Correction To Overall Radiant Exchange Factor

To predict the radiant heat transfer correctly, it is important to have the best estimate of the various parameters. The overall exchange factor used in the previously discussed equations, was based on curves using the gas emissivity and the Aw/aAcp. These curves assumed a tube(black body) emissivity of 0.90. Years ago, this was a good approximation, and still is today for typical carbon steel tubes. Some high alloy tubes and tubes that have been coated may have emissivity properties which may vary dramatically from this 0.90 value. However, care should be taken in assuming that an emissivity value for a given material may be the same for that material when used in a furnace. But, it is probably true that many materials do have an emissivity less than 0.90 even in a furnace setting. The curves below were presented by W. E. Lobo, in a January 1974, Chemical Engineering Progress article as a means to correct for a value different than that used by Lobo & Evans in the original curves.

Exchange Factor Correction
R = (FPc=x/FPc=0.90)/(Pc=x/Pc=0.90)
Ar = Total refractory area, ft2
aAcp = Equivalent cold plane area, ft2
F = Overall exchange factor
Pf = Emissivity of flame or gas envelope
Pc = Emissivity of tube surface
x = Value of the new emissivity

You should note that the curve here is based on Ar/aAcp, where the curve used in the above calculations to obtain the F factor was based on Aw/aAcp.

Aw = Ar - aAcp
Aw = Effective refractory area, ft2
Emissivity Of Tube, Pc:
Emissivity of Gas, Pf:
F factor from previous calculations:
R ratio from curves:
F corrected to new tube emissivity: