## Abstract

This paper applies the Taylor series method to solve the one-dimensional steady laminar flow of a third grade fluid and an Oldroyd six constant fluid between two parallel plates. The fluid flow is produced by an external pressure gradient dp/dx. In each case the governing nonlinear boundary value problem is solved and analytical expressions for the fluid velocity, resistance to flow, volume flow rate and the average fluid velocity are obtained. Figures and tables are presented to illustrate the variation of these quantities with the relevant physical parameters. It is shown that in case of a third grade fluid the fluid velocity and other flow variables increase on decreasing the pressure gradient dp/dx or by increasing the non-Newtonian parameter β. For an Oldroyd six constant fluid the velocity magnitude increases on decreasing the pressure gradient or on increasing the constant α_{1} when α_{2}( < α_{1}) and dp/dx are fixed. Also the fluid velocity increases on increasing the constant α_{2} when α_{1}( < α_{2}) and dp / dx are fixed. Similarly, under the same condition, the resistance to the fluid flow and the volume flow rate increase on increasing α_{1} or α_{2}.

Original language | English (US) |
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Pages (from-to) | 57-71 |

Number of pages | 15 |

Journal | Journal of Mathematical Control Science and Applications |

Volume | 4 |

Issue number | 1 |

State | Published - Jan 1 2018 |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics
- Control and Optimization