https://www.sciencedirect.com/search?qs=flow%20of%20non%20Newtonian%20fluids%20over%20wavy%20surfaces&show=25&sortBy=relevance
It strongly depends on the fluid itself: if it is a thixiotropic or a dilatant fluid like ketchup or honey.
You can find some information in following paper:
Conference Paper ANALYSIS OF AN AUTOMATIC VALVE GEOMETRY FOR CONCRETE AND DRI...
Tu inderstant the behaviour you can perform CFD simulations. Every CFD code has NN-fluid model implemented.
If you need futher help just ask.
Best regards
Franco
The following book deals with wavy surfaces.
Aroon Shenoy, Mikhail Sheremet and Ioan Pop, Convective Flow and Heat Transfer from Wavy Surfaces – Viscous fluids, Porous Media and Nanofluids, CRC Press (2016).
However, the treatment to flow of non-Newtonian fluids over wavy surfaces is scanty. There are mentions of non-Newtonian fluids on pages 17, 18, 106, 137 and cross-reference may get you the information on the effect of wavy surface on pressure drop.
If there is no particular pre-defined profile of the way surface that is of interest, then it might be a good idea to look at equations that are relevant to rough pipes and get some directions of the trends for wavy surfaces.
The following article may be useful.
A. V. Shenoy, Explicit equations for friction factor Reynolds number relation in turbulent flow of power-law fluids through smooth and rough, circular and non-circular pipes, Encyclopedia of Fluid Mechanics, Gulf Publishing Company, Houston, Tx, Supplement 3, Chapter 8, p. 107 (1994).
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