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Stagnation Point Flow of Walters’ B Fluid Using Hybrid Homotopy Analysis Method

  • Research Article - Mechanical Engineering
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Abstract

A hybrid homotopy analysis method is presented in this paper. This method combines the features of homotopy analysis and shooting methods. In this method, the accuracy and speed of convergence is established by dividing the entire domain in subintervals. In each subinterval, the solution is approximated by employing homotopy analysis method using polynomial base functions. The proposed hybrid homotopy analysis method is computationally more efficient and offered not only numerical values, but also closed-form analytic solutions in each subinterval. The proposed method is applied to discuss the stagnation point flow of viscoelastic Walters’ B fluid. The overshoot in the velocity profile predicted in the existing approximate numerical solutions is controlled, and physically realistic solutions are presented for both weakly and strongly viscoelastic Walters’ B fluids. The convergence and accuracy of the obtained solutions is validated through the residual errors. It is evident from the obtained results that proposed hybrid homotopy analysis method is a powerful technique for solving nonlinear problems.

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Author notes

  1. M. Sajid

    Present address: AS-ICTP, Strada Costiera, Trieste, Italy

Authors and Affiliations

  1. Theoretical Physics Division, PINSTECH, P.O. Nilore, Islamabad, 44000, Pakistan

    M. Sajid

  2. Department of Basic Sciences, Riphah International University, Islamabad, 44000, Pakistan

    Ambreen Arshad

  3. Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

    T. Javed

  4. Department of Mathematics, The Isalmia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    Z. Abbas

Authors
  1. M. Sajid
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  2. Ambreen Arshad
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  3. T. Javed
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  4. Z. Abbas
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Correspondence to Z. Abbas.

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Sajid, M., Arshad, A., Javed, T. et al. Stagnation Point Flow of Walters’ B Fluid Using Hybrid Homotopy Analysis Method. Arab J Sci Eng 40, 3313–3319 (2015). https://doi.org/10.1007/s13369-015-1781-z

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  • DOI: https://doi.org/10.1007/s13369-015-1781-z

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