1. Reference problem#

1.1. Geometry#

_images/1000000000000256000001261087239B6AF2363C.png

\(r(A)=417\mathrm{mm}\)

\(r(B)=496\mathrm{mm}\)

\(r(\mathrm{M1})=443.43\mathrm{mm}\)

\(r(\mathrm{M2})=469.67\mathrm{mm}\)

1.2. Material properties#

\(\lambda =19.97W/m°C\)

\(\rho {C}_{p}=4.89488{10}^{6}J/{m}^{3}°C\)

1.3. Boundary conditions and loads#

Exchange \(\lambda \frac{\partial T}{\partial n}{\mid }_{r={r}_{i}}=h({T}_{\mathrm{ext}}-T(r,t))\)

with \(\begin{array}{}h=\text{40000}W/{m}^{2}°C\\ {T}_{\mathrm{ext}}{(A)}_{t=\mathrm{0s}}=289°C\\ {T}_{\mathrm{ext}}{(A)}_{t=\mathrm{12s}}=20°C\end{array}\)

1.4. Initial conditions#

\(T(r,0)=289°C\) for everything \(r\)

Discretization in time (\(t\)):

12

not for

\([0.,12.]\)

either

\(\Delta t=1.s\)

2

not for

\([12.,20.]\)

either

\(\Delta t=4.s\)

4

not for

\([20.,100.]\)

either

\(\Delta t=20.s\)

2

not for

\([100.,200.]\)

either

\(\Delta t=50.s\)

2

not for

\([200.,400.]\)

either

\(\Delta t=100.s\)

8

not for

\([400.,2000.]\)

either

\(\Delta t=200.s\)