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Helical flows of Maxwell fluid between coaxial cylinders with given shear stresses on the boundary. (English) Zbl 1201.35159
Summary: Helical flows for a Maxwell fluid are studied between two infinite coaxial circular cylinders, at time \(t=0^+\); the inner cylinder begins to rotate around its axis and to slide along the same axis due to the torsional and longitudinal time dependent shear stresses. Exact solutions obtained with the help of finite Hankel transform and, presented under series form, satisfy all imposed initial and boundary conditions. The corresponding solutions for Newtonian fluid are also given as limiting cases. Finally, the influence of pertinent parameters-as well as a comparison between Maxwell and Newtonian fluids-on the velocity components and shear stresses is also analyzed by graphical illustrations.

MSC:
35Q35 PDEs in connection with fluid mechanics
35C05 Solutions to PDEs in closed form
35A22 Transform methods (e.g., integral transforms) applied to PDEs
76A05 Non-Newtonian fluids
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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