To continue our discussion where we left off …
The heat energy that is radiated from the metal surface into the cooling chamber or room must be equal to the heat energy lost from the metal, and formula 2b equals formula 3, or (see Fig. 1):
t = Cooling time (hours) for the metal to a mean temperature, T.
G = Weight of the metal (pounds)
c = Specific heat of the metal (BTU/pound-°F)
A = Radiation area (feet2) of the metal part exposed to the cooling chamber or room
e = Emissivity (e=1 for a black body)
Tr = Absolute room temperature (°F)
Tp = Absolute metal temperature (°F) after t hours of cooling
To = Absolute room temperature (°F) for t=0 hours, that is, the temperature at the beginning of cooling.
Note: The above formula for cooling of metals (Fig. 1) is worked out for radiation only. When cooling a metal down to <300°F, heat that is taken away from the metal surface by natural convection must also be counted (heat transfer by natural convection becomes a greater factor at lower temperature than radiant heat transfer).
In most cases when cooling below 300°F, formula 7 can be used, which will give at the same time a safety factor because cooling by radiation only involves longer time.