The application of homotopy analysis method to thin film flows of a third order fluid. (English) Zbl 1146.76588
Summary: 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 M. Siddiqui et al. [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. 7, 1–8 (2006); Chaos Solitons Fractals 35, No. 1, 140–147 (2008; Zbl 1135.76006)] 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 [Zbl 1135.76006] are divergent and hence have no meanings. The variation of velocity field corresponding to pertinent flow parameters is graphically presented and discussed.
MSC:
| 76A20 | Thin fluid films |
| 34A45 | Theoretical approximation of solutions to ordinary differential equations |
| 76A05 | Non-Newtonian fluids |
Citations:
Zbl 1135.76006References:
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| [2] | 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, doi:10.1016/j.chaos.2006.05.026; 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, doi:10.1016/j.chaos.2006.05.026 · Zbl 1135.76006 |
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