2. Benchmark solution#
2.1. Calculation method used for the reference solution#
\(\frac{T(x,t)-{T}_{p}}{{T}_{0}-{T}_{p}}=\frac{4}{\pi }\sum _{n=1}^{\infty }\frac{1}{n}\mathrm{sin}(\frac{n\pi x}{\mathrm{2L}})\mathrm{exp}\left\{-{(\frac{n\pi }{\mathrm{2L}})}^{2}\mathrm{.}\frac{\lambda }{\rho {C}_{p}}\mathrm{.}t\right\}\)
\(x=\) |
abscissa |
\(t=\) |
Time |
\({T}_{0}=\) |
Initial temperature |
\({T}_{p}=\) |
Imposed temperature |
\(n=\) |
|
2.2. Benchmark results#
Temperatures at points \(\mathrm{M1}\) (\(x=0.2\)) and \(\mathrm{M2}\) (\(x=0.8\)), and at various times (\(t=0.1,0.2,0.7\) and \(2.0\)).
The reference values are those given in guide VPCS.
2.3. Uncertainty about the solution#
Digital series.
2.4. Bibliographical references#
J.F. SACCADURA: Introduction to heat transfers, Paris, Technique and documentation (1982).