I have seen there is one when the core is not moving, though the integral of the radial position of the maximum velocity has to be solved numerically.
I am studying a tube heat exchanger with an inserted scraper which could be simplified to the annulus geometry.
Article Fluid flow for modified power law fluids in concentric annul...
I am not aware of it but perhaps other can comment. As soon as you look at more realistic power law behavior such as the Carreau- Yasada model ( which accounts for the low shear and high shear limits) you are forced into computing the velocity field numerically. Not a difficult task with software packages such as Matlab and Mathematica. Attached is a PDF file of a Mathematica notebook that shows how this can be done and also addresses the issue of how to determine best fit parameters for the Carreau model using "experimental data".
Thank you for the answer Dr Higgins. I am not used to Mathematica, but following your advise I've implemented a mathematical model of the power law flow in Matlab which I have validated. I attach the file in case someone is interested.
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