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General second order fluid flow in a pipe

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Abstract

It is more satisfactory for fluid materials between viscous and elastic to introduce the fractional calculus approach into the constitutive relationship. This paper employs the fractional calculus approach to study second fluid flow in a pape. First, we derive the analytical solution which the derivate order is half and then with the analytical solution we verify the reliability of Laplace numerical inversion based on Crump algorithm for the problem, and finally we analyze the characteristics of second order fluid flow in a pipe by using Crump method. The results indicate that the more obvious the viscoelastic properties of fluid is, the more sensitive the depondence of velocity and stress on fractional derivative order is.

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Authors and Affiliations

  1. Department of Petroleum Engineering, Xián Petroleum Institute, 710061, Xián, P.R. China

    He Guangyu

  2. Department of Resources and Environmental Sciences, Beijing Normal University, 100875, Beijing, P. R. China

    Huang Junqi

  3. Institute of Porous Flow and Fluid Mechanics, Academia Sinica, 102801, Langfang, P.R. China

    Liu Ciqun

Authors
  1. He Guangyu
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  2. Huang Junqi
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  3. Liu Ciqun
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Guangyu, H., Junqi, H. & Ciqun, L. General second order fluid flow in a pipe. Appl Math Mech 16, 825–831 (1995). https://doi.org/10.1007/BF02458607

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  • DOI: https://doi.org/10.1007/BF02458607

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