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The thermal boundary layer due to viscous dissipation in impulsively started Poiseuille flow
journal contribution
posted on 2019-01-18, 16:15 authored by Anthony KayViscous dissipation occurs in the boundary layers on the walls of a channel in which a flow is accelerated from rest by the sudden imposition of a pressure gradient. We analyse the thermal boundary layer due to this dissipative heating, obtaining numerical solutions and also asymptotic solutions for the cases of both large and small Prandtl number, with both isothermal and adiabatic wall conditions. With large Pr the temperature rise is controlled by the viscous layer, so is independent of Pr and of the wall condition. With small Pr heat is conducted away from the viscous layer more rapidly, so the temperature rise is reduced as Pr decreases.
History
School
- Science
Department
- Mathematical Sciences
Published in
IMA Journal of Applied MathematicsCitation
KAY, A., 2019. The thermal boundary layer due to viscous dissipation in impulsively started Poiseuille flow. IMA Journal of Applied Mathematics, 84(3), pp. 517–532.Publisher
Oxford University Press on behalf of the Institute of Mathematics and its Applications © The authorVersion
- AM (Accepted Manuscript)
Publisher statement
This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record KAY, A., 2019. The thermal boundary layer due to viscous dissipation in impulsively started Poiseuille flow. IMA Journal of Applied Mathematics, 84(3), pp. 517–532 is available online at: https://academic.oup.com/imamat/article/84/3/517/5301756 and https://doi.org/10.1093/imamat/hxz001.Acceptance date
2019-01-10Publication date
2019-01-28ISSN
0272-4960eISSN
1464-3634Publisher version
Language
- en