6, there is a radial position where the viscosity equals the equivalent Newtonian viscosity and the shear rate is given by the C-Y model.
As above, the equivalent Newtonian viscosity is defined as that giving the same pressure gradient at the same flow rate, and so, from Eq.
The equivalent viscosity [[mu].sub.e] is the Newtonian viscosity giving the same pressure gradient at the same flow rate.
For a values of 0.5, 1, 2, and 3, the percentage errors in wall shear stress for the local power-law model using the tangent to the viscosity curve at the shear rate 8U/D are respectively 1.2, 1.8, 3.2, and 4.3%, and those for the model tangent to the viscosity curve at the equivalent Newtonian viscosity [[mu].sub.e] are 0.9, 1.5, 3.2, and 4.4%.
For the flow rate 0.1 [cm.sup.3] [s.sup.-1], the equivalent Newtonian viscosity is 0.0797 Pa x s and the corresponding shear rate is 0.0996 [s.sup.-1].
where x is the direction along the length of the slot in the flow direction, and the equivalent Newtonian viscosity by
An effective way to implement the truncated power law model is to switch between Newtonian and power-law flow when both give the same pressure gradient using an equivalent Newtonian viscosity. In general, viscosity variation through the die adversely affects performance.
[T.sup.v] is described in the framework of the Newtonian viscosity as following:
For polymer geosynthetics, the parameter [eta]'([[epsilon].sup.ir], [[epsilon].sup.ir]) is not a constant, unlike the Newtonian viscosity. By replacing [T.sup.v] with Eq.
where v is the velocity vector, [rho] the density, f the body force, [sigma] the total stress tensor, p the pressure, [tau] the deviatoric stress tensor, [C.sub.p] the heat capacity of polymer, T the temperature of polymer, k the thermal conductivity of polymer, [[eta].sub.E] the
Newtonian viscosity, and D the rate of strain tensor.