Radiation: view factors

Setting view factor parameters
Testing the view factor quality

The surface to surface radiation is implemented in CrysMAS by so called view factors radiation. The quality of the view factors is important for the quality of the computation result: If there are artificial heat sources or sinks due to inaccurate view factors, increase the view factor precision (i.e. decrease the value specified). View factors are always calculated before temperature, either in an independent run or automatically in the same computation run as temperature.

CrysMAS can handle heat transfer by radiation in perfectly transparent media and for media which show certain transparency windows in a given wavelength domain (Visibility Bands). The physical model used by CrysMAS is that of the gray body radiation: Surfaces of a cavity are emitting a hemispherical flux proportional to σ T 4 and proportionality coefficient ε is called emissivity.

The view factor is defined between two elements of the cavities surface. If i and j are two such elements, the view factor from i to j , F ji represents the fraction of the energy that leaves element i and arrives to j if the assumption of black body radiation. For the gray body, the Γ matrix is of interest. It is defined in the following way:

 

Figure 8. 

q i net = Γ . q em is thereby the difference between absorbed and emitted energy at surface element i . Γ can be directly computed from the view factors and the emissivities. qnet is taken as a heating source density.

The energy leaving element i must arrive at the other elements without loss, therefore the view factors have the following property:

 

Figure 9. 

In the numerical treatment this sum does not exactly equal 1 and the energy inside the furnace is not conserved completely. CrysMAS provides a renormation function for the Γ matrix on the View factors tab of the Numerical parameters dialog.

Note

View factors have to be recomputed, if geometry or emissivity were changed. In either case CrysMAS computes them automatically.