FEM EquationHeat

Description
This equation describes the heat transfer in rigid and fluid bodies.

For info about the math of the equation, see the Elmer models manual, section Heat Equation.

Usage

 * 1) After adding an Elmer solver as described here, select it in the tree view.
 * 2) Now either use the toolbar button [[Image:FEM_EquationHeat.svg|24px]] or the menu.
 * 3) Change the equation's solver settings or the general solver settings if necessary.

Solver Settings
For the general solver settings, see the Elmer solver settings.

The heat equation provides these special settings:
 * : There is also a residual-free-bubbles formulation of the stabilized finite-element method. It is more accurate and does not include any ad hoc terms. However, it may be computationally more expensive. If both and  are false, no stabilization is used and then the results might easily be nonsensical. Note: If during the first solver iteration you get this error: ERROR:: IterSolve: Numerical Error: System diverged over maximum tolerance. The  method failed. In this case set  to true.

Equation:
 * : The type of convection to be used in the heat equation. Note: If this is not set to None, must be to true otherwise the convection term will not be considered for the heat equation.
 * : The model use for phase changes (ice to water etc.). The model  Spatial 1 is the apparent-heat-capacity method, Spatial 2 and Temporal are effective-heat-capacity methods. For more info about the models, see this paper (section 2.5.2.2) (is in German). In the paper it was also shown that Spatial 1 has numerical problems on larger temperature gradients and that Spatial 2 was preferred for the phase change ice to water.

Analysis Feature Information
The heat equation takes the following analysis features into account if they are set:


 * [[Image:FEM_ConstraintBodyHeatSource.svg|32px]] Body heat source
 * [[Image:FEM_ConstraintInitialTemperature.svg|32px]] Initial temperature condition
 * [[Image:FEM_ConstraintTemperature.svg|32px]] Temperature boundary condition

Note
Except for calculations in 2D, for all the above analysis features it is important that they act on a face or a body. Constraints in 3D set to lines or vertices are not recognized by the Elmer solver.

Result
The result is the temperature in Kelvin.