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


Geometry
---------


.. image:: images/10000730000024B1000011E1341612AA0448C428.svg
    :width: 473
    :height: 230


.. _RefImage_10000730000024B1000011E1341612AA0448C428.svg:


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

:math:`\lambda =40W/m°C`

:math:`\rho {C}_{p}=7.3{10}^{-4}J/{m}^{3}°C` or :math:`\beta =\mid \begin{array}{}0\text{à}0°C\\ {220.10}^{-3}J/{m}^{3}\text{à}300°C\end{array}`

To deal with the same problem in nonlinear thermics, we define an affine enthalpy :math:`\beta` whose slope is equal to the specific heat :math:`\rho {C}_{p}`


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

:math:`T(x=0)=100°C={T}_{0}`

:math:`T(x=L)=300°C={T}_{L}`

Heat exchange between the walls located in :math:`x=0.495` and :math:`x=0.505`, with an exchange coefficient of :math:`80W/{m}^{2}°C`.


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


.. csv-table::

    ":math:`T(t=0)=` "," :math:`{T}_{0}` in the left plate"
    "", ":math:`{T}_{L}` in the right plate"