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.
Bibliographical noteThis 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. 263-279.is available online at: https://dx.doi.org/10.1093/imamat/hxaa005
- exact solutions
- plane Poiseuille flow
ASJC Scopus subject areas
- Applied Mathematics