Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method.

*(English)*Zbl 1163.34307Summary: The similarity transform for the steady three-dimensional problem of a condensation film on an inclined rotating disk gives a system of nonlinear ordinary differential equations which are analytically solved by applying a newly developed method namely the homotopy analysis method (HAM). The analytic solutions of the system of nonlinear ordinary differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. The velocity and temperature profiles are shown and the influence of the Prandtl number on the heat transfer and the Nusselt number is discussed in detail. The validity of our results is verified by numerical results.

##### MSC:

34A34 | Nonlinear ordinary differential equations and systems, general theory |

##### Keywords:

homotopy analysis method; system of nonlinear ordinary differential equations; convergence; rotating disk; film thickness
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\textit{M. M. Rashidi} and \textit{S. Dinarvand}, Nonlinear Anal., Real World Appl. 10, No. 4, 2346--2356 (2009; Zbl 1163.34307)

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