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


Geometry
---------


.. image:: images/1000059C00001C5200001C523AE60EA5EC9A169D.svg
    :width: 365
    :height: 365


.. _RefImage_1000059C00001C5200001C523AE60EA5EC9A169D.svg:

Infinite bar with square cross section:

side :math:`\mathrm{2L}=\mathrm{0,10}m`

Point coordinates (in meters):


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C` "," :math:`O`"
    ":math:`x` ", "0.026", "0.350", "0.350", "0.041", "0.0"
    ":math:`y` ", "0.026", "0.350", "0.350", "0.041", "0.0"



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

(:math:`\mathrm{16MND5}` 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`

Microhardness of the various metallurgical phases:


* for :math:`d\mathrm{=}200.\mathit{HV}` ferrite


* for perlite :math:`d\mathrm{=}200.\mathit{HV}`


* for bainite :math:`d\mathrm{=}300.\mathit{HV}`


* for martensite :math:`d=400.\mathrm{HV}`


* for austenite :math:`d=100.\mathrm{HV}`


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

:math:`{T}_{\infty }=15°C`

:math:`h=1675{\mathrm{W.m}}^{-2}\mathrm{.}°{C}^{–1}`


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

:math:`T(x,y\mathrm{,0})=700°\mathrm{C.}`

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

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