A block that is a mm square slides across a flat plate on a thin film of oil. The oil has viscosity (mu) and the film is h mm thick. The block of mass M moves at steady speed U under the influence of constant force F. Indicate the magnitude and direction of the shear stresses on the bottom of the block and top of the plate.

I understand how to find the direction of the shear force. After quick calculations I find:

shear force = (mu)(deltaU/deltay)
I assume a newtonian fluid, thus
shear force = mu (U/y)
Is there a way to solve this without assuming Newtonian fluid?

Question

A block that is a mm square slides across a flat plate on a thin film of oil.  The oil has viscosity (mu) and the film is h mm thick.  The block of mass M moves at steady speed U under the influence of constant force F.  Indicate the magnitude and direction of the shear stresses on the bottom of the block and top of the plate.

I understand how to find the direction of the shear force.  After quick calculations I find:

shear force = (mu)(deltaU/deltay) 
I assume a newtonian fluid, thus
shear force = mu (U/y) 
Is there a way to solve this without assuming Newtonian fluid?