Non-Newtonian channel flow—exact solutions

Paul Griffiths

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)
    345 Downloads (Pure)


    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 date17 Mar 2020
    Publication statusPublished - 26 Apr 2020

    Bibliographical note

    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:


    • exact solutions
    • non-Newtonian
    • plane Poiseuille flow

    ASJC Scopus subject areas

    • Applied Mathematics


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