A cylinder 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
^{[35]}.

The cylinder and the annular plate 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 cylinder (hot) and the plate (cold). 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_cyl_plate.mdl`

):

cases case 1 ebc 1 component radiation_heat NBC VISI_RAD step_size_init 1 step_size_min 1 step_size_max 1 end end adir analysis nonlinear case 1 end

By setting the initial step size, the minimum step size, and the maximum step size to 1, the solver will try to solve the problem for the final step with one step.

The approximate analytical value for the radiation configuration
factor based on pure geometric considerations can be found in the graph of
the text book by Siegel and Howell. For the geometric configuration of
present example the view factor is ~0.4.

^{[35] }R. Siegel, J. R. Howell; Thermal Radiation Heat Transfer, 4th ed.;
Taylor and Francis, New York, 2001