Application of the taylor series method for the flow of non-Newtonian fluids between parallel plates

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 α₁ when α₂( < α₁) and dp/dx are fixed. Also the fluid velocity increases on increasing the constant α₂ when α₁( < α₂) and dp / dx are fixed. Similarly, under the same condition, the resistance to the fluid flow and the volume flow rate increase on increasing α₁ or α₂.