Non-Newtonian channel flow—exact solutions

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1 Citation (Scopus)


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
Article number005
Pages (from-to)263-279
Number of pages17
JournalIMA Journal of Applied Mathematics
Issue number2
Early online date18 Mar 2020
Publication statusPublished - 26 Apr 2020


  • exact solutions
  • non-Newtonian
  • plane Poiseuille flow

ASJC Scopus subject areas

  • Applied Mathematics

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