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Fractional Modelling of Fluid Flow and Transport Phenomena
- 1st Edition - February 3, 2025
- Author: Mohamed F. El-Amin
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 2 6 5 0 8 - 2
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 2 6 5 0 9 - 9
Fractional Modelling of Fluid Flow and Transport Phenomena focuses on mathematical and numerical aspects of fractional-order modeling in fluid flow and transport phenomena. The bo… Read more
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Request a sales quoteFractional Modelling 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.
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.
- Covers advancements in fractional-order fluid flow problems
- Serves as a comprehensive reference on fractional-order modeling of fluid flow and transport phenomena
- Demonstrates the topic with different aspects, including modeling, mathematical, computational, and physical commentary
Engineering researchers, graduate students, scientists, and industry professionals working in fluid dynamics, pure/applied mathematics, differential equations, and numerical analysis. The book is also suitable for courses in fluid dynamics and transport phenomena at the graduate level
1: Introduction to Fractional Calculus and its Applications in Fluid Flow
1.1 Overview of fractional calculus
1.2 Properties of fractional calculus
1.3 Different models of fractional derivatives
1.4 Examples and solved problems
1.5 Fractional derivatives limitations
1.6 Λ-fractional derivative
1.7 Applications of fractional calculus in fluid flow
1.8 Applications of fractional calculus in transport phenomena
1.9 Exercises
2: Fundamentals of Fractional Modeling of Fluid Flow
2.1 Derivation of fractional partial differential equations (PDEs) for fluid flow
2.2 Derivation of fractional mass conservation equation
2.3 Derivation of fractional momentum conservation equation
2.3.1 Fractional rotational momentum
2.3.1 Fractional rotational momentum
2.4 Derivation of fractional energy conservation equation
2.5 Problem
3: Analytical Solutions of Fractional PDEs
3.1 Analytical solutions of fractional heat equation
3.2 Analytical solutions of fractional wave equation
3.3 Analytical solutions of fractional diffusion equation
3.4 Analytical solutions of fractional gas flow in porous media
3.5 Power-series solutions of fractional fluid flow equations
3.6 Problems
4: Numerical Methods for Solving Fractional PDEs
4.1 Numerical schemes for time fractional PDEs
4.2 Numerical schemes for space fractional PDEs
4.3 Finite difference methods
4.4 Finite element methods
4.5 Spectral methods
4.6 Meshless methods
4.7 Numerical Examples
5: Fractional Models of fluid Flow and Heat/Mass Transfer
5.1 Fractional models of heat transfer by conduction
5.2 Fractional models of heat transfer by convection
5.3 Fractional models of mass transfer
5.4 Fractional-Time-Derivative in Advection-Diffusion Equation
5.5 Fractional-Time-Derivative in Navier-Stokes Equations
5.6 Spatial-fractional of boundary-layer flow
5.7 Fractional-Time-Derivative Fluid Flow Equations
5.8 Review questions
6: Fractional Models of Non-Newtonian Fluids
6.1 Fractional models of power-law fluids
6.2 Fractional models of Herschel-Bulkley fluids
6.3 Fractional models of Carreau fluids
6.4 Applications of fractional modeling in polymer processing
6.5 Applications of fractional modeling in food engineering
6.6 Case Studies
6.7 Review questions
7: Fractional Models of Nanofluids and Ferrofluids
7.1 Fractional models of heat transfer in nanofluids and ferrofluids
7.2 Fractional models of mass transfer in nanofluids and ferrofluids
7.3 Fractional models of fluid flow in nanofluids and ferrofluids
7.4 Applications of fractional-order modeling in nanotechnology
7.5 Case studies
7.6 Review questions
8: Fractional Models of Turbulent Flows
8.1 Fractional models of turbulent heat transfer
8.2 Fractional models of turbulent mass transfer
8.3 Fractional models of turbulent fluid flow
8.4 Applications of fractional modeling in turbulent combustion
8.5 Applications of fractional modeling in aerospace engineering
8.6 Case studies
8.7 Review questions
9: Fractional Models of Multi-Phase Flow
9.1 Fractional models of fluid flow in porous media
9.2 Fractional models of two-phase flow
9.3 Fractional models of three-phase flow
9.4 Applications of fractional modeling in flow in porous media
9.5 Fractional modeling of multiphase flow in porous media
9.6 Applications of fractional modeling in reservoir simulation
9.7 Case studies
9.8 Review questions
10: Fractional Models of Electrohydrodynamics
10.1 Fractional Models of Electroosmosis
10.2 Fractional Models of Electrophoresis
10.3 Fractional Models of Dielectrophoresis
10.4 Applications of Fractional Modeling in Electrokinetics
10.5 Case studies
10.6 Review questions
11: Fractional Models in Renewable Energy Systems
11.1 Fractional Models of Wind Energy
11.2 Fractional Models of Solar Energy
11.3 Fractional Models of Bioenergy
11.4 Applications of Fractional Modeling in Renewable Energy Systems
11.5 Case studies
11.6 Review questions
1.1 Overview of fractional calculus
1.2 Properties of fractional calculus
1.3 Different models of fractional derivatives
