## 4. Radiation Plate to a Plate

A plate steadily radiates heat on a plate. This example demonstrates the view factor capabilities of B2000++. An analytical solution is available for the view factor in the text book by Siegel and Howell [34].

Two rectangular plates are meshed independently one of the other as shown in the figure below. If only radiation elements (Q4 elements) are used, the solution will consist of exchanged heat between the hot and the cold plate. Since all nodes have prescribed temperatures there are no unknowns. However, B2000++ has to solve for the non-linear essential boundary conditions imposed by the radiation. Special attention has to be brought to the directions of the normals of the surfaces (see figure). If the normals are not oriented properly the structures will not radiate in the desired directions.

Radiation problems are nonlinear as specified in the adir command below. The linear transient response is calculated with the default non-linear solver of B2000++, with the parameters defined in the case command (see input file radiation_plate_plate.mdl):

cases
case 1
ebc                      1
step_size_init           1
step_size_min            1
step_size_max            1
end
end

end