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


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

The reference solution is the one given in sheet TPLV07 /89 of guide VPCS.

It is an analytical solution given by the following formula:

:math:`\begin{array}{cc}T(x,y,z)& =\mathrm{ax}+\mathrm{by}+\mathrm{cz}+d\\ & =-\mathrm{45x}-\mathrm{80y}-\mathrm{60z}+22.5\end{array}`


.. image:: images/Object_2.svg
    :width: 419
    :height: 341


.. _RefImage_Object_2.svg:

Since the normal flux density imposed on face :math:`y=0.1` is constant, the resulting normal flow is determined analytically.


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

Temperature at the points mentioned in the table above.

Value of the normal flow resulting on the face located in :math:`y=0.1`.


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

None (analytical solution).


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

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