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Control of homogeneous shear flow of multimode Maxwell fluids

โœ Scribed by Evgeny Savelev; Michael Renardy

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
485 KB
Volume
165
Category
Article
ISSN
0377-0257

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โœฆ Synopsis

We consider a homogeneous parallel shear flow of a multimode Maxwell fluid. This problem results in a set of ordinary differential equations for the stresses. In this system, we view the shear rate as a control and consider the problem of steering the system to a given state of stress. The objective is to steer the system from given initial stresses to a final state of stress, allowing the shear rate to vary in an arbitrary fashion. We show that this problem is related to a calculus of variations problem. For the case of two modes, we obtain a characterization of the set of achievable streses.

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