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.
1. Chapter 1. Introduction to Differential Transformation Method - p. 1 2. 1.1. Introduction - p. 1 3. 1.2. Principle of Differential Transformation Method - p. 2 4. 1.3. Multistep Differential Transformation Method - p. 7 5. 1.4. Hybrid Differential Transformation Method and Finite Difference Method - p. 13 6. 1.5. Differential Transformation Method Applying on Initial-Value Problems and Ordinary Differential Equations - p. 20 7. 1.6. Two-Dimensional Differential Transformation Method for Partial Differential Equations - p. 25 8. 1.7. Differential Transformation Method–Padé Approximation - p. 36 9. 1.8. Differential Transformation Method on Singular Two-Point Boundary Value Problem - p. 44 10. Chapter 2. Differential Transformation Method in Advance - p. 55 11. 2.1. Introduction - p. 55 12. 2.2. Differential Transformation Method for Higher-Order Initial Value Problems - p. 55 13. 2.3. Fractional Differential Transform Method - p. 59 14. 2.4. Differential Transformation Method for Integro-Differential Equation - p. 64 15. 2.5. Differential Transformation Method for Eigenvalue Problems - p. 71 16. 2.6. Two-Dimensional Differential Transformation Method for Fractional Order Partial Differential Equations - p. 84 17. 2.7. Reduced Differential Transform Method - p. 90 18. 2.8. Modified Differential Transformation Method - p. 96 19. Chapter 3. DTM for Heat Transfer Problems - p. 103 20. 3.1. Introduction - p. 103 21. 3.2. Longitudinal Fins With Constant Profile - p. 103 22. 3.3. Natural Convection Flow of a Non-Newtonian Nanofluid - p. 112 23. 3.4. Two-Dimensional Heat Transfer in Longitudinal Rectangular and Convex Parabolic Fins - p. 120 24. 3.5. Thermal Boundary Layer on Flat Plate - p. 127 25. 3.6. Falkner–Skan Wedge Flow - p. 133 26. 3.7. Free Convection Problem - p. 140 27. Chapter 4. DTM for Fluids Flow Analysis - p. 153 28. Chapter 5. DTM for Nanofluids and Nanostructures Modeling - p. 197 29. 5.1. Introduction - p. 197 30. 5.2. Nanofluid in Divergent/Convergent Channels - p. 197 31. 5.3. MHD Couette Nanofluid Flow - p. 207 32. 5.4. Nanofluid Between Parallel Plates - p. 217 33. 5.5. Vibration Analysis of Nanobeams - p. 224 34. 5.6. Buckling Analysis of a Single-Walled Carbon Nanotube - p. 236 35. Chapter 6. DTM for Magnetohydrodynamic (MHD) and Porous Medium Flows - p. 239 36. 6.1. Introduction - p. 239 37. 6.2. Magnetohydrodynamic Couette Fluid Flow Between Parallel Plates - p. 239 38. 6.3. Micropolar Fluid in a Porous Channel - p. 247 39. 6.4. Magnetohydrodynamic Viscous Flow Between Porous Surfaces - p. 258 40. Chapter 7. DTM for Particles Motion, Sedimentation, and Combustion - p. 283 41. 7.1. Introduction - p. 283 42. 7.2. Motion of a Spherical Particle on a Rotating Parabola - p. 283 43. 7.3. Motion of a Spherical Particle in Plane Couette Fluid Flow - p. 287 44. 7.4. Nonspherical Particles Sedimentation - p. 301 45. 7.5. Motion of a Spherical Particle in a Fluid Forced Vortex - p. 308 46. 7.6. Combustion of Microparticles - p. 315 47. 7.7. Unsteady Sedimentation of Spherical Particles - p. 318 48. 7.8. Transient Vertically Motion of a Soluble Particle - p. 328 49. Chapter 8. DTM for Solid Mechanics, Vibration, and Deflection - p. 337 50. 8.1. Introduction - p. 337 51. 8.2. Deflection Prediction of a Cantilever Beam - p. 338 52. 8.3. Vibration Analysis of Stepped FGM Beams - p. 343 53. 8.4. Piezoelectric Modal Sensors for Cantilever Beams - p. 351 54. 8.5. Damped System With High Nonlinearity - p. 358 55. 8.6. Free Vibration of a Centrifugally Stiffened Beam - p. 361 56. 8.7. Deflections of Orthotropic Rectangular Plate - p. 364 57. 8.8. Free Vibration of Circular Plates - p. 369 58. 8.9. Vibration of Pipes Conveying Fluid - p. 378 59. 8.10. Piezoelectric Modal Sensor for Nonuniform Euler–Bernoulli Beams With Rectangular Cross Section - p. 383 60. 8.11. Free Vibrations of Oscillators - p. 393 61. 8.12. Composite Sandwich Beams With Viscoelastic Core - p. 397 62. Index - p. 405
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.
