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


Geometry
---------


.. image:: images/10000000000001360000010A5387FB2F1F17128C.png
    :width: 2.8134in
    :height: 2.3465in


.. _RefImage_10000000000001360000010A5387FB2F1F17128C.png:

Inner sphere :math:`({S}_{1})` has a radius :math:`{R}_{1}=0.35m`.

Inner sphere :math:`({S}_{2})` has a radius :math:`{R}_{2}=0.45m`.


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

Inner sphere :math:`({S}_{1})` is made of steel:

:math:`{\rho }_{s}=7800\mathrm{kg}/{m}^{3}`

:math:`E=2.1{10}^{11}\mathrm{Pa}`

:math:`\nu =0.3`

The fluid filling the volume between :math:`({S}_{1})` and :math:`({S}_{2})` is water with a density of :math:`{\rho }_{f}=\mathrm{1 000 }\mathrm{kg}/{m}^{3}` (equivalent thermal characteristics: :math:`\lambda =1`, :math:`{\rho }_{f}{C}_{p}=1000`).

We go to model the fluid by 3D thermal modeling.


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

A zero temperature is assumed at a point in the fluid mesh.

The springs are embedded at the level of the massif at points :math:`{P}_{1}` and :math:`{P}_{2}`.