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


Geometry
---------

We are dealing with a one-dimensional problem in Cartesian coordinates. The "structure" considered is finally a segment of length 1


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


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

A pressure varying linearly from :math:`P` in :math:`x\mathrm{=}0` to :math:`0` in :math:`x\mathrm{=}1` is imposed:

.. image:: images/Object_1.svg
    :width: 97
    :height: 22


.. _RefImage_Object_1.svg:

In :math:`x\mathrm{=}0`: the temperature is imposed zero

In :math:`x\mathrm{=}1`: the temperature is set to 1.


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

:math:`T(x)\mathrm{=}0` everywhere

We are interested in the permanent regime