solidConductionSolver
Description
In the solidConduction solver, the temperature distribution is obtained from
the solution of the heat diffusion or energy conservation equation.
Formulation
For an arbitrary body with volume V, bounded by a surface S with outward normal n, this equation can be expressed as:
\[
\begin{aligned}
\int \rho c_p \frac{dT}{dt} dt = \int_S \vec{q''} \cdot \vec{n} dS + \int_V Q dV
\end{aligned}
\]
where:
- \(\rho\) is density kg/m\(^3\)
- \(c_p\) is the specific heat capacity in J/kg/K/
- \(Q\) is the volumetric heat source in W/m\(^3\)
- \(q''\) is the surface heat flux W/m\(^2\)
Using Fourier's law, one can express the heat flux in terms of the temperature gradient as:
\[
\begin{aligned}
\vec{q''} = k \nabla T
\end{aligned}
\]
where \(k\) is thermal conductivity in W/m/k.
Thus, the final form of the equation (applying the Gauss-Green theorem) is:
\[
\begin{aligned}
\int \rho c_p \frac{dT}{dt} dt = \int_V \nabla(k\nabla T) dV + \int_V Q dV
\end{aligned}
\]
Options
As a thermalSubSolver class, solidConduction requires the user to specify a
few additional parameters in the thermalOptions sub-dictionary located
within the solverDict.
Parameters in thermalOptions:
| heatFluxSummary | It activates the calculation of the heat flowing out from every surface of the domain, printing this information on the terminal. It is set to false by default. |
| calculateEnthalpy | It activates the calculation of the enthalpy deposited in the fuel materials (useful for RIA cases). It is set to false by default. |
Usage
Here is an example of the solverDict to be used for activating the
solidConduction thermal solver: