HEAT TRANSFER IN THE RADIANT SECTION OF PETROLEUM HEATERS (part2): 1 - 2 - 3 - 4

CONCLUSIONS AND RECOMMENDATIONS

The theoretical radiant equation as developed in this paper is recommended for the solution of heat transfer problems in the radiant section of tubular heaters using fuel oil or gaseous fuel.
The equation is believed to be valid for any condition of air preheat, inert gas recirculation, percentage of excess air, or radiant rate. The effect of furnace volume on the amount of heat liberation necessary to maintain any given radiant rate is adequately handled by the use of the flame emissivity as outlined previously. The results indicate that the f plot represents an accurate and simple method of simultaneously allowing for the effect of flame emissivity and the amount of refractory surface present in the radiant section.
The Wilson, Lobo, and Hottel empirical equation is not recommended for use on furnaces differing widely from those used to determine the constants of the equation. However, the equation may be used with safety on box-type heaters (see Figures 16, 17, 18, 20 and 21) when the greatest accuracy is not required and subject to the following qualifications :

NOMENCLATURE

Ao	=	total outside tube area exposed to radiation, sq.ft.
AR	=	effective refractory area, sq.ft.
A'R	=	actual refractory area, sq.ft.
AT	=	total wall area in combustion section, sq.ft.
Acp	=	area of plane replacing tubes, sq.ft.
C	=	actual firing rate of fuel/sq.ft. of exposed tube area, lbs./hr./sq.ft.
Co	=	equivalent firing rate of good bituminous coal/sq.ft. of projected tube area, lbs./hr./sq.ft.
CA	=	firing rate based on projected tube area, lbs./hr./sq.ft.
E	=	effectiveness factor of the cold surface
Frc	=	fraction of all the radiation emitted from all the refractory in all directions, which, if not absorbed by the gas, would hit cold surface, aAcp
FS	=	angle-emissivity factor
G	=	air-fuel ratio, lbs. air /lb. of fuel
H	=	total net heat input to combustion chamber, B.t.u./hr.
hc	=	convection coefficient, B.t.u./hr./sq.ft./°F.
L	=	mean length of radiant beam, feet
N	=	hourly heat capacity, B.t.u./hr./°F.
Pe	=	emissivity of tube surface
Pf	=	emissivity of flame
PCO2	=	partial pressure of CO2, atmospheres
PH2O	=	partial pressure of water vapor, atmospheres
MCPavg.	=	mean molal heat capacity between 60° and temperature, tg
Q	=	net heat liberated from combustion of the fuel, B.t.u./hour
q	=	heat transferred to oil, B.t.u./hour
q'	=	heat transferred by radiation, B.t.u./hour
q"	=	net heat transferred to all surfaces in the radiant section, B.t.u./hour
Se	=	equivalent "effective" heating surface, sq.ft.
Tg	=	temperature of products of combustion leaving combustion chamber, °F. + 460°
Ts	=	tube skin temperature, °F. + 460°
t	=	temperature, °F.
tg	=	temperature of flue gas leaving combustion chamber, °F.
t'f	=	Pseudo-flame temperature, °F.
a	=	factor by which Acp must be reduced to obtain effective cold surface, aAcp (effective tube area)
b	=	fraction of total net heat input lost from the external furnace walls
f	=	overall exchange factor
m	=	fraction of heat available above 60° F. absorbed by cold surfaces in the combustion chamber

LITERATURE CITED
1.	Hottel, Trans. A.I.Ch.E. 19, 173 (1927); Ind. Eng. Chem. 19, 888 (1927)
2.	Wilson, Lobo, Hottel, Ind. Eng. Chem. 24, 486 (1932)
3.	Hudson, Engineer 70, 523 (1890)
4.	Orrok, Trans. A.S.M.E. 1148 (1925)
5.	Hottel, Unpublished notes on Radiant Heat Transmission, Mass. Inst. of Tech. (1938)
6.	DeBaufre, Trans. A.S.M.E. 53 (14), 253 (1931)
7.	Mekler, Nat. Pet. News 30 (30), R355 (1938)
8.	Hottel, Trans. A.S.M.E., Fuels Steam Power 53 (14), 265 (1931)
9.	Hottel, Unpublished notes on Radiant Heat Transmission, Mass. Inst. of Tech. (1938)
10.	Hottel, in Chem. Eng. Handbook 1, 888 (1934)
11.	Hottel, Ibid. 1, 910 (1934)
12.	Hottel, Ibid. 1, 892 (1934)

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