Fractional Modeling of Fluid Flow and Transport Phenomena focuses on mathematical and numerical aspects of fractional-order modeling in fluid flow and transport phenomena. The book covers fundamental concepts, advancements, and practical applications, including modeling developments, numerical solutions, and convergence analysis for both time and space fractional order models. Various types of flows are explored, such as single- and multi-phase flows in porous media, involving different fluid types like Newtonian, non-Newtonian, nanofluids, and ferrofluids. This book serves as a comprehensive reference on fractional-order modeling of fluid flow and transport phenomena, offering a single resource that is currently unavailable.
Fractional-order modeling has gained traction in engineering and science, particularly in fluid dynamics and transport phenomena. However, its mathematical and numerical advancements have progressed relatively slowly compared to other aspects. Therefore, this book emphasizes the fractional-order modeling of fluid flow and transport phenomena to bridge this gap. Each chapter in the book delves into a specific topic closely related to the others, ensuring a cohesive and self-contained structure.
1. 5.1 Introduction - p. 100 2. 5.2 Fractional forward Euler method - p. 100 3. 5.3 Generalized fractional forward Euler method - p. 101 4. 5.4 The s-stage explicit fractional-order Runge–Kutta method - p. 103 5. 5.5 The 2-stage fractional Runge–Kutta method - p. 105 6. 5.6 The 3-stage EFORK method - p. 106 7. 5.7 2-stage implicit fractional-order Runge–Kutta method - p. 107 8. 5.8 Finite difference methods - p. 110 9. 5.9 Finite element methods - p. 117 10. 5.10 Spectral element methods - p. 123 11. 5.11 Meshless methods - p. 131 12. 5.12 Problems - p. 138 13. Declaration of generative AI and AI-assisted technologies in the writing process - p. 139 14. References - p. 139 15. Chapter 6. Fractional-order models of fluid flow, heat and mass transfer - p. 143 16. Abstract - p. 143 17. 6.1 Preliminaries - p. 143 18. 6.2 Fractional-order Navier–Stokes equations - p. 144 19. 6.3 Semianalytical solution for fractional Navier–Stokes equations - p. 151 20. 6.4 Fractional modeling of heat transfer - p. 153 21. 6.5 Review questions - p. 168 22. 6.6 Problems - p. 169 23. Declaration of generative AI and AI-assisted technologies in the writing process - p. 170 24. References - p. 170 25. Chapter 7. Fractional-order models of non-Newtonian fluids - p. 173 26. Chapter 8. Fractional-order models of nanofluids and ferrofluids - p. 203 27. Chapter 9. Fractional models of turbulent flows - p. 223 28. Chapter 10. Fractional-order derivatives for multiphase flow in porous media - p. 233 29. Chapter 11. Fractional models of magneto- and electrohydrodynamics - p. 259 30. Chapter 12. Fractional models in renewable energy systems - p. 269 31. Appendix A. Cell-centered finite difference method - p. 279 32. Index - p. 283
Fractional Modeling of Fluid Flow and Transport Phenomena focuses on mathematical and numerical aspects of fractional-order modeling in fluid flow and transport phenomena. The book covers fundamental concepts, advancements, and practical applications, including modeling developments, numerical solutions, and convergence analysis for both time and space fractional order models. Various types of flows are explored, such as single- and multi-phase flows in porous media, involving different fluid types like Newtonian, non-Newtonian, nanofluids, and ferrofluids. This book serves as a comprehensive reference on fractional-order modeling of fluid flow and transport phenomena, offering a single resource that is currently unavailable.
Fractional-order modeling has gained traction in engineering and science, particularly in fluid dynamics and transport phenomena. However, its mathematical and numerical advancements have progressed relatively slowly compared to other aspects. Therefore, this book emphasizes the fractional-order modeling of fluid flow and transport phenomena to bridge this gap. Each chapter in the book delves into a specific topic closely related to the others, ensuring a cohesive and self-contained structure.
1. 5.1 Introduction - p. 100 2. 5.2 Fractional forward Euler method - p. 100 3. 5.3 Generalized fractional forward Euler method - p. 101 4. 5.4 The s-stage explicit fractional-order Runge–Kutta method - p. 103 5. 5.5 The 2-stage fractional Runge–Kutta method - p. 105 6. 5.6 The 3-stage EFORK method - p. 106 7. 5.7 2-stage implicit fractional-order Runge–Kutta method - p. 107 8. 5.8 Finite difference methods - p. 110 9. 5.9 Finite element methods - p. 117 10. 5.10 Spectral element methods - p. 123 11. 5.11 Meshless methods - p. 131 12. 5.12 Problems - p. 138 13. Declaration of generative AI and AI-assisted technologies in the writing process - p. 139 14. References - p. 139 15. Chapter 6. Fractional-order models of fluid flow, heat and mass transfer - p. 143 16. Abstract - p. 143 17. 6.1 Preliminaries - p. 143 18. 6.2 Fractional-order Navier–Stokes equations - p. 144 19. 6.3 Semianalytical solution for fractional Navier–Stokes equations - p. 151 20. 6.4 Fractional modeling of heat transfer - p. 153 21. 6.5 Review questions - p. 168 22. 6.6 Problems - p. 169 23. Declaration of generative AI and AI-assisted technologies in the writing process - p. 170 24. References - p. 170 25. Chapter 7. Fractional-order models of non-Newtonian fluids - p. 173 26. Chapter 8. Fractional-order models of nanofluids and ferrofluids - p. 203 27. Chapter 9. Fractional models of turbulent flows - p. 223 28. Chapter 10. Fractional-order derivatives for multiphase flow in porous media - p. 233 29. Chapter 11. Fractional models of magneto- and electrohydrodynamics - p. 259 30. Chapter 12. Fractional models in renewable energy systems - p. 269 31. Appendix A. Cell-centered finite difference method - p. 279 32. Index - p. 283
