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 |
|---|---|
| Article number | 005 |
| Pages (from-to) | 263-279 |
| Number of pages | 17 |
| Journal | IMA Journal of Applied Mathematics |
| Volume | 85 |
| Issue number | 2 |
| Early online date | 18 Mar 2020 |
| DOIs | |
| Publication status | Published - 26 Apr 2020 |
Keywords
- exact solutions
- non-Newtonian
- plane Poiseuille flow
ASJC Scopus subject areas
- Applied Mathematics
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Cite this
Griffiths, P. (2020). Non-Newtonian channel flow—exact solutions. IMA Journal of Applied Mathematics, 85(2), 263-279. [005]. https://doi.org/10.1093/imamat/hxaa005