I've seen the following equation in my Incropera & DeWitt text book (it's also in a colleague's text by White), and an equivalent variation on the web at
This should give the net amount of heat being transferred from surface 1 to surface 2. It is not the total being radiated from surface 1 or received by surface 2. (Unless certain conditions are met, e.g. F12=1 & A1=A2.) Or at least that's my understanding.
It is my belief that this equation is erroneous. I don't have a direct proof for that, but anecdotal evidence. I would like your opinions on this. Does anyone know for sure if this equation is correct? If it's incorrect, do you have the correct version?
My evidence for its error was this: Consider two rectangles aligned above each other. Each is at a different temperature, but uniform over its area. Using the equation above (assuming it's correct) I get the net radiative heat exchange between the two rectangles. Next, divide those two rectangles each into four smaller rectangles (say, 1,2,3,4 on one rectangle and A,B,C,D on the other). I can calculate the view factors F1A,F1B,F1C,F1D (etc). If I calculate the total heat using the above equation, by summing the 16 individual results (1234 - ABCD), I find that the sum of the parts equals the whole only when the emissivities are both 1.0!
Essentially, what happens is that the 1/(A1*F12) term dominates the terms with emissivities. Those terms are zero when the emissivities are 1.0, so this doesn't matter then, but when the emissivities are less than one, it seems to cause great problems!
The view factors (or shape factors, or configuration factors, depending on what text you read) are complex for the two cases (the whole, and each of the parts), but are available in the literature, or at
I'd appreciate any comments anyone can make.
Thanks,
-Paul