1. Reference problem#
1.1. Geometry#
\(\stackrel{ˉ}{\mathrm{AB}}=\stackrel{ˉ}{\mathrm{BC}}=L=0.1m\)
\(x(\mathrm{M1})=0.02m\)
\(x(\mathrm{M2})=0.08m\)
1.2. Material properties#
\(\lambda =1W/m°C\)
\(\rho {C}_{P}=1000J/{m}^{3}°C\)
1.3. Boundary conditions and loads#
exchange \(\lambda {\frac{\partial T}{\partial n}\mid }_{x=\pm L}=h({T}_{\mathrm{ext}}-T(x,t))\)
with: \(h=100.W/{m}^{2}°C\)
\(\{\begin{array}{}{T}_{\mathrm{ext}}{(C)}_{t=0}=100.\\ {T}_{\mathrm{ext}}{(C)}_{t={10}^{-2}}=0.\end{array}\)
1.4. Initial conditions#
\(T(x,0)=100°C\) for everything \(x\)
Discretization in time (t):
10 steps for |
\([0.,\mathrm{1.D}–2]\) |
either |
\(\Delta t={10}^{–3}s\) |
9 steps for |
\([1D–2,\mathrm{1.D}–1]\) |
either |
\(\Delta t={10}^{–2}s\) |
9 steps for |
\([\mathrm{1.D}–1,1.]\) |
either |
\(\Delta t={10}^{–1}s\) |
5 steps for |
\([1.,2.]\) |
either |
\(\Delta t=2.{10}^{–1}s\) |
8 steps for |
\([2.,10.]\) |
either |
\(\Delta t=1s\) |