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Mathematical Problems in Engineering
Volume 2016, Article ID 4293721, 14 pages
http://dx.doi.org/10.1155/2016/4293721
Research Article

Unsteady Squeezing Flow of Casson Fluid with Magnetohydrodynamic Effect and Passing through Porous Medium

1Department of Mathematics, National University of Computer and Emerging Sciences, Peshawar, Pakistan
2Department of Computer Sciences, National University of Computer and Emerging Sciences, Peshawar, Pakistan
3Department of Basic Sciences and Humanities, University of Engineering and Technology, Peshawar, Pakistan

Received 22 August 2016; Revised 26 October 2016; Accepted 1 December 2016

Academic Editor: Michael Vynnycky

Copyright © 2016 Hamid Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. W. Mrill, A. M. Benis, E. R. Gilliland, T. K. Sherwood, and E. W. Salzman, “Pressure-flow relations of human blood in hollow fibers at low flow rates,” Journal of Applied Physiology, vol. 20, no. 5, pp. 954–967, 1965. View at Google Scholar
  2. D. A. McDonald, Blood Flows in Arteries, Arnold, London, UK, 2nd edition, 1974.
  3. H. I. Andersson and B. S. Dandapat, “Flow of a powerlaw fluid over a stretching sheet,” Applied Analysis of Continuous Media, vol. 1, no. 339, 1992. View at Google Scholar
  4. M. Sajid, I. Ahmad, T. Hayat, and M. Ayub, “Unsteady flow and heat transfer of a second grade fluid over a stretching sheet,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 1, pp. 96–108, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. N. Casson, Rheology of Dispersed System, vol. 84, Pergamon Press, Oxford, UK, 1959.
  6. R. K. Dash, K. N. Mehta, and G. Jayaraman, “Casson fluid flow in a pipe filled with a homogeneous porous medium,” International Journal of Engineering Science, vol. 34, no. 10, pp. 1145–1156, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. N. T. M. Eldabe and M. G. E. Salwa, “Heat transfer of mhd non-newtonian casson fluid flow between two rotating cylinder,” Journal of the Physical Society of Japan, vol. 64, p. 4164, 1995. View at Google Scholar
  8. M. H. Hamdan, “An alternative approach to exact solutions of a special class of Navier-Stokes flows,” Applied Mathematics and Computation, vol. 93, no. 1, pp. 83–90, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. M. H. Hamdan and F. M. Allan, “A note on the generalized Beltrami flow through porous media,” International Journal of Pure and Applied Mathematics, vol. 27, no. 4, pp. 491–500, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. K. Vafai and C. L. Tien, “Boundary and inertia effects on flow and heat transfer in porous media,” International Journal of Heat and Mass Transfer, vol. 24, no. 2, pp. 195–203, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. S. Islam, M. R. Mohyuddin, and C. Y. Zhou, “Few exact solutions of non-Newtonian fluid in porous medium with hall effect,” Journal of Porous Media, vol. 11, no. 7, pp. 669–680, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Vafai, Handbook of Porous Media, CRC Press, Taylor and Francis, Boca Raton, Fla, USA, 2nd edition, 2005. View at Publisher · View at Google Scholar
  13. S. Abbasbandy, “A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 59–63, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. M. A. Abdou and A. A. Soliman, “Variational iteration method for solving BURger's and coupled BURger's equations,” Journal of Computational and Applied Mathematics, vol. 181, no. 2, pp. 245–251, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. J.-H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters. A, vol. 350, no. 1-2, pp. 87–88, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 7–14, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. N. Herişanu and V. Marinca, “Optimal homotopy perturbation method for a non-conservative dynamical system of a rotating electrical machine,” Zeitschrift fur Naturforschung A, vol. 67, no. 8-9, pp. 509–516, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. F. Wang, W. Li, and H. Zhang, “A new extended homotopy perturbation method for nonlinear differential equations,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 1471–1477, 2012. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Nazari-Golshan, S. S. Nourazar, H. Ghafoori-Fard, A. Yildirim, and A. Campo, “A modified homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane-Emden equations,” Applied Mathematics Letters, vol. 26, no. 10, pp. 1018–1025, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. M. Qayyum and H. Khan, “Behavioral study of unsteady squeezing flowthrough porous medium,” Journal of Porous Media, vol. 19, no. 1, pp. 83–94, 2016. View at Publisher · View at Google Scholar
  23. M. Qayyum, H. Khan, M. T. Rahim, and I. Ullah, “Modeling and analysis of unsteady axisymmetric squeezing fluid flow through porous medium channel with slip boundary,” PLoS ONE, vol. 10, no. 3, Article ID e0117368, 2015. View at Publisher · View at Google Scholar · View at Scopus
  24. H. Aminikhah, “The combined Laplace transform and new homotopy perturbation methods for stiff systems of ODEs,” Applied Mathematical Modelling, vol. 36, no. 8, pp. 3638–3644, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. U. Filobello-Nino, H. Vazquez-Leal, B. Benhammouda et al., “Nonlinearities distribution Laplace transform-homotopy perturbation method,” SpringerPlus, vol. 3, article 594, 2014. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Mustafa, T. Hayat, and S. Obaidat, “On heat and mass transfer in the unsteady squeezing flow between parallel plates,” Meccanica, vol. 47, no. 7, pp. 1581–1589, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. M. Esmaeilpour and D. D. Ganji, “Solution of the Jeffery-Hamel flow problem by optimal homotopy asymptotic method,” Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3405–3411, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. A.-M. Wazwaz, “Approximate solutions to boundary value problems of higher order by the modified decomposition method,” Computers & Mathematics with Applications, vol. 40, no. 6-7, pp. 679–691, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. M. Aslam Noor and S. T. Mohyud-Din, “Variational iteration technique for solving higher order boundary value problems,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1929–1942, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  30. J. C. Butcher, “A history of Runge-Kutta methods,” Applied Numerical Mathematics, vol. 20, no. 3, pp. 247–260, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. O. Khan, F. Khan, C. Ragusa, and B. Montrucchio, “Review of parallel and distributed architectures for micromagnetic codes,” COMPEL, vol. 32, no. 6, pp. 1891–1900, 2013. View at Publisher · View at Google Scholar · View at Scopus
  32. S. Nadeem, R. Mehmood, and N. S. Akbar, “Oblique stagnation point flow of a casson-nano fluid towards a stretching surface with heat transfer,” Journal of Computational and Theoretical Nanoscience, vol. 11, no. 6, pp. 1422–1432, 2014. View at Publisher · View at Google Scholar · View at Scopus
  33. M. Nakamura and T. Sawada, “Numerical study on the laminar pulsatile flow of slurries,” Journal of Non-Newtonian Fluid Mechanics, vol. 22, no. 2, pp. 191–206, 1966. View at Publisher · View at Google Scholar · View at Scopus
  34. C.-Y. Wang, “The squeezing of a fluid between two plates,” Journal of Applied Mechanics, vol. 43, no. 4, p. 579, 1976. View at Publisher · View at Google Scholar
  35. U. Khan, N. Ahmed, S. I. U. Khan, S. Bano, and S. T. Mohyud-din, “Unsteady squeezing flow of a casson fluid between parallel plates,” World Journal of Modelling and Simulation, vol. 10, no. 4, pp. 308–319, 2014. View at Google Scholar · View at Scopus