Couette Flow Between two Cylinders

Hello. I need to solve this problem using PDEtools or just Matlab. I need to calculate the velocity between two coaxial rotating cylinders. The viscosity should depend on r, for example, as unit step function. I should solve it in a rectangle area and in a cylindrical area, and then compare the results... The equation

Then radial component

How can I do it? Thanks

Answer 1

[Precise Simulation]

Here is a CFD tutorial that might help on how to set up and solve Taylor Couette flow with the CFDTool or FEATool MATLAB toolboxes:

https://www.featool.com/model-showcase/04_fluid_dynamics_09_swirl_flow1

Answer 2

[Shadaab Siddiqie]

From my understanding you want to solve differential equations. Here are the references that might help you.