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

Calculation method used for the reference solution
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:math:`T=\frac{Q{L}^{2}}{2\lambda }(1-{(\frac{x}{L})}^{2}-\frac{32}{\pi }\sum _{i=0}^{\infty }\frac{{(-1)}^{i}}{{(\mathrm{2i}+1)}^{3}}\mathrm{cos}(\frac{\mathrm{2i}+1}{\mathrm{2L}}\pi )\mathrm{exp}(\frac{-\lambda }{\rho c}{(\frac{\mathrm{2i}+1}{\mathrm{2L}}\pi )}^{2}t))`

Reference values are obtained with :math:`i=1000`.


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

Temperature at points :math:`E` and :math:`F` at times :math:`t=0.25` and :math:`0.5s`


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

Analytical solution.


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


* B.M. Nicolaï, J. de Baerdemaeker, "Computation of heat conduction in materials with random variable thermophysical properties", Int. J. num. Meth. Engng, vol. 36, pp. 523-536, 1993.