Vol. 7, No. 1, 2019

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A note on Couette flow of micropolar fluids according to Eringen's theory

Wilhelm Rickert, Elena N. Vilchevskaya and Wolfgang H. Müller

Vol. 7 (2019), No. 1, 25–50
DOI: 10.2140/memocs.2019.7.25
Abstract

In order to model the flow of liquids with internal rotational degrees of freedom the theory of micropolar fluids according to Eringen is applied. The essentials of the theory are outlined and then specialized to Couette flow. The profiles for linear and angular velocities will be computed, and in particular, we shall also study the rise in temperature due to viscous dissipation, which is frequently ignored by mechanicians. Closed-form solutions for all three fields are derived for different boundary conditions. The question as to how the boundary conditions are realized physically will be discussed.

Keywords
polar materials, theory of constitutive functions, closed-form solutions
Mathematical Subject Classification 2010
Primary: 74A35, 74A20
Milestones
Received: 8 June 2018
Revised: 16 August 2018
Accepted: 20 September 2018
Published: 22 April 2019

Communicated by Francesco dell'Isola
Authors
Wilhelm Rickert
Institut für Mechanik
Fachgebiet Kontinuumsmechanik und Materialtheorie
Technische Universität Berlin
Berlin
Germany
Elena N. Vilchevskaya
Applied Research Laboratory
Institute for Problems in Mechanical Engineering
Russian Academy of Sciences
Saint Petersburg
Russia
Wolfgang H. Müller
Institut für Mechanik
Fachgebiet Kontinuumsmechanik und Materialtheorie
Technische Universität Berlin
Berlin
Germany