2. Benchmark solution

2.1. Calculation method used for the reference solution

\(T=\frac{Q{L}^{2}}{2\lambda }(1-{(\frac{x}{L})}^{2}-\frac{32}{\pi }\sum _{i=0}^{\infty }\frac{{(-1)}^{i}}{{(\mathrm{2i}+1)}^{3}}\mathrm{cos}(\frac{\mathrm{2i}+1}{\mathrm{2L}}\pi )\mathrm{exp}(\frac{-\lambda }{\rho c}{(\frac{\mathrm{2i}+1}{\mathrm{2L}}\pi )}^{2}t))\)

Reference values are obtained with \(i=1000\).

2.2. Benchmark results

Temperature at points \(E\) and \(F\) at times \(t=0.25\) and \(0.5s\)

2.3. Uncertainty about the solution

Analytical solution.

2.4. 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.