Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

:math:`T(r)={T}_{i}+\Phi \mathrm{log}(\frac{r}{{R}_{i}})`

with: :math:`\mathrm{\{}\begin{array}{ccc}\Phi & \mathrm{=}& \frac{{T}_{e}\mathrm{-}\mathit{Ti}}{\mathrm{log}(\frac{{R}_{e}}{{R}_{i}})}\\ & & \text{les flux}\mathit{radiaux}\text{}(\lambda \frac{\mathrm{\partial }T}{\mathrm{\partial }r})\text{sur les parois du cylindre sont :}\\ {\Phi }_{i}& \mathrm{=}& \text{+}\lambda \mathrm{.}\frac{\Phi }{{R}_{i}}\\ {\Phi }_{e}& \mathrm{=}& \text{+}\lambda \mathrm{.}\frac{\Phi }{{R}_{e}}\end{array}`


.. csv-table::

    ":math:`{T}_{i}:` ", "Internal" skin temperature"
    ":math:`{T}_{e}:` ", "External" skin temperature"



Benchmark results
----------------------

Temperatures and flows at points :math:`A`, :math:`B`,, :math:`D`, :math:`F`.

To test the 'MASS_THER' option (operator CALC_MATR_ELEM), you must use a value given by an object JEVEUX, which corresponds to a checksum.

It is a pure numerical non-regression test.

To test, we activate the debug mode of Calcul.f90 and then we compare the values of the output fields of MASS_THER in CALC_MATR_ELEM with the same thing as the THER_LINEAIRE of the test.


Uncertainty about the solution
---------------------------

Analytical solution.