Regarding Implementation of Hershel Bulkley Model in Viscosity correlation
 

Hello I am trying to simulate the filling of A356 alloy in semisolid state using Flow 3D. Although Flow 3D has module for semisolid filling with viscosity model of Carreau Model. But I am using Herschel Bulkley's (HB) model for modelling viscosity.
According to HB model, following is the expression for shear stress.

tau = tau_0 (f_s) + exp (B f_s) * k * (gamma_dot) ^ n -------------(1)

from experiments we have determined values for tau_0, B and k for different solid fraction (f_s) say for f_s = 0.25, 0.4 and 0.5 etc.

so if the equation (1) is divided by gamma_dot (which is shear rate) then it will give apparent viscosity. and further terms can be rearranged matching with the corresponding carreau model in flow 3D.
Like matching tau_0 (f_s) / (gamma_dot) will be equivalent to lambda / gamma_dot so tau_0 (f_s) will be equal to labda. similarly other terms can be matched and values can be fed.

but i want to ask how gamma_dot is going to be calculated because the viscosity is dependent upon gamma_dot (ie. shear rate also).

How this can be given as input???