Carreau Yasuda model is expressed by the following equation. This model has five parameters, zero shear viscosity, infinite shear viscosity, time constant, transition parameter, and power law exponent.
This model has a well defined upper (zero shear viscosity) and lower (infinite shear viscosity) limits for the polymer viscosity. Typically, the value of transition parameter is 2. Time constant lambda alters the nonlinear behavior of the fluid and its dependence on the shear rate. If the time constant is 0, then the fluid becomes Newtonian, with a high value for the time constant, eta becomes a strong function of shear rate. By suitable choice of parameters, many other models can be mimicked by this model.
Syntax
Syntax of the data packet Polymer is as follows:
Polymer 
PolymerName 
{ 

ConstitutuveModel = 
"Carreau" 

Density = 
ρ 

SpecificHeat = 
Cp(T) 

Conductivity = 
K(T) 

CoeffOfThermalExpansion = 
βT 

VolumetricHeatSource = 
Qvol 

TimeConstant = 
λ 

Exponent = 
n 

ZeroShearViscosity = 
η0 

InfiniteShearViscosity = 
ηinf 

TransitionParameter = 
a 

TemperatureDependence = 
"None" } 
Parameter 
Description 
Units 
Data Type 
Condition 
Typical Value 
ConstitutiveModel 
Describes the model used 
None 
String 
Required 
"Carreau" 
Density 
Density of the polymer 
kg/m^3 
Constant 
Required 
995.0 
SpecificHeat 
Specific heat at constant pressure 
J/kg/K 
Constant / F(T) 
Required 
2000.0 
Conductivity 
Thermal conductivity 
W/m/K 
Constant / F(T) 
Required 
0.167 
CoeffOfThermalExpansion 
Indicates the change in volume with change in temperature 
1/K 
Constant 
Required 
1.0e05 
VolumetricHeatSource 
Heat generated/ removed in the volume by methods like electrical heating 
W/m^3 
Constant 
Required 
0.0 
Exponent 
Power law index, defines the dependency of viscosity on shear rate. 
None 
Constant 
Required 
0.66 
ZeroShearViscosity 
Value of viscosity as shear rate tends to 0 
Pas 
Constant 
Required 
100.00 
InfiniteShearViscosity 
Value of viscosity as shear rate tends to infinity 
Pas 
Constant 
Required 
0.1 
TransitionParameter 
A parameter of Carreau Yasuda model 
None 
Constant 
Required 
2 
TimeConstant 
A parameter of Carreau Yasuda model 
s 
Constant 
Required 
1 
TemperatureDependence 
None 
String 
Required 
"WLF" 

ReferenceTemperature 
Temperature at which data is calculated for the initialization step. 
K 
Constant 
Required only if TD is not "None" 
533 
FreezeTemperature 
This is the no flow temperature. Below this temperature, material ceases to flow. 
K 
Constant 
Required only if TD is not "None" 
350 
ActivationEnergy 
A parameter required by Arrhenius model. 
J/mol 
Constant 
Required only if TD is Exp(Q/RT) 
16628 
UniversalGasConstant 
A parameter from state equation PV = nRT, R is universal Gas constant. 
J/mol/K 
Constant 
Required only if TD is Exp(Q/RT) 
8.314 
TemperatureSensitivity 
A derived parameter which has the same physical meaning as Q/R. 
K 
Constant 
Required only if TD is Exp(Tb/T) 
2000 K 
WLFConstant1 
Constant C1 of WLF model 
None 
Constant 
Required only if TD is WLF 
17.44 
WLFConstant2 
Constant C2 of WLF model. This is like DeltaT, hence the value is same in K and Celsius. 
K 
Constant 
Required only if TD is WLF 
51.6 
GlassTransitionTemperature 
Temperature below with polymer molecules ceases to move (frozen). There are few definitions of this term. 
K 
Constant 
Required only if TD is WLF 
320 
Beta 
Parameter in the relationship Exp(Beta(DeltaT)) 
None 
Constant 
Required only if TD is Exp(Beta(DeltaT)) 
0.005 
F(T)  Function of Temperature. Can be specified as a TABLE1 or Tcl function.
TD  TemperatureDependence