1.4 Examples and solved problems
1.5 Fractional derivatives limitations
1.6 Λ-fractional derivative
1.7 Applications of fractional calculus in fluid flow
1.8 Applications of fractional calculus in transport phenomena
1.9 Exercises
2: Fundamentals of Fractional Modeling of Fluid Flow
2.1 Derivation of fractional partial differential equations (PDEs) for fluid flow
2.2 Derivation of fractional mass conservation equation
2.3 Derivation of fractional momentum conservation equation
2.3.1 Fractional rotational momentum
2.3.1 Fractional rotational momentum
2.4 Derivation of fractional energy conservation equation
2.5 Problem
3: Analytical Solutions of Fractional PDEs
3.1 Analytical solutions of fractional heat equation
3.2 Analytical solutions of fractional wave equation
3.3 Analytical solutions of fractional diffusion equation
3.4 Analytical solutions of fractional gas flow in porous media
3.5 Power-series solutions of fractional fluid flow equations
3.6 Problems
4: Numerical Methods for Solving Fractional PDEs
4.1 Numerical schemes for time fractional PDEs
4.2 Numerical schemes for space fractional PDEs
4.3 Finite difference methods
4.4 Finite element methods
4.5 Spectral methods
4.6 Meshless methods
4.7 Numerical Examples
5: Fractional Models of fluid Flow and Heat/Mass Transfer
5.1 Fractional models of heat transfer by conduction
5.2 Fractional models of heat transfer by convection
5.3 Fractional models of mass transfer
5.4 Fractional-Time-Derivative in Advection-Diffusion Equation
5.5 Fractional-Time-Derivative in Navier-Stokes Equations
5.6 Spatial-fractional of boundary-layer flow
5.7 Fractional-Time-Derivative Fluid Flow Equations
5.8 Review questions
6: Fractional Models of Non-Newtonian Fluids
6.1 Fractional models of power-law fluids
6.2 Fractional models of Herschel-Bulkley fluids
6.3 Fractional models of Carreau fluids
6.4 Applications of fractional modeling in polymer processing
6.5 Applications of fractional modeling in food engineering
6.6 Case Studies
6.7 Review questions
7: Fractional Models of Nanofluids and Ferrofluids
7.1 Fractional models of heat transfer in nanofluids and ferrofluids
7.2 Fractional models of mass transfer in nanofluids and ferrofluids
7.3 Fractional models of fluid flow in nanofluids and ferrofluids
7.4 Applications of fractional-order modeling in nanotechnology
7.5 Case studies
7.6 Review questions
8: Fractional Models of Turbulent Flows
8.1 Fractional models of turbulent heat transfer
8.2 Fractional models of turbulent mass transfer
8.3 Fractional models of turbulent fluid flow
8.4 Applications of fractional modeling in turbulent combustion
8.5 Applications of fractional modeling in aerospace engineering
8.6 Case studies
8.7 Review questions
9: Fractional Models of Multi-Phase Flow
9.1 Fractional models of fluid flow in porous media
9.2 Fractional models of two-phase flow
9.3 Fractional models of three-phase flow
9.4 Applications of fractional modeling in flow in porous media
9.5 Fractional modeling of multiphase flow in porous media
9.6 Applications of fractional modeling in reservoir simulation
9.7 Case studies
9.8 Review questions
10: Fractional Models of Electrohydrodynamics
10.1 Fractional Models of Electroosmosis
10.2 Fractional Models of Electrophoresis
10.3 Fractional Models of Dielectrophoresis
10.4 Applications of Fractional Modeling in Electrokinetics
10.5 Case studies
10.6 Review questions
11: Fractional Models in Renewable Energy Systems
11.1 Fractional Models of Wind Energy
11.2 Fractional Models of Solar Energy
11.3 Fractional Models of Bioenergy
11.4 Applications of Fractional Modeling in Renewable Energy Systems
11.5 Case studies
11.6 Review questions
- No. of pages: 220
- Language: English
- Edition: 1
- Published: February 3, 2025
- Imprint: Academic Press
- Paperback ISBN: 9780443265082
- eBook ISBN: 9780443265099
ME
Mohamed F. El-Amin
Dr. Mohamed F. El-Amin is a Full Professor of Applied Mathematics and Computational Sciences at Effat University, Saudi Arabia. He is also a Visiting Professor at King Abdullah University of Science and Technology, Saudi Arabia, and is a Full Professor at Aswan University, Egypt. As a mathematician, he has over 25 years of research experience in the field of computational sciences, applied mathematics, transport in porous media, heat/mass transfer, fluid dynamics, turbulence, reservoir simulation, and other aspects of complex systems. After obtaining his PhD in 2001, he held research positions in several universities including South Valley University (Egypt), Stuttgart University (Germany), Kyushu University (Japan), and KAUST. Dr. El-Amin is the editor of several journal special issues and the editor of books including Numerical Modeling of Nanoparticle Transport in Porous Media: MATLAB/Python Approach, Elsevier.
Dr. El-Amin's key areas of research are computational mathematics and fluid flow modeling, with applications in several areas - including but not limited to reservoir simulation, transport phenomena, nanofluids flow, multiphase flow, transport in porous media, heat and mass transfer, hydrogen energy, boundary layer flow, magnetohydrodynamics, and non-Newtonian fluids.Affiliations and expertise
Effat University, Jeddah, Saudi Arabia