Can someone tell me how to insert the non-Newtonian correlations (of a fluid) in the Navier-stokes equations and solve them. I mean discretize the equations and do the rest to solve the set of linear equations in Fortran, C++, or Matlab.

Thanks

See for example

Finite Element Analysis of Non-Newtonian Flow Huang, Li, Usmani Springer

or

Numerical Simulation of Non-Newtonian Flow Crochet Elsevier