I know what a non newtonian fluid is, although it has been a long time since I studied them at Uni, my question was related to the statment you made that water is non-newtonian in nature as there is nothing that I can find that indicates any sort of time or shear rate viscosity variation.
Pump the water through a pipe, add a heat source to the pipe, does the viscosity of the water change along the pipe? Yes, therefore it’s non-Newtonian as you’ve introduced a time dependance to the viscosity .
You make an assumption that a fluid is newtonian to make the maths simple, pretty much all liquids are going to thin with a change in temperature. In reality it will be non-newtonian to a degree. Just like the ideal gas law is applicable to most cases even though we know it doesn’t model the behavior of real gasses.