Radiation loss from the vent

From Karlsson and Quintiere [1], it can be shown that for an enclosure with blackbody surfaces (ew = 1), the radiation heat transfer rate out of the vent of area A0 is 

for large fully developed fires, eg is near 1 or Tw Tg, then it follows that 

The total heat losses in a fully developed fire can then be approximated as 

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