Boundary layer flow and heat transfer of viscoelastic fluid embedded in a non-Darcy porous medium with double fractional Maxwell model

Jinhu Zhao; Jinhu Zhao

doi:10.3934/nhm.2025038

Networks and Heterogeneous Media

2025, Volume 20, Issue 3: 885-902. doi: 10.3934/nhm.2025038

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Boundary layer flow and heat transfer of viscoelastic fluid embedded in a non-Darcy porous medium with double fractional Maxwell model

Jinhu Zhao ^,

School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, China

Received: 21 May 2025 Revised: 29 June 2025 Accepted: 10 July 2025 Published: 25 July 2025

A novel numerical simulation was conducted for boundary layer flow and heat transfer of viscoelastic fluid in a non-Darcy porous medium. The double fractional Maxwell model and generalized Fourier's law were employed in constitutive relation and heat transport, respectively. The strongly coupled and nonlinear fractional governing equations were formulated, which were solved and validated by the finite volume method combined with the fractional L1 scheme. The influences of fractional derivative parameters, Darcy number, porosity, and inertial parameter on the transport fields are discussed. Our results demonstrated that the different fractional derivative parameters exhibit opposite influences on velocity/temperature distributions. Moreover, the inertial effects induce velocity profile crossover that marks the transition between viscous and inertial dominance. These findings redefine our understanding of energy transport in complex porous systems.
- boundary layer flow,
- non-Darcy porous medium,
- double fractional Maxwell model,
- fractional finite volume method
Citation: Jinhu Zhao. Boundary layer flow and heat transfer of viscoelastic fluid embedded in a non-Darcy porous medium with double fractional Maxwell model[J]. Networks and Heterogeneous Media, 2025, 20(3): 885-902. doi: 10.3934/nhm.2025038

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Abstract

A novel numerical simulation was conducted for boundary layer flow and heat transfer of viscoelastic fluid in a non-Darcy porous medium. The double fractional Maxwell model and generalized Fourier's law were employed in constitutive relation and heat transport, respectively. The strongly coupled and nonlinear fractional governing equations were formulated, which were solved and validated by the finite volume method combined with the fractional L1 scheme. The influences of fractional derivative parameters, Darcy number, porosity, and inertial parameter on the transport fields are discussed. Our results demonstrated that the different fractional derivative parameters exhibit opposite influences on velocity/temperature distributions. Moreover, the inertial effects induce velocity profile crossover that marks the transition between viscous and inertial dominance. These findings redefine our understanding of energy transport in complex porous systems.

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