Material
The material properties
- volumetric mass density $\rho$,
- specific heat capacity $c$ and
- thermal conductivity $\lambda$
can be specified as
- temperature-independent (here called static) or
- temperature-dependent (here called dynamic)
In case of temperature-independent material properties, the variables $\rho$, $c$ and $\lambda$ are defined as constant real values.
In case of temperature-dependent material properties, the variables $\rho$, $c$ and $\lambda$ are defined via Vectors. If the specific heat capacity is defined by
\[c(\theta) = 11 + 22~\theta + 33~\theta^2\]
with temperature $\theta$, then the corresponding Vector is implemented as c = [11, 22, 33]. If at least one material property is temperature-dependent then the other properties have to be implemented as Vectors.
Anisotropic heat conduction
Additional to the specification temperature-dependent vs. -independent the thermal conductivity can be assumed as isotropic or anisotropic.
In case of anisotropic heat conduction the thermal conductivity of the geometrical object depends on the spatial direction. Mathematically noted, the thermal conductivity $\lambda$ is now a matrix or matrix-valued function, e.g. for cuboids
\[\lambda = \begin{pmatrix} \lambda_{x} & 0 & 0 \\ 0 & \lambda_{y} & 0 \\ 0 & 0 & \lambda_{z} \end{pmatrix}\]
or
\[\lambda(\theta) = \begin{pmatrix} \lambda_{x}(\theta) & 0 & 0 \\ 0 & \lambda_{y}(\theta) & 0 \\ 0 & 0 & \lambda_{z}(\theta) \end{pmatrix}.\]
So for anisotropic heat conduction two (for 2D = plate) or three components (for 3D = cuboid) of thermal conductivity $\lambda$ have to be defined.
In conclusion, the material can be defined as
- temperature-independent and isotropic:
StaticIsoProperty - temperature-dependent and isotropic:
DynamicIsoProperty - temperature-independent and anisotropic:
StaticAnisoProperty - temperature-dependent and anisotropic:
DynamicAnisoProperty