Explicit solution for some generalized fluids in laminar flow with slip boundary conditions
- Mathematics Department, Colleges of Science and Arts, AlKamel, University of Jeddah, KSA \(\&\) University of Tunis El Manar, National Engineering School at Tunis, LAMSIN, 1002, Tunis, Tunisia
Tarig. M. Elzaki
- Mathematics Department, Colleges of Science and Arts, AlKamel, University of Jeddah, KSA
In this study, we present a new approximation method to give an explicit solution of a laminar flow using a Sisko
model. This is a problem of a generalized Newtonian fluid with slip boundary conditions. The proposed method
is based on the variational iteration method (VIM) combined with an approximation step. This method is validated
where the exact solution is available. In addition, in order to enrich the discussion, a numerical method is
presented. The results illustrate that the VIM may be more effective that the finite difference method for a dilatant
fluid. However, the VIM will be inappropriate for pseudoplastic fluid cases.
- Sisko model
- variational iteration method
- dilatant fluid
- pseudoplastic fluid
N. Ali, A. Zaman, M. Sajid, Unsteady blood flow through a tapered stenotic artery using Sisko model, Comput. & Fluids, 101 (2014), 42–49.
M. M. Bhatti, T. Abbas, M. M. Rashidi, Numerical Study of Entropy Generation with Nonlinear Thermal Radiation on Magnetohydrodynamics non-Newtonian Nanofluid Through a Porous Shrinking Sheet, J. Magnet., 21 (2016), 468–475.
M. M. Bhatti, R. Ellahi, A. Zeeshan, Study of variable magnetic field on the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct having compliant walls, J. Mol. Liq., 222 (2016), 101–108.
M. M. Bhatti, A. Zeeshan, Analytic study of heat transfer with variable viscosity on solid particle motion in dusty Jeffery fluid, Modern Phys. Lett. B, 2016 (2016), 13 pages.
M. M. Bhatti, A. Zeeshan, R. Ellahi, Endoscope analysis on peristaltic blood flow of Sisko fluid with Titanium magnetonanoparticles, Comput. Biol. Med., 78 (2016), 29–41.
M. M. Bhatti, A. Zeeshan, N. Ijaz, O. A. Beg, A. Kadir , Mathematical modelling of nonlinear thermal radiation effects on EMHD peristaltic pumping of viscoelastic dusty fluid through a porous medium duct, Eng. Sci. Tech. Int. J., 20 (2017), 1129–1139.
R. Ellahi, M. M. Bhatti, I. Pop , Effects of Hall and Ion Slip on MHD peristaltic flow of Jeffrey fluid in a non-Uniform rectangular duct, Internat. J. Numer. Methods Heat Fluid Flow, 26 (2016), 1802–1820.
R. Ellahi, E. Shivanian, S. Abbasbandy, T. Hayat, Numerical study of magnetohydrodynamics generalized Couette flow of Eyring-Powell fluid with heat transfer and slip condition, Internat. J. Numer. Methods Heat Fluid Flow, 26 (2016), 1433–1445.
L. L. Ferrás, J. M. Nóbrega, F. T. Pinho, Analytical solutions for Newtonian and inelastic non-Newtonian flows with wall slip, J. Non-Newtonian Fluid Mech., 175–176 (2012), 76–88.
J.-H. He, Variational iteration method a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech., 34 (1999), 699–708.
O. Martin, Modified variational iteration method for the analysis of viscoelastic beams, Appl. Math. Model., 40 (2016), 7988–7995.
A. D. Polyanin, V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, Second edition, Chapman & Hall/CRC, Boca Raton, London, New York (2003)
S. U. Rahman, R. Ellahi, S. Nadeem, Q. M. Zaigham Zia, Simultaneous effects of nanoparticles and slip on Jeffrey fluid through tapered artery with mild stenosis, J. Mol. Liq., 218 (2016), 484–493.
A. W. Sisko, The flow of lubricating greases, Ind. Eng. Chem., 50 (1958), 1789–1792.
A.-M. Wazwaz , The variational iteration method for solving a system of PDES, Comput. Math. Appl., 54 (2007), 895– 902.
I. S. Weir, W. J. Bailey, A statistical study of rheological models for drilling fluids: Society of Petroleum Engineers, SPE Journal, 1 (1996), 473–486.