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


Geometry
---------

A cylindrical specimen slice with a diameter :math:`160\mathit{mm}` is modelled.


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    :height: 173


.. _RefImage_1000224200003A8E000018DFB0C2A2A264AB8EC7.svg:


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

Each model makes it possible to validate a diffusion coefficient.

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    :width: 412
    :height: 173


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, namely:


* modeling A: Mensi's law

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        :height: 173


    .. _RefImage_Object_2.svg:


* B modeling: Granger's law

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        :height: 173


    .. _RefImage_Object_3.svg:


* C modeling: definition of :math:`D` in the form of a tablecloth


* D modeling: Bazant's law

    .. image:: images/Object_4.svg
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        :height: 173


    .. _RefImage_Object_4.svg:

The coefficients used are those recommended by Granger in his thesis [:ref:`bib1 <bib1>`]:


+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|SECH_MENSI: |:math:`A\mathrm{=}0.74{10}^{\mathrm{-}13}{m}^{2}\mathrm{/}s`                                                                                                                                                                                                                                                                                                  |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            | :math:`B\mathrm{=}0.05`                                                                                                                                                                                                                                                                                                                                      |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            |                                                                                                                                                                                                                                                                                                                                                              |
+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|SECH_GRANGER|:math:`A\mathrm{=}0.74{10}^{\mathrm{-}13}{m}^{2}\mathrm{/}s`                                                                                                                                                                                                                                                                                                  |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            | :math:`B\mathrm{=}0.05` :math:`{T}_{0}\mathrm{=}293°K` :math:`{Q}_{s}\mathrm{/}R\mathrm{=}4700{K}^{\mathrm{-}1}`                                                                                                                                                                                                                                             |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            |                                                                                                                                                                                                                                                                                                                                                              |
+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|SECH_NAPPE  |We enter Mensi's law                                                                                                                                                                                                                                                                                                                                          |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            |                                                                                                                                                                                                                                                                                                                                                              |
+            + .. image:: images/100047E8000036150000207ACBE9C75B4F76E784.svg                                                                                                                                                                                                                                                                                               +
|            |    :width: 412                                                                                                                                                                                                                                                                                                                                               |
+            +    :height: 173                                                                                                                                                                                                                                                                                                                                              +
|            |                                                                                                                                                                                                                                                                                                                                                              |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            |                                                                                                                                                                                                                                                                                                                                                              |
+            + in tablecloth form                                                                                                                                                                                                                                                                                                                                           +
|            |                                                                                                                                                                                                                                                                                                                                                              |
+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|SECH_BAZANT |:math:`\mathit{D1}\mathrm{=}3.0{10}^{\mathrm{-}10}{m}^{2}\mathrm{/}s`                                                                                                                                                                                                                                                                                         |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            | :math:`\alpha \mathrm{=}0.04` :math:`n\mathrm{=}6`                                                                                                                                                                                                                                                                                                           |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            | .. image:: images/Object_5.svg                                                                                                                                                                                                                                                                                                                               |
+            +    :width: 412                                                                                                                                                                                                                                                                                                                                               +
|            |    :height: 173                                                                                                                                                                                                                                                                                                                                              |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            |                                                                                                                                                                                                                                                                                                                                                              |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            | with :math:`{C}_{0}\mathrm{=}128.8l\mathrm{/}{m}^{3}` and :math:`{C}_{\mathit{eq}}\mathrm{=}58.8l\mathrm{/}{m}^{3}`                                                                                                                                                                                                                                          |
+            +                                                                                                                                                                                                                                                                                                                                                              +
|            |                                                                                                                                                                                                                                                                                                                                                              |
+------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+



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

The drying calculation is carried out over a period of 5 years.


* the temperature remains uniform and is :math:`20°C`


* we apply to :math:`\mathit{FE}`: :math:`{C}_{\mathit{eq}}\mathrm{=}58.8l\mathrm{/}{m}^{3}`


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

The initial conditions consist of the initial temperature, which is taken to be :math:`20°C`, and the initial water concentration, which is equal

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.