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Some analytical solutions for second-grade fluid flows for cylindrical geometries. (English) Zbl 1090.76006
Summary: This paper deals with some unsteady flow problems for second-grade fluids. The flows are generated by a sudden application of constant pressure gradient or by an impulsive motion of boundary. The velocities of the flows are described by partial differential equations. Exact analytic solutions of some of these differential equations are obtained. The well-known solutions for Navier-Stokes fluid appear as limiting cases of our solutions.
MSC:
76A05Non-Newtonian fluids
76M45Asymptotic methods, singular perturbations (fluid mechanics)