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On comparison of the solutions for an axisymmetric flow. (English) Zbl 1173.76039

Summary: Recently, P. D. Ariel [Comput. Math. Appl. 54, No. 7–8, 1169–1183 (2007; Zbl 1138.76030)] explored the axially stretching flow of a viscous fluid in the presence of a velocity slip. He computed the solutions by noniterative technique, the homotopy perturbation method (HPM), and the perturbation and asymptotic methods (for small and large values of the slip parameter, respectively). Through comparison among these solutions, he claimed that HPM solution is the best solution showing close agreement with an exact solution. Here, we recomputed the flow problem considered in Ariel’s work for the series solution by homotopy analysis method (HAM). It is found that HAM solution is identical with the presented exact solution in Ariel’s work. Furthermore, the HAM solution is better than the HPM solution.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects

Citations:

Zbl 1138.76030
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References:

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