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2025-02-01
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Abstract
This chapter is devoted to fractional-order fluid flow models, focusing on heat and mass transfer phenomena. The fractional Navier–Stokes equations, integrating both mass and momentum conservation principles, are formulated to encompass a broad range of physical scenarios, including compressible and incompressible fluids, viscous dynamics, and other forces. The chapter introduces conformable fractional derivatives, which generalize traditional time derivatives to capture more complex behaviors. These fractional operators enable the modeling of nonlocal interactions and memory effects, which are essential for accurately describing fluid flow in various engineering and scientific contexts. Specific models of fractional fluid flow are explored, including the fractional-order Navier–Stokes equations and their applications to Poiseuille flow and the time fractional Burgers equation. Semianalytical solutions for these equations are provided using the Adomian decomposition method, highlighting the efficiency and accuracy of fractional modeling techniques. The integration of heat and mass transfer into these models is also discussed, extending their applicability to scenarios where temperature and concentration gradients play a crucial role. The chapter includes case studies and numerical examples that demonstrate the effectiveness of fractional fluid flow models in real-world applications.
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Book title
Fractional Modeling of Fluid Flow and Transport Phenomena