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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 202
    :height: 163


.. _RefImage_Object_1.svg:


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

The material has the following thermal characteristics:

Thermal conductivity: :math:`{k}_{s}=6\mathrm{kJ}/h/m/°K`

enthalpy volume change: :math:`\Delta H=2.4105\mathrm{kJ}/{m}^{3}`,

and the following characteristics relating to moisturizing behavior:

Heat by hydration level: :math:`{Q}_{0}=1.4904105\mathrm{kJ}/{m}^{3}`

Arrhenius constant: :math:`\mathrm{Ar}=4000/°K`.

**Note:**

The Arrhenius constant is always expressed in degrees Kelvin. Temperatures are expressed in :math:`°C`.

Affinity as a function of hydration:


.. csv-table::

    "**Degree of hydration** :math:`h` ", "**Affinity** :math:`A(h)(1/h)`"
    "0", "6510"
    "0.008", "6360"
    "0.016", "2485"
    "0.019", "2460"
    "0.038", "9520"
    "0.047", "21800"
    "0.08", "37600"
    "0.138", "51600"
    "0.232", "51400"
    "0.351", "28200"
    "0.44", "16100"
    "0.5", "11700"
    "0.63", "5570"
    "0.73", "4240"
    "0.81", "1780"
    "0.88", "302"
    "0.97", "50"
    "1.00", "0"



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

A zero heat flux is imposed on all faces of the solid. Charging is only initiated by a heat source dependent on hydration :math:`\Delta Q={Q}_{0}\Delta h`.


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

The initial temperature is :math:`20.9°C`


Discretization in time
-----------------------

The explicit integration of hydration requires fine temporal discretization until the end of the hydration phenomenon:

From :math:`t=0` to :math:`t=\mathrm{20h}`, :math:`\Delta t=\mathrm{7,5}\mathrm{min}` is 160 steps.

From :math:`t=\mathrm{20h}` to :math:`t=\mathrm{60h}`, :math:`\Delta t=1h` is 40 steps.