.. _V4.43.001:

**v4.43.001** TPNV01 - Hollow sphere: convection, radiation
===============================================================

**Summary:**

This test is the result of the independent validation of version 3 in non-linear stationary heat.

This is a volume problem represented by two models, one 3D, the other axisymmetric.

The features tested are as follows:


* 3D thermal element,


* axisymmetric thermal element,


* convection and radiation limit conditions.

The advantage of the test lies in taking radiation into account.

The results are compared to an analytical solution on a test VPCS.


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A
    R_sultats_de_la_mod_lisation_A
    Mod_lisation_B
    R_sultats_de_la_mod_lisation_B
    Mod_lisation_C
    Synth_se_des_r_sultats