Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

Analytical solution.

Temperature varying linearly in :math:`\theta`.

In :math:`(r,\theta ,z)`

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

:math:`\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 }`


Benchmark results
----------------------

Temperatures at points :math:`A` and :math:`B`, next flow :math:`Y` at point :math:`A`.

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


Uncertainty about the solution
---------------------------

Analytical solution.


Bibliographical references
---------------------------


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