Non-Newtonian channel flow—exact solutions

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In this short communication, exact solutions are obtained for a range of non-Newtonian flows between stationary parallel plates. The pressure-driven flow of fluids with a variational viscosity that adheres to the Carreau governing relationship are considered. Solutions are obtained for both shear-thinning (viscosity decreasing with increasing shear-rate) and shear-thickening (viscosity increasing with increasing shear-rate) flows. A discussion is presented regarding the requirements for such analytical solutions to exist. The dependence of the flow rate on the channel half width and the governing non-Newtonian parameters is also considered.
Original languageEnglish
Pages (from-to)263-279
Number of pages17
JournalIMA Journal of Applied Mathematics
Issue number2
Early online date17 Mar 2020
Publication statusPublished - 26 Apr 2020

Bibliographical note

© The Author(s) 2020. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is a pre-copyedited, author-produced version of an article accepted for
publication in IMA Journal of Applied Mathematics following peer review. The version of record Griffiths, P 2020, 'Non-Newtonian channel flow—exact solutions', IMA Journal of Applied Mathematics, vol. 85, no. 2, 005, pp. available online at:


  • Non-Newtonian
  • Exact Solutions
  • Plane Poiseuille Flow


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