Differential Transformation Method for Mechanical Engineering Problems

Differential Transformation Method for Mechanical Engineering Problems

1st Edition - November 17, 2016

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  • Authors: Mohammad Hatami, Davood Domairry Ganji, Mohsen Sheikholeslami
  • Paperback ISBN: 9780128051900
  • eBook ISBN: 9780128053409

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Differential Transformation Method for Mechanical Engineering Problems focuses on applying DTM to a range of mechanical engineering applications. The authors modify traditional DTM to produce two additional methods, multi-step differential transformation method (Ms-DTM) and the hybrid differential transformation method and finite difference method (Hybrid DTM-FDM). It is then demonstrated how these can be a suitable series solution for engineering and physical problems, such as the motion of a spherical particle, nanofluid flow and heat transfer, and micropolar fluid flow and heat transfer.

Key Features

  • Presents the differential transformation method and why it holds an advantage over higher-order Taylor series methods
  • Includes a full mathematical introduction to DTM, Ms-DTM, and Hybrid DTM
  • Covers the use of these methods for solving a range of problems in areas such as nanofluid flow, heat transfer, and motion of a spherical particle in different conditions
  • Provides numerous examples and exercises which will help the reader fully grasp the practical applications of these new methods


PG students and researchers in fluid dynamics and heat transfer

Table of Contents

  • Chapter 1. Introduction to Differential Transformation Method

    • 1.1. Introduction
    • 1.2. Principle of Differential Transformation Method
    • 1.3. Multistep Differential Transformation Method
    • 1.4. Hybrid Differential Transformation Method and Finite Difference Method
    • 1.5. Differential Transformation Method Applying on Initial-Value Problems and Ordinary Differential Equations
    • 1.6. Two-Dimensional Differential Transformation Method for Partial Differential Equations
    • 1.7. Differential Transformation Method–Padé Approximation
    • 1.8. Differential Transformation Method on Singular Two-Point Boundary Value Problem

    Chapter 2. Differential Transformation Method in Advance

    • 2.1. Introduction
    • 2.2. Differential Transformation Method for Higher-Order Initial Value Problems
    • 2.3. Fractional Differential Transform Method
    • 2.4. Differential Transformation Method for Integro-Differential Equation
    • 2.5. Differential Transformation Method for Eigenvalue Problems
    • 2.6. Two-Dimensional Differential Transformation Method for Fractional Order Partial Differential Equations
    • 2.7. Reduced Differential Transform Method
    • 2.8. Modified Differential Transformation Method

    Chapter 3. DTM for Heat Transfer Problems

    • 3.1. Introduction
    • 3.2. Longitudinal Fins With Constant Profile
    • 3.3. Natural Convection Flow of a Non-Newtonian Nanofluid
    • 3.4. Two-Dimensional Heat Transfer in Longitudinal Rectangular and Convex Parabolic Fins
    • 3.5. Thermal Boundary Layer on Flat Plate
    • 3.6. Falkner–Skan Wedge Flow
    • 3.7. Free Convection Problem

    Chapter 4. DTM for Fluids Flow Analysis

    • 4.1. Introduction
    • 4.2. Two-Dimensional Viscous Flow
    • 4.3. Magnetohydrodynamic Boundary Layer
    • 4.4. Nanofluid Flow Over a Flat Plate
    • 4.5. Non-Newtonian Fluid Flow Analysis

    Chapter 5. DTM for Nanofluids and Nanostructures Modeling

    • 5.1. Introduction
    • 5.2. Nanofluid in Divergent/Convergent Channels
    • 5.3. MHD Couette Nanofluid Flow
    • 5.4. Nanofluid Between Parallel Plates
    • 5.5. Vibration Analysis of Nanobeams
    • 5.6. Buckling Analysis of a Single-Walled Carbon Nanotube

    Chapter 6. DTM for Magnetohydrodynamic (MHD) and Porous Medium Flows

    • 6.1. Introduction
    • 6.2. Magnetohydrodynamic Couette Fluid Flow Between Parallel Plates
    • 6.3. Micropolar Fluid in a Porous Channel
    • 6.4. Magnetohydrodynamic Viscous Flow Between Porous Surfaces

    Chapter 7. DTM for Particles Motion, Sedimentation, and Combustion

    • 7.1. Introduction
    • 7.2. Motion of a Spherical Particle on a Rotating Parabola
    • 7.3. Motion of a Spherical Particle in Plane Couette Fluid Flow
    • 7.4. Nonspherical Particles Sedimentation
    • 7.5. Motion of a Spherical Particle in a Fluid Forced Vortex
    • 7.6. Combustion of Microparticles
    • 7.7. Unsteady Sedimentation of Spherical Particles
    • 7.8. Transient Vertically Motion of a Soluble Particle

    Chapter 8. DTM for Solid Mechanics, Vibration, and Deflection

    • 8.1. Introduction
    • 8.2. Deflection Prediction of a Cantilever Beam
    • 8.3. Vibration Analysis of Stepped FGM Beams
    • 8.4. Piezoelectric Modal Sensors for Cantilever Beams
    • 8.5. Damped System With High Nonlinearity
    • 8.6. Free Vibration of a Centrifugally Stiffened Beam
    • 8.7. Deflections of Orthotropic Rectangular Plate
    • 8.8. Free Vibration of Circular Plates
    • 8.9. Vibration of Pipes Conveying Fluid
    • 8.10. Piezoelectric Modal Sensor for Nonuniform Euler–Bernoulli Beams With Rectangular Cross Section
    • 8.11. Free Vibrations of Oscillators
    • 8.12. Composite Sandwich Beams With Viscoelastic Core

Product details

  • No. of pages: 422
  • Language: English
  • Copyright: © Academic Press 2016
  • Published: November 17, 2016
  • Imprint: Academic Press
  • Paperback ISBN: 9780128051900
  • eBook ISBN: 9780128053409

About the Authors

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

Davood Domairry Ganji

D. D. Ganji is a Professor of Mechanical Engineering and the Director of the Graduate Program at Babol Noshirvani University of Technology in Iran, as well as a consultant in nonlinear dynamics and the Dean of the National Elite Foundation of Iran. He has a Ph.D. in Mechanical Engineering from Tarbiat Modarres University. He is the Editor-in-Chief of International Journal of Nonlinear Dynamic and Engineering Science, and Editor of International Journal of Nonlinear Sciences and Numerical Simulation and International Journal of Differential Equations.

Affiliations and Expertise

Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

Mohsen Sheikholeslami

Dr. Mohsen Sheikholeslami works at the Babol Noshirvani University of Technology’s Department of Mechanical Engineering, Iran. His research interests include Computational Fluid Dynamics, nanofluid simulation, mesoscopic modeling of fluid, nonlinear science, magnetohydrodynamics, ferrohydrodynamics, and electrohydrodynamics. He authored several papers and books across various areas of mechanical engineering. He was selected as a Web of Science Highly Cited Researcher (Top 0.01%) in 2016 and 2017. He is also the author of the books Applications of Nanofluid for Heat Transfer Enhancement; Application of Semi-Analytical Methods for Nanofluid Flow and Heat Transfer; Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method; and External Magnetic Field Effects on Hydrothermal Treatment of Nanofluid, all published by Elsevier.

Affiliations and Expertise

Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

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