2. Benchmark solution#

2.1. Calculation method used for the reference solution#

The reference solution is the one given in sheet TPLV06 /89 of guide VPCS.

  • Temperature according to \(r\):

\(T={T}_{i}+\frac{Q}{6\lambda }\left[\frac{({R}_{e}^{2}-{R}_{i}^{2})\left[\frac{1}{{R}_{i}}-\frac{1}{r}\right]}{\left[\frac{1}{{R}_{i}}-\frac{1}{{R}_{e}}\right]}-({r}^{2}-{R}_{i}^{2})\right]\)

  • Flux density as a function of \(r\):

\(\phi =-4\pi {r}^{2}\lambda \frac{\mathrm{dT}}{\mathrm{dr}}=-\frac{2\pi Q}{3}\left[({R}_{e}^{2}-{R}_{i}^{2})\left[\frac{1}{{R}_{i}}-\frac{1}{{R}_{e}}\right]-2{r}^{3}\right]\)

2.2. Benchmark results#

Temperature in \(r=1.25\); \(1.5\) and \(1.75m\)

2.3. Uncertainty about the solution#

Analytical solution.

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