Abstract
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 language | English |
|---|---|
| Pages (from-to) | 263-279 |
| Number of pages | 17 |
| Journal | IMA Journal of Applied Mathematics |
| Volume | 85 |
| Issue number | 2 |
| Early online date | 17 Mar 2020 |
| DOIs | |
| Publication status | Published - 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 forpublication 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
Keywords
- Non-Newtonian
- Exact Solutions
- Plane Poiseuille Flow