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Isotropic / anisotropic materials
Introduction
The studied materials can be isotropic or anisotropic. In other words, the thermal conductivity is:
-
independent of the direction of the applied temperature gradient (isotropic material)
-
dependent on the direction of the applied temperature gradient (anisotropic material)
These two cases are presented in the following sections.
Isotropic materials
Isotropic materials are characterized by a thermal conductivity, which is independent of the direction of the applied temperature gradient.
The 
and 
vectors
are always collinear.
The dependence between 
and 
is a
scalar relationship,
which is written as: 
Anisotropic materials
Anisotropic materials are characterized by a thermal conductivity, which is dependent on the direction of the applied temperature gradient.
The 
and 
vectors
are not collinear.
The dependence between and 
is a
vector relationship,
which is written as: 
with k conductivity tensor:
… in Flux
The model provided in Flux is a simplified model.
The vector dependence between 
and 
which is written as: 
can therefore be expressed in the form of three curves:
, 
, 
The conductivity tensor is written: 