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Chapter 3: Fundamentals of Fractional Modeling of Fluid Flow, of the Book: Fractional Modelling of Fluid Flow and Transport Phenomena

El-Amin, Mohamed F.
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Fractional Mass Equation, Fractional Momentum Equation, Fractional Energy Equation, Fluid Dynamics, Fractional Differential Equations (FDEs), Anomalous Diffusion, Fractional Heat Conduction, Fractional Heat Convection-Conduction, Fractional Darcy’s Law, Fractional Darcy’s Law with memory
Date
2024-07-31
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NSMTU - Book Chapters
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Abstract
As the primary focus of this book is employing fractional modeling in the study of fluid dynamics and transport phenomena, this chapter presents the basics of fractional modeling of fluid flow. It begins with exploring fractional differential equations and discusses their advantages and challenges. Subsequent sections focus on the derivations of fractional-order formulations for conserving mass and momentum. The chapter also introduces the derivation of the fractional energy conservation equation, including models for heat conduction, heat convection-conduction, and general transport phenomena. Additionally, the discussion extends to fluid flow in porous media, featuring adaptations of Darcy’s Law that incorporate time and space memory effects and address anomalous diffusion processes.
Department
NSMTU
Publisher
Elseiver
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Book title
Fractional Modelling of Fluid Flow and Transport Phenomena
Journal title
Open Access
http://hdl.handle.net/20.500.14131/1690
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