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


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

An analytical solution is available in the case of a cylinder of infinite length:

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


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


.. csv-table::

    ":math:`r(m)` "," :math:`T(°C)`"
    ".30000", "105.55"
    ".32275", "99.21"
    ".34550", "93.30"
    ".36825", "87.76"
    ".39100", "82.56"


Temperature value as a function of :math:`r`


.. csv-table::

    ":math:`r(m)` "," :math:`\phi (W/{m}^{2})`"
    ".300", "11577.49"
    ".391", "8822.98"


Value of the flow as a function of :math:`r`


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

Exact solution.


Bibliographical references
---------------------------


* Guide for the validation of structural calculation software packages. French Society of Mechanics AFNOR 1990 ISBN 2-12-486611-7