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


Presentation
------------

In this test case, we study the pure thermal behavior of a porous medium saturated by a single fluid: water in its liquid phase. In *Code_Aster*, this is a THM model. The associated law of fluid behavior is of type LIQU_SATU.


Geometry
---------


.. image:: images/Object_7.svg
    :width: 250
    :height: 242


.. _RefImage_Object_7.svg:

Coordinates of points :math:`(m)`:

:math:`A\text{:}\mathrm{-}\mathrm{0,5}\text{}\mathrm{-}\mathrm{0,5}\text{}C\text{:}\mathrm{0,5}\text{}\mathrm{0,5}`

:math:`B\mathrm{:}\text{}\mathrm{0,5}\text{}\mathrm{-}\mathrm{0,5}\text{}D\text{:}\mathrm{-}\mathrm{0,5}\text{}\mathrm{0,5}`


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


.. csv-table::

    "solid", "Density :math:`({\mathrm{kg.m}}^{-3})`
    Drained Young's module :math:`E(\mathrm{Pa})`
    Poisson's ratio
    Coefficient of thermal expansion of solid :math:`({K}^{-1})` "," :math:`2\mathrm{\times }{10}^{3}`
    :math:`225.\mathrm{\times }{10}^{6}`
    :math:`0.`
    :math:`8.\mathrm{\times }{10}^{\mathrm{-}6}`"
    "Thermal", "Homogenized conductivity :math:`({\mathrm{W.K}}^{-1.}{m}^{-1})`
    Derivative of conductivity homogenized with respect to temperature", ":math:`1.7`
    :math:`0.`"
    "Homogenization coefficients", "Biot coefficient"
    Porosity", ":math:`{10}^{-12}`
    :math:`0.4`"
    "Homogenized coefficients", "Density :math:`({\mathrm{kg.m}}^{-3})`
    Constant stress heat :math:`({\mathrm{J.K}}^{-1})` "," :math:`1.6\times {10}^{3}`
    :math:`2.85\times {10}^{6}`"



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


* Full item:


*
    * trips :math:`{u}_{x}=0.0m,{u}_{y}=0.0m,{u}_{z}=0.0m`.


    * fluid pressure :math:`\mathrm{PRE1}=0.0\mathrm{Pa}`


* Underside:


    * temperature :math:`T=273K`


* Upper side:


    * heat flow :math:`\mathrm{FLUN}=0.5{\mathrm{J.s}}^{-1}\mathrm{.}{m}^{-2}`


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

The displacement fields, pressure, temperature are initially all zero, but the reference temperature is not zero. It is worth :math:`{T}_{0}=273K`.