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Homotopy analysis of Couette and Poiseuille flows for fourth-grade fluids. (English) Zbl 1080.76008

Summary: We consider the steady flow of a fourth-grade fluid between two parallel plates. Depending upon the relative motion of the plates, we analyze four types of flows: Couette flow, plug flow, Poiseuille flow and generalized Couette flow. In each case, the nonlinear differential equation describing the velocity field is solved using perturbation technique and homotopy analysis method. The pressure distribution is also found. It is observed that the homotopy analysis method is more efficient and flexible than the perturbation technique.

MSC:

76A05 Non-Newtonian fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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