2. Benchmark solution

2.1. Calculation method used for the reference solution

Analytical solution.

Temperature varying linearly in \(\theta\).

In \((r,\theta ,z)\)

\(T(\theta )=[T(C)-T(A)]\mathrm{.}\frac{2}{\pi }\mathrm{.}\theta +T(A)\)

\(\phi (A)\mathrm{.}Y=-{\lambda }_{}\theta \mathrm{.}\frac{1}{r}\mathrm{.}\frac{\partial T}{\partial \theta }=-{\lambda }_{\theta }\mathrm{.}\frac{1}{r(A)}[T(C)-T(A)]\mathrm{.}\frac{2}{\pi }\)

2.2. Benchmark results

Temperatures at points \(A\) and \(B\), next flow \(Y\) at point \(A\).

\(T(A)=100.\) \(T(B)=50.\) \(\phi (A)\mathrm{.}Y=\frac{100.}{2\pi }\approx 15.915\)

2.3. Uncertainty about the solution

Analytical solution.

2.4. Bibliographical references

N. RICHARD: « Development of thermal anisotropy in*Aster software « , Technical Note HM-18/94/0011.