porous plate

    5.6 Non-Newtonian nanofluid in porous media between two coaxial cylinders

    5.7 MHD nanofluid flow in a Semi-Porous Channel

    5.8 Nanofluid in Microchannel Heat Sink (MCHS) cooling

    5.9 Carbon Nano-Tube (CNT)-Water between Rotating Disks

    5.10 References

Product details

  • No. of pages: 384
  • Language: English
  • Copyright: © Academic Press 2017
  • Published: October 30, 2017
  • Imprint: Academic Press
  • eBook ISBN: 9780128132197
  • Paperback ISBN: 9780128132180

About the Author

Mohammad Hatami

Dr. Mohammad Hatami is currently an Associate Professor in the Department of Mechanical Engineering at Ferdowsi University of Mashhad, Iran. He completed his Ph.D. in energy conversion at Babol University of Technology whilst working as a Ph.D. visiting scholar researcher at Eindhoven University of Technology (TU/e) in the Netherlands. Dr. Hatami was previously a post-doctoral researcher at the State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, in China. He has published more than 150 research papers in the field of mathematical and numerical modelling of nanofluids, and acts as editor-in-chief of the Quarterly Journal of Mechanical Engineering and Innovation in Technology, Associate Editor of Fluid Dynamic & Material Processing, and an Editor for the International Journal of Mechanical Engineering (IJME), American Journal of Modelling and Optimization, and American Journal of Mechanical Engineering.

Affiliations and Expertise

Assistant Professor, Department of Mechanical Engineering, Esfarayen University of Technology, Esfarayen, North Khorasan, Iran

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