Navier Stokes Equation for Non-newtonian fluid?
 

What should be the modification in General Navier Stokes Eqaution to account for the Non newtonian fluids?
Can somebody please explain?

you have to consider a non-linear relation between stress and velocity gradient

Thanks for the reply FMDenaro..
yes it is understood that for non-newtonian fluid, the shear stress of fluid is not in linear relation with velocity gradient.. the momentum equations contains the viscosity.. how the equations will be modified ? or do we need to modify it at all?

viscosity will be function of the velocity ... many functional relations are proposed in literature

You need to acquire a model for the viscosity. The most simple to use is the "power law model" which is time independent. There are other models for mixtures (less than 5% concentration by volume), which simply apply a coefficient to the viscosity. There are also discontinuous models where if u<x, eta = infinity, if u>x eta = a small number, etc. It is up to you to do the research, but you might get better answers looking in a rheology book.

To answer this question, you don't use the N-S equations, you use the Cauchy Equation, which is a more general form of N-S.

Thanks H0T_S0UP!