To size a heat exchanger, I need to know (among other things) the Reynolds number (Re) as an indication of the flow conditions. The Re number depends on the viscosity. In a shear thinning fluid, I can't assume a constant viscosity, instead it will depend on the shear rate that is not constant throughout the pipe. I've asked on Physics SE about the shear rate in turbulent shear thinning fluid flow in a pipe, but received no helpful answer.
Here at Engineering.SE, I am not looking for an in-depth examination of the beauty of the Navier-Stokes equation, but for a practical approach to sizing a heat exchange for such a fluid. How to go about it?