Index

Arrhenius law

Ver:1
 

DESCRIPTION

For a generalized Newtonian fluid, the constitutive equation has the form

S = 2 * eta * D

where S is the extra-stress tensor, D is the rate of deformation tensor, and eta is the viscosity.

The temperature dependence of the viscosity is denoted by a function H(T), where T is the temperature.
H(T) comes as a factor in the viscosity law:

eta(g,T) = F(g)*H(T)

For the Arrhenius law, the function H(T) is written as follows :

H(T) = exp [ alpha / ( T - T0 ) - alpha / ( Talpha - T0 ) ]

where alpha is the ratio of the activation energy to the Blotzman constant, Talpha is a reference temperature,
and T0 is a scaling temperature when non-absolute temperature scales are used.

By default, alpha = Talpha = T0 = 0.
 
 

  OPTIONS  
 -1   Upper level menu
  1   Modify  alfa   = 0.0000000E+00
  2   Modify  talfa  = 0.0000000E+00
  3   Modify  t0     = 0.0000000E+00
NOTES If non-absolute temperatures are used, a scaling temperature T0 must be given
(e.g. T0 = -273.15 if Celcius temperature scale is used).

A high value of the parameter alpha leads to strong non-linearities. A Picard iteration is recommended
instead of a full Newton iteration. In case the program diverges, an evolution scheme (on alpha) must be used.

The units for alpha, Talpha and T0 are :
 
parameter
mass
length
time
temperature
alfa
-
-
-
1
talfa
-
-
-
1
t0
-
-
-
1

SEE ALSO
  • generalized Newtonian fluids (UM)
  • continuum equations (UM)
  • temperature dependence of viscosity (RM)
  • evolution (UM)
  • s-dependence (RM)
  • create a new task (RM)
  • system of units (RM)
    •