1. Chapter 1. Introduction to Differential Transformation Method - p. 1 2. 1.1. Introduction - p. 1 3. 1.2. Principle of Differential Transformation Method - p. 2 4. 1.3. Multistep Differential Transformation Method - p. 7 5. 1.4. Hybrid Differential Transformation Method and Finite Difference Method - p. 13 6. 1.5. Differential Transformation Method Applying on Initial-Value Problems and Ordinary Differential Equations - p. 20 7. 1.6. Two-Dimensional Differential Transformation Method for Partial Differential Equations - p. 25 8. 1.7. Differential Transformation Method–Padé Approximation - p. 36 9. 1.8. Differential Transformation Method on Singular Two-Point Boundary Value Problem - p. 44 10. Chapter 2. Differential Transformation Method in Advance - p. 55 11. 2.1. Introduction - p. 55 12. 2.2. Differential Transformation Method for Higher-Order Initial Value Problems - p. 55 13. 2.3. Fractional Differential Transform Method - p. 59 14. 2.4. Differential Transformation Method for Integro-Differential Equation - p. 64 15. 2.5. Differential Transformation Method for Eigenvalue Problems - p. 71 16. 2.6. Two-Dimensional Differential Transformation Method for Fractional Order Partial Differential Equations - p. 84 17. 2.7. Reduced Differential Transform Method - p. 90 18. 2.8. Modified Differential Transformation Method - p. 96 19. Chapter 3. DTM for Heat Transfer Problems - p. 103 20. 3.1. Introduction - p. 103 21. 3.2. Longitudinal Fins With Constant Profile - p. 103 22. 3.3. Natural Convection Flow of a Non-Newtonian Nanofluid - p. 112 23. 3.4. Two-Dimensional Heat Transfer in Longitudinal Rectangular and Convex Parabolic Fins - p. 120 24. 3.5. Thermal Boundary Layer on Flat Plate - p. 127 25. 3.6. Falkner–Skan Wedge Flow - p. 133 26. 3.7. Free Convection Problem - p. 140 27. Chapter 4. DTM for Fluids Flow Analysis - p. 153 28. Chapter 5. DTM for Nanofluids and Nanostructures Modeling - p. 197 29. 5.1. Introduction - p. 197 30. 5.2. Nanofluid in Divergent/Convergent Channels - p. 197 31. 5.3. MHD Couette Nanofluid Flow - p. 207 32. 5.4. Nanofluid Between Parallel Plates - p. 217 33. 5.5. Vibration Analysis of Nanobeams - p. 224 34. 5.6. Buckling Analysis of a Single-Walled Carbon Nanotube - p. 236 35. Chapter 6. DTM for Magnetohydrodynamic (MHD) and Porous Medium Flows - p. 239 36. 6.1. Introduction - p. 239 37. 6.2. Magnetohydrodynamic Couette Fluid Flow Between Parallel Plates - p. 239 38. 6.3. Micropolar Fluid in a Porous Channel - p. 247 39. 6.4. Magnetohydrodynamic Viscous Flow Between Porous Surfaces - p. 258 40. Chapter 7. DTM for Particles Motion, Sedimentation, and Combustion - p. 283 41. 7.1. Introduction - p. 283 42. 7.2. Motion of a Spherical Particle on a Rotating Parabola - p. 283 43. 7.3. Motion of a Spherical Particle in Plane Couette Fluid Flow - p. 287 44. 7.4. Nonspherical Particles Sedimentation - p. 301 45. 7.5. Motion of a Spherical Particle in a Fluid Forced Vortex - p. 308 46. 7.6. Combustion of Microparticles - p. 315 47. 7.7. Unsteady Sedimentation of Spherical Particles - p. 318 48. 7.8. Transient Vertically Motion of a Soluble Particle - p. 328 49. Chapter 8. DTM for Solid Mechanics, Vibration, and Deflection - p. 337 50. 8.1. Introduction - p. 337 51. 8.2. Deflection Prediction of a Cantilever Beam - p. 338 52. 8.3. Vibration Analysis of Stepped FGM Beams - p. 343 53. 8.4. Piezoelectric Modal Sensors for Cantilever Beams - p. 351 54. 8.5. Damped System With High Nonlinearity - p. 358 55. 8.6. Free Vibration of a Centrifugally Stiffened Beam - p. 361 56. 8.7. Deflections of Orthotropic Rectangular Plate - p. 364 57. 8.8. Free Vibration of Circular Plates - p. 369 58. 8.9. Vibration of Pipes Conveying Fluid - p. 378 59. 8.10. Piezoelectric Modal Sensor for Nonuniform Euler–Bernoulli Beams With Rectangular Cross Section - p. 383 60. 8.11. Free Vibrations of Oscillators - p. 393 61. 8.12. Composite Sandwich Beams With Viscoelastic Core - p. 397 62. Index - p. 405
