1. Reference problem#

1.1. Geometry#

_images/10000730000024B1000011E1341612AA0448C428.svg

1.2. Material properties#

\(\lambda =40W/m°C\)

\(\rho {C}_{p}=7.3{10}^{-4}J/{m}^{3}°C\) or \(\beta =\mid \begin{array}{}0\text{à}0°C\\ {220.10}^{-3}J/{m}^{3}\text{à}300°C\end{array}\)

To deal with the same problem in nonlinear thermics, we define an affine enthalpy \(\beta\) whose slope is equal to the specific heat \(\rho {C}_{p}\)

1.3. Boundary conditions and loads#

\(T(x=0)=100°C={T}_{0}\)

\(T(x=L)=300°C={T}_{L}\)

Heat exchange between the walls located in \(x=0.495\) and \(x=0.505\), with an exchange coefficient of \(80W/{m}^{2}°C\).

1.4. Initial conditions#

\(T(t=0)=\)

\({T}_{0}\) in the left plate

\({T}_{L}\) in the right plate