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.
1. Chapter 1. Introduction to Analytical Methods - p. 1 2. 1.1. Introduction - p. 1 3. 1.2. Adomian Decomposition Method - p. 1 4. 1.3. Variational Iteration Method - p. 8 5. 1.4. Differential Transformation Method - p. 11 6. 1.5. Homotopy Perturbation Method - p. 18 7. 1.6. Homotopy Analysis Method - p. 21 8. 1.7. Weighted Residual Methods - p. 33 9. 1.8. Differential Quadrature Method - p. 49 10. 1.9. Optimal Homotopy Asymptotic Method - p. 61 11. Chapter 2. Weighted Residual Methods Principles and Modifications - p. 83 12. 2.1. Introduction - p. 83 13. 2.2. Weighted Residual Methods Principles - p. 83 14. 2.3. WRMs for Coupled Equations - p. 90 15. 2.4. Optimal WRMs for Infinite Boundary Conditions - p. 99 16. 2.5. Combined WRMs With Other Analytical Methods - p. 117 17. 2.6. Modified WRMs for Combined Boundary Conditions - p. 130 18. 2.7. Hybrid WRMs for Partial Differential Equations - p. 135 19. 2.8. Multistep Polynomial WRMs for Fractional Order Differential Equations - p. 142 20. 2.9. Padé Approximation and Other Analytical Methods - p. 146 21. Chapter 3. Weighted Residual Methods in Fluid Mechanic Applications - p. 153 22. 3.1. Introduction - p. 153 23. 3.2. Nanofluid Flow in a Porous Channel - p. 153 24. 3.3. Nanofluid Flow Between Parallel Disks - p. 159 25. 3.4. Jeffery–Hamel Flow - p. 165 26. 3.5. Condensation Flow Over Inclined Disks - p. 174 27. 3.6. Electrohydrodynamic (EHD) Flow - p. 181 28. 3.7. Magnetohydrodynamic (MHD) Flow in Divergent/Convergent Channels - p. 185 29. 3.8. Nanofluid Flow in a Microchannel Heat Sink - p. 194 30. 3.9. Nanofluid Flow in Expanding and Contracting Gaps - p. 202 31. Chapter 4. Weighted Residual Methods in Heat Transfer and Energy Conversion Applications - p. 217 32. 4.1. Introduction - p. 217 33. 4.2. Heat Transfer of Longitudinal, Convective–Radiative, Porous Fins - p. 218 34. 4.3. Heat Transfer of Circular, Convective–Radiative, Porous Fins - p. 238 35. 4.4. Heat Transfer of Convective–Radiative, Semispherical Fins - p. 243 36. 4.5. Refrigeration of Fully Wet, Circular, Porous Fins - p. 250 37. 4.6. Refrigeration of Fully Wet, Semispherical, Porous Fins - p. 260 38. 4.7. Nanofluids Condensation and Heat Transfer - p. 265 39. 4.8. Nanofluid Heat Transfer in Circular, Concentric Heat Pipes - p. 277 40. 4.9. Nanofluid Heat Transfer in a Microchannel Heat Sink - p. 283 41. Chapter 5. WRMs in Nanoengineering Applications - p. 297 42. 5.1. Introduction - p. 297 43. 5.2. Natural Convection of Non-Newtonian Nanofluid - p. 297 44. 5.3. MHD Jeffery–Hamel Nanofluid Flow - p. 302 45. 5.4. MHD Nanofluids Over a Cylindrical Tube - p. 311 46. 5.5. Forced Convection for MHD Nanofluid Flow Over a Porous Plate - p. 320 47. 5.6. Non-Newtonian Nanofluid in Porous Media Between Two Coaxial Cylinders - p. 328 48. 5.7. MHD Nanofluid Flow in a Semiporous Channel - p. 335 49. 5.8. Nanofluid in Microchannel Heat Sink (MCHS) Cooling - p. 341 50. 5.9. Carbon Nanotube (CNT)-Water Between Rotating Disks - p. 348 51. Index - p. 365
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.
