1. Reference problem#

1.1. Geometry#

Bar Section

It is an infinite bar with a square section on side \(L=0.05m\).

Material properties are described by the following parameters:

(16 MND5 steel)

\(\rho {C}_{P}=5260000{\mathrm{J.m}}^{-3}\mathrm{.}°{C}^{-1}\)

\(\lambda =33.5{\mathrm{W.m}}^{-1}\mathrm{.}°{C}^{-1}\)

Coefficient for metallurgy:

TRC « standard »

\(\mathrm{AR3}=830°C\), \(\mathrm{alpha}=-0.0306\)

\(\mathrm{MS0}=400°C\), \(\mathrm{AC1}=724°C\), \(\mathrm{AC3}=846°C\)

\({\tau }_{1}=0.034\), \({\tau }_{3}=0.034\)

\({\lambda }_{0}=0.117\), \(\mathrm{qsr}=37500\),

\(\mathrm{D10}=3.31\), \(\mathrm{wsr}=12860\).

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

\(T(x,y,t=0)=700°C\)

\(T(x,y,t=200)=900°C\)

\(T(x,y,t=1100)=900°C\)

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

The following variables are initialized to the following values:

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

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

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

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

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