1. Reference problem#

1.1. Geometry#

Inner radius

\({R}_{i}=0.03m\)

Outside radius

\({R}_{e}=0.05m\)

Height

\(l=0.40m\)

1.2. Material properties#

\({\lambda }_{t}=2.89W/m°C\)

thermal conductivity along the \(r\) axis

\({\lambda }_{z}=40.0W/m°C\)

thermal conductivity along the \(z\) axis

\(\lambda\) circumferential:

any

1.3. Boundary conditions and loads#

  • flow density \(\varphi =-500W/\mathrm{m²}\) across the surface \(z=0\) (outgoing flow),

  • flow density \(\varphi =+500W/\mathrm{m²}\) across the surface \(z=0.4\) (incoming flow),

  • convection on the inner surface: \(h=377.0W/\mathrm{m2}°C\),

  • convection on the outer surface: \(h=339.3W/\mathrm{m2}°C\),

  • linear variation in outside temperatures:

  • on the surface \({R}_{i}\): \({T}_{i}^{e}=130°C\) in \(z=0\); \({T}_{i}^{e}=135°C\) in \(z=0.4\) \(({T}_{i}^{e}=130+12.5z)\)

  • on the surface \({R}_{e}\): \({T}_{e}^{e}=20°C\) in \(z=0\); \({T}_{e}^{e}=25°C\) in \(z=0.4\) \(({T}_{e}^{e}=20+12.5z)\)

1.4. Initial conditions#

Not applicable.