1. Chapter 1. Introduction to Analytical Methods - p. 1 2. 1.1. Introduction - p. 1 3. 1.2. Adomian Decomposition Method - p. 1 4. 1.3. Variational Iteration Method - p. 8 5. 1.4. Differential Transformation Method - p. 11 6. 1.5. Homotopy Perturbation Method - p. 18 7. 1.6. Homotopy Analysis Method - p. 21 8. 1.7. Weighted Residual Methods - p. 33 9. 1.8. Differential Quadrature Method - p. 49 10. 1.9. Optimal Homotopy Asymptotic Method - p. 61 11. Chapter 2. Weighted Residual Methods Principles and Modifications - p. 83 12. 2.1. Introduction - p. 83 13. 2.2. Weighted Residual Methods Principles - p. 83 14. 2.3. WRMs for Coupled Equations - p. 90 15. 2.4. Optimal WRMs for Infinite Boundary Conditions - p. 99 16. 2.5. Combined WRMs With Other Analytical Methods - p. 117 17. 2.6. Modified WRMs for Combined Boundary Conditions - p. 130 18. 2.7. Hybrid WRMs for Partial Differential Equations - p. 135 19. 2.8. Multistep Polynomial WRMs for Fractional Order Differential Equations - p. 142 20. 2.9. Padé Approximation and Other Analytical Methods - p. 146 21. Chapter 3. Weighted Residual Methods in Fluid Mechanic Applications - p. 153 22. 3.1. Introduction - p. 153 23. 3.2. Nanofluid Flow in a Porous Channel - p. 153 24. 3.3. Nanofluid Flow Between Parallel Disks - p. 159 25. 3.4. Jeffery–Hamel Flow - p. 165 26. 3.5. Condensation Flow Over Inclined Disks - p. 174 27. 3.6. Electrohydrodynamic (EHD) Flow - p. 181 28. 3.7. Magnetohydrodynamic (MHD) Flow in Divergent/Convergent Channels - p. 185 29. 3.8. Nanofluid Flow in a Microchannel Heat Sink - p. 194 30. 3.9. Nanofluid Flow in Expanding and Contracting Gaps - p. 202 31. Chapter 4. Weighted Residual Methods in Heat Transfer and Energy Conversion Applications - p. 217 32. 4.1. Introduction - p. 217 33. 4.2. Heat Transfer of Longitudinal, Convective–Radiative, Porous Fins - p. 218 34. 4.3. Heat Transfer of Circular, Convective–Radiative, Porous Fins - p. 238 35. 4.4. Heat Transfer of Convective–Radiative, Semispherical Fins - p. 243 36. 4.5. Refrigeration of Fully Wet, Circular, Porous Fins - p. 250 37. 4.6. Refrigeration of Fully Wet, Semispherical, Porous Fins - p. 260 38. 4.7. Nanofluids Condensation and Heat Transfer - p. 265 39. 4.8. Nanofluid Heat Transfer in Circular, Concentric Heat Pipes - p. 277 40. 4.9. Nanofluid Heat Transfer in a Microchannel Heat Sink - p. 283 41. Chapter 5. WRMs in Nanoengineering Applications - p. 297 42. 5.1. Introduction - p. 297 43. 5.2. Natural Convection of Non-Newtonian Nanofluid - p. 297 44. 5.3. MHD Jeffery–Hamel Nanofluid Flow - p. 302 45. 5.4. MHD Nanofluids Over a Cylindrical Tube - p. 311 46. 5.5. Forced Convection for MHD Nanofluid Flow Over a Porous Plate - p. 320 47. 5.6. Non-Newtonian Nanofluid in Porous Media Between Two Coaxial Cylinders - p. 328 48. 5.7. MHD Nanofluid Flow in a Semiporous Channel - p. 335 49. 5.8. Nanofluid in Microchannel Heat Sink (MCHS) Cooling - p. 341 50. 5.9. Carbon Nanotube (CNT)-Water Between Rotating Disks - p. 348 51. Index - p. 365
