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


Geometry
---------


.. image:: images/10000CBE0000313200000FD00F25CA2D7CA2FD7F.svg
    :width: 634
    :height: 204


.. _RefImage_10000CBE0000313200000FD00F25CA2D7CA2FD7F.svg:


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

These are the characteristics of aluminum indicated by s for the solid phase and by l for the liquid phase. They are assumed to be constant within each phase.


.. csv-table::

    "Density", ":math:`{\rho }_{S}=2550\mathrm{kg}/{m}^{3}` "," :math:`{\rho }_{1}=2390\mathrm{kg}/{m}^{3}`"
    "Volume heat", ":math:`{c}_{S}=3.{10}^{6}J/{m}^{3}°C` "," :math:`{c}_{1}=2.58{10}^{6}J/{m}^{3}°C`"
    "Thermal conductivity", ":math:`{k}_{S}=210W/m°C` "," :math:`{k}_{1}=95W/m°C`"
    "Latent heat of fusion", ":math:`L=437.44{10}^{-3}\mathrm{J.kg}` ", ""
    "Melting temperature", ":math:`{T}_{m}=660.°C` ", ""
    "Volume enthalpy change", ":math:`\Delta H=1.08048{10}^{9}J/{m}^{3}` ", ""



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

Temperature imposed at the extremities.

:math:`{T}_{0}=580°C` in :math:`x=0`

:math:`{T}_{i}=740°C` in :math:`x=l`


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

Uniform initial temperature

:math:`{T}_{\mathrm{init}}={T}_{i}=740°C`