solving nonnewtonian fluid
HI
I want to solve the flow with nonnewtonian fluid in a tube using numerical method. The carrau model is used as a constitute equation. mu=viscosity gamma=shear rate (mumu_inf)/(mu_0  mu_inf) = (1 + (lamuda*gamma)^2)^((n1)/2) The governing eq. 0=dp/dz + 1/r * d(mu*r*dw/dr)/dr I would like to solve this, but have no idea. For newtonian fluid, it's so simple to analyze this. The constitue eq. and governing eq. are coupled. How can I deal with this problem using numerical approach(tips or algorithm)? If anyone know how to solve this or some open sources availalbe on site or at ftp, please let me know. I would much appreciate your help. Thanks in advance. Peace in God. 
Re: solving nonnewtonian fluid
Your problem equations are: (1)constitutive equation; (2)momentum conservation equation; (3)mass conservation equation.
Solve these three equations by Newton method since they are nonlinear. Your unknowns are pressure, velocity and viscosity. You don't need boundary codnition for your constitutive equation since it's a linear algebraic equation. From mathematical view, this way should work. I don't know if it's practical or not in your case. 
Re: solving nonnewtonian fluid
I just want to know the solving procedure in numerical approach. Normally, I prefer interative method(SOR), not newton method.

Re: solving nonnewtonian fluid
Why not just solve it by iteration/quadrature:
(1) Guess w (w_g) and calculate mu (2) update w (w_*) by integrating the momentum equation (it's a simple quadrature). (3) obtain a new guess for w from w = (1q)w_* + q*w_g (4) repeat from 1 until converged. In 3 q is a relaxation parameter used to stop the iteration oscillating (which it will do if q=1 ). 
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