Differential Transformation Method for Mechanical Engineering Problems

1st Edition - November 17, 2016
Authors: Mohammad Hatami, Davood Domairry Ganji, Mohsen Sheikholeslami
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 0 5 1 9 0 - 0
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 0 5 3 4 0 - 9

Differential Transformation Method for Mechanical Engineering Problems focuses on applying DTM to a range of mechanical engineering applications. The authors modify tradition… Read more

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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.

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

Mohammad Hatami

Mohammad Hatami is a Mechanical Engineering Associate Professor at Esfarayen University of Technology, Esfarayen, North Khorasan, Iran. He also was an associate professor at Ferdowsi University of Mashhad, and was selected as a young talent associate professor at Xi'an Jiaotong University. 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 200 research papers and 10 books/chapter books in the field of experimental, mathematical and numerical modelling of nanofluids, heat recovery 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

Associate 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 is the Head of the Renewable Energy Systems and Nanofluid Applications in Heat Transfer Laboratory at the Babol Noshirvani University of Technology, in Iran. He was the first scientist to develop a novel numerical method (CVFEM) in the field of heat transfer and published a book based on this work, entitled "Application of Control Volume Based Finite Element Method (CVFEM) for Nanofluid Flow and Heat Transfer". He was selected as a Web of Science Highly Cited Researcher (Top 0.01%) by Clarivate Analytics, and he was ranked first in the field of mechanical engineering and transport globally (2020-2021) according to data published by Elsevier. Dr. Sheikholeslami has authored a number of books and is a member of the Editorial Boards of the ‘International Journal of Heat and Technology’ and ‘Recent Patents on Nanotechnology’.

Affiliations and expertise

Babol Noshirvani University of Technology, Babol, Iran