Stress tensor for non-Newtonian fluid

[ccrook]

How does one setup the stress tensor for a non-Newtonian fluid? I know that for any fluid the normals should be the pressure and for a power law fluid the shear stress in the direction of flow is related by K(du/dy)^n. Does this mean that all other components are 0 for a symmetric pipe or rectangular duct?

 

[Chestermiller]

How does one setup the stress tensor for a non-Newtonian fluid? I know that for any fluid the normals should be the pressure and for a power law fluid the shear stress in the direction of flow is related by K(du/dy)^n. Does this mean that all other components are 0 for a symmetric pipe or rectangular duct?

For a purely viscous non-Newtonian fluid (not viscoelastic), you use exactly the same form of equation as for a Newtonian fluid (see Bird, Stewart, and Lightfoot), except that you represent the viscosity as a function of the 2nd invariant of the rate of deformation tensor. There is a form of this functionality that gives the same behavior as a power law fluid for simple shear flows.

Chet