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Analytical Solution of Fractional Oldroyd-B Fluid via Fluctuating Duct

Author

Listed:
  • Ying Qing Song
  • Aamir Farooq
  • Muhammad Kamran
  • Sadique Rehman
  • Muhammad Tamoor
  • Rewayat Khan
  • Asfand Fahad
  • Muhammad Imran Qureshi
  • Muhammad Imran Asjad

Abstract

This investigation focuses on the mixed initial boundary value problem with Caputo fractional derivatives. The studied pour an incompressible fractionalized Oldroyd-B fluid prompted by fluctuating rectangular tube. The explicit expression of the velocity field and shear stresses for the fractional model are obtained by utilizing the integral transforms, i.e., double finite Fourier sine transform and Laplace transform. Furthermore, the confirmation of the analytical solutions is also analyzed by utilizing the Tzou’s and Stehfest’s algorithms in the tabular form. In limited cases, ordinary Oldroyd-B fluid similar solutions and classical Maxwell and fractional Maxwell fluid are derived. The flow field’s graphs with the influences of relevant parameters are also mentioned.

Suggested Citation

  • Ying Qing Song & Aamir Farooq & Muhammad Kamran & Sadique Rehman & Muhammad Tamoor & Rewayat Khan & Asfand Fahad & Muhammad Imran Qureshi & Muhammad Imran Asjad, 2021. "Analytical Solution of Fractional Oldroyd-B Fluid via Fluctuating Duct," Complexity, Hindawi, vol. 2021, pages 1-16, November.
    • Handle: RePEc:hin:complx:9576873
    DOI: 10.1155/2021/9576873
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