2. Benchmark solution#

2.1. Calculation method used for the reference solution#

The reference solution is the one given in sheet TPLA05 /89 of the guide VPCS

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  • Temperature according to \(z\): \(T(z)=\frac{-\varphi }{\lambda r}z(z-L)+{T}_{1}\mathrm{.}\frac{z}{L}\)

  • \(T(z=0)=0\) \(T(z=L)={T}_{1}\).

The cylinder is assumed to be infinitely long (\(L\gg r\))

The minimum temperature is \(-4.17°C\) in \(z=0.083m\)

2.2. Benchmark results#

Temperature in \(z=0.,0.1,\mathrm{...},0.8,0.9,1.0\)

2.3. Uncertainty about the solution#

\(<1\text{\%}\)

Approximate analytical solution (approximation: \(T=\mathrm{cte}\), for all \(r\))

2.4. Bibliographical references#

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