Hyperbolicity and change of type in the flow of viscoelastic fluids through channels

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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