Yeah!

First question: is it a laminar or a turbulent flow?In the laminar case the problem is trivial but not so under turbulent conditions. And the second question: is your fluid a shear-thinning or shear-thickening fluid?

It is a shear thinning fluid with laminar flow.

OK, dear Sampada - but where is the problem? What you didnt mention is steady state or non-stationary flow.

Any how, you need to iteratively solve the problem by first estimating the shear distribution with a Newtonian guess for the viscosity, from the shear you estimate the real-world viscosity and repeat the shear calculation with this new guess for the viscosity etc. until convergence. If you cannot achieve convergence then a delay equation can be recommended, sort of nudging. Cheers.