Analysis of Couette and Poiseuille flows for fourth-grade fluids and Oldroyd 6-constant fluids with the perturbation technique

The steady laminar flow of a fourth-grade fluid and an incompressible Oldroyd 6-constant fluid, between two parallel plates is considered. Depending upon the relative motion of the plates we analyze three types of flows: Couette flow, Poiseuille flow and generalized Couette flow. In each case, the nonlinear differential equation describing the velocity field is solved using perturbation technique. The velocity profiles for each non-Newtonian model are presented, moreover in several diagrams the accuracy of solutions are discussed. It is observed that the results of perturbation method for fluids with small ε are very exact.

کلیدواژه ها:

fourth-grade fluid ، Oldroyd 6-constant fluid ، perturbation method ، Couette flow ، Poiseuille flow