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


Geometry
---------

Each square is meshed with a distinct element type.


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+ .. image:: images/10003FD6000019F2000019657F7021F55C4ED73B.svg                                                                                                  + .. image:: images/10009C0800001D5200001B386CEE347C10C3FE20.svg                                                              +
|    :width: 243                                                                                                                                                  |    :width: 2.7626in                                                                                                         |
+    :height: 229                                                                                                                                                 +    :height: 2.4571in                                                                                                        +
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|**For all 2D modellings.** **For 3D modellings.** (**Note:** in AXISet AXIS_DIAG, the axis of rotation is OY and the x-axis therefore corresponds to the radius).|(**Note:** in 3D_ DIAG, only the 4 hexahedra at the bottom left are meshed).                                                 |
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Material properties
-----------------------

The thermal properties applied to the model are:


* :math:`\lambda \mathrm{=}1.0W\mathrm{/}m°C`


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

Not defined.


Temperature field
--------------------

The temperature field is directly assigned to the model from a function. For each modeling, the flow calculation is tested for a linear thermal field and for a quadratic thermal field.

For 2D models PLAN and PLAN_DIAG (models A and B), the two fields successively affected are:


* :math:`T(X,Y)\mathrm{=}\mathrm{2.X}+\mathrm{3.Y}`


* :math:`T(X,Y)\mathrm{=}{\mathrm{2.X}}^{2}+{\mathrm{3.Y}}^{2}`

For 2D models AXIS and AXIS_DIAG (C and D models), the two fields successively affected are:


* :math:`T(X,Y,Z)\mathrm{=}\mathrm{2.R}+\mathrm{3.Y}` (with :math:`R\mathrm{=}\sqrt{{X}^{2}+{Z}^{2}}\mathrm{=}X` in the :math:`(\mathit{OXY})` mesh plane)


* :math:`T(X,Y,Z)\mathrm{=}{\mathrm{2.R}}^{2}+{\mathrm{3.Y}}^{2}`

For 3D and 3D_ DIAG models (E and F models), the two fields successively affected are:


* :math:`T(X,Y,Z)\mathrm{=}\mathrm{2.X}+\mathrm{3.Y}+\mathrm{4.Z}`


* :math:`T(X,Y,Z)\mathrm{=}{\mathrm{2.X}}^{2}+{\mathrm{3.Y}}^{2}+{\mathrm{4Z}}^{2}`