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Couette and Poiseuille flows of an Oldroyd 6-constant fluid with magnetic field. (English) Zbl 1067.35074
The inadequacy of the classical Navier-Stokes model when describing rheologically complex fluids has led to the formulation of several non-Newtonian fluid models. This paper considers the Oldroyd 6-constant fluid model governed by a nonlinear differential equation. The three nonlinear boundary value problems are solved using a homotopy analysis and a numerical method. The solutions for a Navier-Stokes fluid, as well as those corresponding to an Oldroyd 3-constant fluid, and for a Maxwell fluid, are shown to appear as limiting cases.

35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
76A05 Non-Newtonian fluids
Full Text: DOI
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