Reference problem
=====================


Geometry
----------


.. csv-table::

    "Inner radius", ":math:`{R}_{i}=0.03m`"
    "Outside radius", ":math:`{R}_{e}=0.05m`"
    "Height", ":math:`l=0.40m`"



Material properties
-----------------------


.. csv-table::

    ":math:`{\lambda }_{t}=2.89W/m°C` ", "thermal conductivity along the :math:`r` axis"
    ":math:`{\lambda }_{z}=40.0W/m°C` ", "thermal conductivity along the :math:`z` axis"
    ":math:`\lambda` circumferential:", "any"



Boundary conditions and loads
-------------------------------------


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


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


* convection on the inner surface: :math:`h=377.0W/\mathrm{m2}°C`,


* convection on the outer surface: :math:`h=339.3W/\mathrm{m2}°C`,


* linear variation in outside temperatures:


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


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


Initial conditions
--------------------

Not applicable.