A Expansion in powers of the shear rate and time

For the stationary flows (9.107), we find the following relations for each order of y and so on. 

By solving these equations order by order, we obtain 

Similarly, for the start-up flows (9.146), each order in the time expansion is given by Hr) = y (rF), 

Upon such decomposition, we are led to the three types of angular integrals. They are defined by 

After carrying out all angular integrals, we are left with the radial integrals. 

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