t = G°-°c / A°-°e °-°0.01°-°ρ(t)
This formula (1) can be used to calculate the heat-up time of a thin metal or the time to heat the outside of a thicker section of metal (NOTE: This formula does NOT take into account the soak time required for the center of a thicker section to reach temperature).
t = Heating time (hours) for the metal to a mean temperature, T.
G = Weight of the metal (pounds)
c = Specific heat of the metal (BTU/lb-°F)
A = Radiation area (feet2) of the metal part exposed to the furnace chamber
e = Emissivity (e=1 for a black body)
To the calculated heating time, 10-20% should be added as a safety factor (and to account for small errors in the data). As the outside temperature is a small amount larger than the average assumed metal temperature during heating, the above safety factor for the formula is only good up to approximately 3 inches of metal thickness. As the metal thickness increases (up to approximately 20 inches) the safety factor increases to 30-50%.
The calculated points for the function ρ(t), where room temperature is 70°F are given in the tables 1-5 that follow and plotted in Curves 35, 36 and 37. The accurate heating (and cooling) of bodies can be calculated using the Fourier series.