Dear Colleagues,
I am looking for a series solution of the velocity in a rectangular cross-section in the presence of a power-law fluid in laminar regime. I found the expression of the average velocity, see Laminar Non-Newtonian FluidFlow in Noncircular Ducts and Microchannels, by Muzychka and Edge, Journal of Fluids Engineering - ASME, 2008, but I could not find the expression for the maximum velocity. Any suggestion?
Sincerely
Sandro
Have a look here https://www.researchgate.net/post/What_is_the_velocity_profile_of_laminar_flow_in_a_square_pipe
there is a paper attached by Janusz Pudykiewicz
Unfortunately, the link above in the previous reply concerns rather trivial matters. Specifically, it only discusses only the linearly viscous Newtonian fluid. These results are all very well known, see for example, Panton's "Incompressible Flow" textbook.
More to the point of the question asked: There is classic paper studying the flow of a power-law fluid in a rectangular channel, numerically, Article The Flow of Power-Law Fluids in Rectangular Ducts
It is claimed therein that an analytical solution does not exist due to the nonlinearity of the unidirectional flow problem for the power-law fluid. I tend to agree.
Nevertheless, I do wonder if an accurate matched asymptotic expansion (blending the "slot" flow of a power-law fluid flow, which has an exact solution, with another solution within the frictional boundary layers near the lateral side-walls) could be found for this problem?
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