5. Radiation of Cylinder to Plate

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 of cylinder to plate: Mesh and normals

Figure 101. Radiation of cylinder to plate: Mesh and normals


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.

Radiation of a cylinder: Accumulated heat.

Figure 102. Radiation of a cylinder: Accumulated heat.


Radiation of a cylinder: Accumulated heat, detail (different scale).

Figure 103. Radiation of a cylinder: Accumulated heat, detail (different scale).


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