Numerical solution of hybrid method for third grade flow due to variable accelerated plate in a rotating frame

  • Abstract
  • Keywords
  • References
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  • Abstract

    The aim of this article is to obtain numerical solution for incompressible unsteady flow for third grade fluid induced by variable accelerated plate. Numerical solution is obtained by using Hybrid method which combine between finite difference method (FDM) and asymptotic interpolation method. The influence of difference values of material constant parameters on the velocity flow fluid are discussed and shown graphically.


  • Keywords

    Asymptotic interpolation method; Finite difference method; Rotating frame; Third grade fluid; Variable accelerated.

  • References

      [1] Andrianov IV & Awrejcewicz J (2001), New trends in asymptotic approaches: Summation and interpolation methods. Applied Mechanics Reviews 54, 69–92.

      [2] Abdul Aziz Z, Nazari M, Salah F, Ching DL (2012), Constant accelerated flow for a third-grade fluid in a porous medium and a rotating frame with the homotopy analysis method. Mathematical Problems in Engineering 2012, 1–14.

      [3] Hayat T, Wang Y & Hutter K (2002), Flow of a fourth grade fluid. Mathematical Models and Methods in Applied Sciences, 12, 797–811.

      [4] Hayat T & Wang Y (2003), Magnetohydrodynamic flow due to noncoaxial rotations of a porous disk and a fourth grade fluid at infinity. Mathematical Problems in Engineering 2003, 47–64.

      [5] Hayat T, Naz R & Abbasbandy S (2011), Poiseuille flow of a third grade fluid in a porous medium. Transport in Porous Media 87, 355–366.

      [6] Liu Y & Mahadevan S (2009), Fatigue limit prediction of notched components using short crack growth theory and an asymptotic interpolation method. Engineering Fracture Mechanics 76, 2317–2331.

      [7] Nayak I, Nayak AK & Padhly S (2012), Numerical solution for the flow and heat transfer of a third-grade fluid past a porous vertical plate. Advanced Studies Theory in Physics 6, 615–624.

      [8] Nazari M (2014), Approximate analytical solutions for viscoelastic differential type flow models using homotopy analysis method. PhD thesis, Universiti Teknologi Malaysia.

      [9] Rana MA, Ahmad A & Qamar R (2012), Chapter 8: Magnetohydrodynamic rotating flow of a fourth grade fluid between two parallel infinite plates. In L. Zheng (Ed.), Topics in Magnetohydrodynamics. Rijeka: InTech, pp. 189–210.

      [10] Shahzad F, Hayat T & Ayub M (2008), Stokes’ first problem for the rotating flow of a third grade fluid. Nonlinear Analysis: Real World Applications 9, 1794–1799.

      [11] Tan W & Masuoka T (2005), Stokes’s first problem for a second grade fluid in a porous half-space with heated boundary. International Journal of Non-Linear Mechanics 40, 515–522.

      [12] Tomé MF, Mangiavacchi N, Cuminato JA, Castelo A & McKee S (2002), A finite difference technique for simulating unsteady viscoelastic free surface flows. Journal of Non-Newtonian Fluid Mechanics 106, 61-106.

      [13] Tomé MF, Grossi L, Castelo A, Cuminato JA, Mangiavacchi N, Ferreira VG, de Sousa FS & McKee S (2004), A numerical method for solving three-dimensional generalized Newtonian free surface flows. Journal of Non-Newtonian Fluid Mechanics 123, 85–103.

      [14] Tomé MF, Castelo A, Ferreira VG & McKee S (2008), A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows. Journal of Non-Newtonian Fluid Mechanics 154, 179–206.

      [15] Vyaz’min AV, Denisov IA & Polyanin AD (2001), Method of asymptotic interpolation in problems of chemical hydrodynamics and mass transfer. Theoretical Foundations of Chemical Engineering 35, 1–8.




Article ID: 11361
DOI: 10.14419/ijet.v7i2.15.11361

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