where Ts is an auxiliary dependent variable defined on the product space. The remaining quantities are recalled below:
The constraint T = Ts is specified on each side of the extra dimension to connect
T to
Ts.
where ds is the layer thickness (SI unit: m).
The heat source Qs is a density distributed in the layer while
q0 is the received out-of-plane heat flux.
with roti the rotation tensor of layer
i:
and A the transformation matrix between the local and global coordinates systems:
where the u and
d subscripts refer to the upside and downside of the layer, respectively.
When the material has a multilayer structure, ks and
ds in the expressions above are replaced by
dtot and
ktot, which are defined according to
Equation 4-78 and
Equation 4-79: