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


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

:math:`T(x,y)=\frac{4{T}_{P}}{\pi }\frac{\sum _{n=0}^{\infty }{e}^{[-(\mathrm{2n}+1)\pi y/l]}}{\mathrm{2n}+1}\mathrm{.}\mathrm{sin}\left[\frac{(\mathrm{2n}+1)\pi x}{l}\right]`


.. csv-table::

    "where", ":math:`x`:", "abscissa"
    "", ":math:`y`:", "ordered"
    "", ":math:`{T}_{p}`:", "temperature imposed on the side :math:`[\mathrm{AB}]`"
    "", ":math:`n=` "," :math:`\mathrm{0,1}\mathrm{,2}\mathrm{,3},\dots`"


Reference values are obtained with :math:`n=1000`


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

Temperature at points :math:`E,F,G,H,I,J,K`


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

Analytical solution.


References
----------


1. J.R. Welty, C.E. Wicks, R.E. Wilson, R.E. Wilson, "Fundamentals of Momentum Heat and Mass Transfer", third edition, John Wiley & Sons, 1983.