title: Steady flows of second-grade fluids in a channel
metadata.name: dc.contributor.author
metadata.value: Baranovskii, Evgenii S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Artemov, Mikhail A
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-01-31T08:53:26Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-01-31T08:53:26Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Baranovskii E. S., Artemov M. A. Steady flows of second-grade fluids in a channel. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017, vol. 13, iss. 4, pp. 342–353.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.401
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9044
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper, we study mathematical models describing steady flows of second-grade fluids in a
  plane channel. The flows are driven by constant pressure gradient.We consider various boundary
  conditions on the channel walls, namely, the no-slip condition, the free-slip condition, threshold
  slip conditions, and mixed boundary conditions. For each of the boundary value problems, we
  construct exact solutions, which characterize the velocity and pressure fields in the channel.
  Using these solutions, we show that the pressure significantly depends on the normal stress
  coefficient α, especially in those subdomains, where the change of flow velocity is large (in the
  transverse direction of the channel). At the same time, the velocity field is independent of α,
  and therefore coincides with the velocity field that occurs in the case of a Newtonian fluid (when
  α = 0). Moreover, we establish that the key point in a description of stick-slip flows is value of
  ξh, where ξ is module of the gradient pressure, h is the half-channel height. If ξh exceeds some
  threshold value, then the slip regime holds at solid surfaces, otherwise the fluid adheres to the
  channel walls. If it is assumed that the free-slip condition (Navier’s condition) is provided on
  one part of the boundary, while on the other one a stick-slip condition holds, then for the slip
  regime the corresponding threshold value is reduced to a certain extent, but not by more than
  half. Refs 15.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа Е. С. Барановского выполнена при финансовой поддержке Российского фонда фундаментальных исследований (грант № 16-31-00182 мол_а).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 13; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: non-Newtonian fluids
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: second-grade fluids
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the Poiseuille flow
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: slip boundary conditions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: boundary value problems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: exact solutions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Steady flows of second-grade fluids in a channel
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01-Baranovsky.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9044/1/01-Baranovsky.pdf
resources.format: Adobe PDF
resources.size: 232,76 kB