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Diffusion of a line vortex in a second grade fluid embedded in a stagnation point flow. (English) Zbl 1211.76007

Summary: The diffusion of a line vortex embedded in a radially inward axisymmetric stagnation point flow for a second grade fluid is considered. This flow is the diffusion of a line vortex for a second grade fluid when a stagnation point flow is superimposed. The velocity field is in the form of \(\upsilon r = - \alpha r, \upsilon \theta = \upsilon (r, t), \upsilon z = 2\alpha z\), where \(r, \theta , z\) are cylindrical polar coordinates and \(\alpha \) is a constant related to the inward flow. An exact solution of the governing equation is given. It is found that for small values of the time the solution approaches the diffusion of a line vortex in a second grade fluid and for large values of the time the solution tends to the flow of a line vortex in a second grade fluid embedded in a radially inward axisymmetric stagnation point flow.

MSC:

76A05 Non-Newtonian fluids
76D17 Viscous vortex flows
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