Reference problem
=====================


Geometry
---------

We consider a wall of thickness :math:`L=2m`.


.. image:: images/1000000000000426000002FAE3C74AA6C927178A.jpg
    :width: 3.7008in
    :height: 2.6417in


.. _RefImage_1000000000000426000002FAE3C74AA6C927178A.jpg:


Material properties
----------------------

The thermal properties are:


* :math:`\rho \mathrm{Cp}=1J/{m}^{3}°C`


* :math:`\lambda (W/m°C)` varies as follows:


    .. image:: images/100002010000055a0000031624 CECA3F57638E8A .png
        :width: 3.1492 in
        :height: 1.8154 in


    .. _refImage_100002010000055a0000031624 CECA3F57638E8A .png:


Boundary conditions and loads
-------------------------------------

On edge :math:`\mathrm{SI}`, a cooling flow of :math:`-1W/{m}^{2}` is imposed.

On edge :math:`\mathrm{SE}`, a temperature of :math:`100°C` is imposed.


Initial conditions
--------------------

At the initial moment, the temperature is uniform and equal to :math:`100°C`.


Temporal discretization
-------------------------

The calculation takes place on :math:`\mathrm{200s}` with a time step of: :math:`\mathrm{0,1}s` between 0 and :math:`\mathrm{40s}` then :math:`\mathrm{0,05}s` between :math:`\mathrm{40s}` and :math:`\mathrm{80s}` and finally :math:`\mathrm{0,1}s` until :math:`\mathrm{200s}`.