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A fractional-order Maxwell model for non-Newtonian fluids

Author

Listed:
  • Carrera, Y.
  • Avila-de la Rosa, G.
  • Vernon-Carter, E.J.
  • Alvarez-Ramirez, J.

Abstract

This work considers an extension of the fractional-order Maxwell arrangement to incorporate a relaxation process with non-Newtonian viscosity behavior. The resulting model becomes a fractional-order nonlinear differential equation with stable solution converging asymptotically to a unique equilibrium point. Expressions for the corresponding storage and loss moduli as function of strain frequency and amplitude are computed via a first-harmonic analysis of the differential equation. Some distinctive features and their relationship to the classical and fractional-order linear Maxwell models are discussed. Three examples are used to illustrate the ability of the fractional-order Maxwell model to describe experimental data.

Suggested Citation

  • Carrera, Y. & Avila-de la Rosa, G. & Vernon-Carter, E.J. & Alvarez-Ramirez, J., 2017. "A fractional-order Maxwell model for non-Newtonian fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 276-285.
    • Handle: RePEc:eee:phsmap:v:482:y:2017:i:c:p:276-285
    DOI: 10.1016/j.physa.2017.04.085
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    References listed on IDEAS

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    1. Fan, Wenping & Jiang, Xiaoyun & Qi, Haitao, 2015. "Parameter estimation for the generalized fractional element network Zener model based on the Bayesian method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 40-49.
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    Cited by:

    1. Ahmed, Jawad & Khan, Masood & Ahmad, Latif, 2020. "Radiative heat flux effect in flow of Maxwell nanofluid over a spiraling disk with chemically reaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    2. Shah, Nehad Ali & Chung, Jae Dong & Vieru, Dumitru & Fetecau, Constantin, 2021. "Unsteady flows of Maxwell fluids with shear rate memory and pressure-dependent viscosity in a rectangular channel," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Dang, Rongqi & Chen, Yiming, 2021. "Fractional modelling and numerical simulations of variable-section viscoelastic arches," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. Lei, Dong & Liang, Yingjie & Xiao, Rui, 2018. "A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 465-475.
    5. Tabatabaei, S. Sepehr & Dehghan, Mohammad Reza & Talebi, Heidar Ali, 2022. "Real-time prediction of soft tissue deformation; a non-integer order modeling scheme and a practical verification for the theoretical concept," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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