HeatConduction¶

Type:: section
Appearance:: simple
Excludes:: ContinuumMechanics, Electromagnetics

Heat conduction problems address the computation of the temperature distribution $\SField{T}$ within a body. Such systems are governed by the heat equation (sometimes also called heat conduction equation):

$\begin{eqnarray*} \partial_t \left(c \rho \SField{T} \right) & = & \divo k \grad \SField{T}+\SField{q}, \end{eqnarray*}$

where $c$ is the specific heat capacity, $\rho$ is the mass density, $k$ is the heat conductivity, and $\SField{q}$ is a thermal source density.

Heat convection or heat radiation within the body is not supported. On the boundaries one may impose convection-like conditions or Stefan-Boltzmann radiation conditions, c.f., boundary condition section Thermal.

The table below lists field quantities, which are implicitly defined within the solution fieldbag. This way they can be used by subsequent post-processes.

Quantity	Expression	JCM Tag
thermal flux density	$k\nabla \SField{T}$	ThermalFluxDensity
thermal energy density	$c\rho \SField{T}$	ThermalEnergy