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


Geometry
---------


.. image:: images/10000000000001450000010544C605D9C3A7B20B.png
    :width: 3.2783in
    :height: 2.6492in


.. _RefImage_10000000000001450000010544C605D9C3A7B20B.png:

Bar Section

It is an infinite bar with a square section on side :math:`L=0.05m`.


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

Material properties are described by the following parameters:

(16 MND5 steel)

:math:`\rho {C}_{P}=5260000{\mathrm{J.m}}^{-3}\mathrm{.}°{C}^{-1}`

:math:`\lambda =33.5{\mathrm{W.m}}^{-1}\mathrm{.}°{C}^{-1}`

Coefficient for metallurgy:

TRC "standard"

:math:`\mathrm{AR3}=830°C`, :math:`\mathrm{alpha}=-0.0306`

:math:`\mathrm{MS0}=400°C`, :math:`\mathrm{AC1}=724°C`, :math:`\mathrm{AC3}=846°C`

:math:`{\tau }_{1}=0.034`, :math:`{\tau }_{3}=0.034`

:math:`{\lambda }_{0}=0.117`, :math:`\mathrm{qsr}=37500`,

:math:`\mathrm{D10}=3.31`, :math:`\mathrm{wsr}=12860`.


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

The temperature is imposed all over the bar at times :math:`t\mathrm{=}\mathrm{0s}`, :math:`\mathrm{200s}`, :math:`\mathrm{1100s}` and :math:`\mathrm{1900s}`.

:math:`T(x,y,t=0)=700°C`

:math:`T(x,y,t=200)=900°C`

:math:`T(x,y,t=1100)=900°C`

:math:`T(x,y,t\mathrm{=}1900)\mathrm{=}100°C`


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

The following variables are initialized to the following values:

:math:`\mathrm{Zf}(x,y\mathrm{,0})=0.7`

:math:`\mathrm{Zp}(x,y\mathrm{,0})=0.0`

:math:`\mathrm{Zb}(x,y\mathrm{,0})=0.3`

:math:`\mathrm{Zm}(x,y\mathrm{,0})=0.0`

:math:`d(x,y\mathrm{,0})=0.0`