I`m studying free convection of non-newtonian fluid inside cylindrical geometry using comsol multiphysics. The fluid can be represented by power law with power law index 0.5.
The disadvantage of power law is that it is defined only within certain range of shear rate. When the convection is just starting, shear rate is close to zero. The corresponding viscosity of the fluid at close to zero shear rate as given by power law is infinite. But in reality, even at zero shear rate, the fluid does have a finite viscosity. So when my simulator solves for the initial period with close to zero viscosity, the viscosity is infinity and the only heat transfer mode is conduction.
Now, It is also mentioned that, when the shear rate is below 0.01 S^-1, it should be assumed constant. But this condition cannot be given to the simulator.
My question is, with the specifications given for the fluid (eg. power law index, consistency index etc.), can I convert this power law model to carreau model?
It will solve my problem of discontinuity, as when the shear rate will be very low, the term inside bracket will be 1 and only constant viscosity term will remain. I will assume infinite shear viscosity as 0, as my fluid is never going to have very high viscosity anyway.
Unfortunately, you do not have sufficient information to do the conversion in a rational way. The power law only tells you about the central part of the Carreau law. The values of the critical sher rate and zero shear viscosity are undefined. You need more data, either from the literature or the lab. If you cannot get that, you will have to guess :-).
Thank you.
What if I assume value of lambda as 1, infinite shear viscosity as 0, and zero shear viscosity as the viscosity at minimum allowable shear rate that is 0.01 S^-1..
Because as the shear rate will be close to 0, the term entire term inside the bracket will become 1 and what will remain is the minimum allowable viscosity.
And the shear rate will not reach a very high value anyway, so we can just eliminate term infinite shear viscosity by assuming it zero.
I hope I could made my point clear.
See section VII.2.8 eq.(4)-(6) in the book:
https://www.academia.edu/11942882/Mec%C3%A1nica_y_Termodin%C3%A1mica_de_Sistemas_Materiales_Continuos
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