Hyperbolicity and change of type in the flow viscoelastic fluids through pipes |
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| Institution: | 1. Centro de Investigación en Creatividad y Educación Superior, Department of Mechanical Engineering, Universidad de Santiago de Chile, Santiago, Chile;2. Department of Mathematics and Statistical Sciences & Department of Mechanical, Energy and Industrial Engineering, Botswana International University of Science and Technology, Palapye, Botswana;1. Centro de Investigación en Creatividad y Educación Superior & Departmento de Ingeniería Mechánica, Universidad de Santiago de Chile, Santiago, Chile;2. Department of Mathematics and Statistical Sciences & Department of Mechanical, Energy and Industrial Engineering, Bostwana International University of Science and Technology, Palapye, Bostwana;1. Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Iran;2. Gort Engovation – Engineering Sciences, 15 Southmere Ave., Bradford BD73NU, UK |
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| Abstract: | We consider the steady flow of an upper convected Maxwell fluid through a pipe with wavy walls. The analysis is an extension to round pipes of the methods introduced by Yoo and Joseph 1] to study the same problem in plane channels. As in the channel problem, the vorticity in a small cylinder at the center of the pipe becomes hyperbolic when the centerline velocity is larger than the speed of shear waves into rest. The region of hyperbolicity is smaller, but the decay of vorticity is less, when the elasticity parameter is larger. |
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