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**Study of a third grade non-Newtonian fluid flow between two parallel plates using the multi-step differential transform method.**
*(English)*
Zbl 1232.76003

Summary: The multi-step differential transform method (MDTM), one of the most effective method, is implemented to compute an approximate solution of the system of nonlinear differential equations governing the problem. It has been attempted to show the reliability and performance of the MDTM in comparison with the numerical method (fourth-order Runge-Kutta) and other analytical methods such as HPM, HAM and DTM in solving this problem. The first differential equation is the plane Couette flow equation which serves as a useful model for many interesting problems in engineering. The second one is the Fully-developed plane Poiseuille flow equation and finally the third one is the plane Couette-Poiseuille flow.

### MSC:

76A05 | Non-Newtonian fluids |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |

### Keywords:

non-Newtonian fluid; third grade fluid; Couette flow; Poiseuille flow; Couette-Poiseuille flow; multi-step differential transform method (MDTM)
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\textit{M. Keimanesh} et al., Comput. Math. Appl. 62, No. 8, 2871--2891 (2011; Zbl 1232.76003)

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### References:

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