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The application of homotopy analysis method to thin film flows of a third order fluid

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  • Sajid, M.
  • Hayat, T.

Abstract

The aim of the current article is to provide the analytic solutions to two thin film flows of a third order fluid. These are: (i) when the fluid moves on a belt and (ii) when the fluid moves down an inclined plane. Both problems have been solved using homotopy analysis method (HAM). These problems were already solved by Siddiqui et al. [Siddiqui AM, Mahmood R, Ghori QK. Thin film flow of a third grade fluid on a moving belt by He’s homotopy perturbation method. Int J Non-Linear Sci Numer Simul 2006;7:1–8, Siddiqui AM, Mahmood R, Ghori QK. Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane. Chaos, Solitons & Fractals in press] using homotopy perturbation method (HPM) and traditional perturbation technique. With the help of two examples, it is shown that HPM is a special case of HAM. It has been noted that the solution up to second order is not enough in the case of flow on a moving belt. It is explicitly proved that the solutions of the flow down an inclined plane given in reference [Siddiqui AM, Mahmood R, Ghori QK. Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane. Chaos, Solitons & Fractals in press] are divergent and hence have no meanings. The variation of velocity field corresponding to pertinent flow parameters is graphically presented and discussed.

Suggested Citation

  • Sajid, M. & Hayat, T., 2008. "The application of homotopy analysis method to thin film flows of a third order fluid," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 506-515.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:2:p:506-515
    DOI: 10.1016/j.chaos.2006.11.034
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    References listed on IDEAS

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    1. Wu, Yongyan & Wang, Chun & Liao, Shi-Jun, 2005. "Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1733-1740.
    2. Wu, Wan & Liao, Shi-Jun, 2005. "Solving solitary waves with discontinuity by means of the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 177-185.
    3. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    4. Tan, Yue & Xu, Hang & Liao, Shi-Jun, 2007. "Explicit series solution of travelling waves with a front of Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 462-472.
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    Cited by:

    1. Alomari, A.K. & Noorani, M.S.M. & Nazar, R., 2009. "On the homotopy analysis method for the exact solutions of Helmholtz equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1873-1879.
    2. Adesanya, Samuel O. & Makinde, Oluwole D., 2015. "Irreversibility analysis in a couple stress film flow along an inclined heated plate with adiabatic free surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 222-229.
    3. Yadav, Pramod Kumar & Yadav, Nitisha, 2024. "Magnetohydrodynamic study of Micropolar fluid flow in the porous walled channel with variable viscosity and thermal conductivity: HAM Solution," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. AL-Jawary, M.A., 2017. "A semi-analytical iterative method for solving nonlinear thin film flow problems," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 52-56.

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