This is quite embarasing since it ought to be easy, but I just can't
figure it out.

I'm trying to figure out the equations for solving a thermal
radiation-problem in which I have N surfaces out of which M < N have a
known (high) temperature. I need to calculate the temperature of the
other N-M surfaces.

I know everything I need to know, the area of the surfaces, the
emissivity of each surface and the view-factors for each combination of
surfaces. All surfaces are grey and diffuse.

One of my problems is that this is not an enclosure so I can't assume
that all the radiation from the hot surfaces will actually end up
somewhere. Some equations I've seen assumed that the sum of all the
radiation reaching all surfaces from one of the hot surfaces was equal
to epsilon * sigma * T^4, but for me that is not true. Depending on the
model it's possible that all radiation from a hot surface is lost.

Anyone have a easy, step by step explanation of how the equationa
should be set ut?

--
Erik Wikström