2.4.3 Gebhard method
The Gebhart method describes the radiative heat transfer in terms of heat coming from one surface and absorbed by another, including all reflections. The Gebhart matrix traces exactly the radiative transfer contribution of each surface to the others.
In general the (Fourier) equation of thermal energy flow equilibrium can be written as:
Bij is called the ‘Radiative exchange factor’ or ‘Gebhart factor’, which is the fraction of the emitted radiation by one surface, absorbed by the other surface (including reflections).
The radiative exchange from surface i to j can thus be written as:
The Gebhart factor can be calculated by solving the following equation (iteratively):
Where Fij is the view factor, defined as the fraction of the radiation emitted by surface i and directly incident on surface j.
For view factor the following relation may be used:
Simplified cases are discussed in the next paragraphs.