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EMPIRICAL FURNACE EQUATIONS
The following empirical equations have been classified into two
major groups according to whether they are similar to the Hudson or
the DeBaufre type equation.
Hudson3 correlated the data on several types of steam-boiler
furnaces by the simple equation:
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(1) |
m = fraction of total heat input to the furnace (above the steam
temperature) which is absorbed by the ultimate heat receiver.
G = air-fuel ratio, lbs. air / lb. fuel fired
C = pounds of fuel per hour per sq. ft. of water-cooled surface.
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(2) |
m = fraction of heat transferred above atmospheric temperature
G = air-fuel ratio, lbs. air / lb. fuel fired
Co = pounds of equivalent good bituminous coal per hour per sq. ft.
of water-cooled surface.
Wilson, Lobo and Hottel 2 modified the Orrok equation and correlated
the performance on ten of twelve furnaces. Their recommended
equation is:
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(3) |
m = fraction of total heat input above 60°F. absorbed by the cold
surface
a Acp = effectiveness of tube surface as compared to a continuous
cold plane, sq. ft.
Q = net heat liberated from combustion of the fuel, B.t.u. per hour
G = air-fuel ratio, lbs. air per lb. fuel fired.
Hottel 5 has proposed the following type of equation:
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(4) |
H = total net heat input from all sources, B.t.u. per hour
N = the hourly mean heat capacity of the flue gas between the
temperature of the gas leaving the chamber and a base temperature of
60° F. B.t.u./hour/°F.
f = an overall exchange factor defined by the equation:
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(5) |
where
q = heat transferred by radiation, B.t.u./hour
Tg = temperature of the gas or hot surface, °F. + 460
Ts = temperature of cold surface, °F. + 460.
The overall exchange factor makes allowance for variation in
effective flame emissivity, arrangement of refractory and non-black
conditions in the furnace chamber. The constants in the above
equation are very tentative so that it is only to be considered as
illustrating a method. The f concept has been satisfactorily used in
the equation presented in this paper and has been defined and
discussed under the derivation of the theoretical equation.
DeBaufre 6 proposed an empirical equation which is similar to the
basic Stefan-Boltzmann equation:
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(6) |
q = heat transferred, B.t.u./hour
Ao = total tube surface exposed to radiation, sq. ft.
Tg = temperature of the products of combustion leaving the furnace
chamber, °F. + 460
Ts = temperature of cold surface, °F. + 460
E = effectiveness factor of the cold surface.
DeBaufre attempted to correlate E as a function of the rate of heat
liberation per unit of furnace volume but the correlation was poor.
For black body conditions E would have a maximum value of 0.173, the
Stefan-Boltzmann constant.
Mekler7 proposes the equation:
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(7) |
q = heat transferred by radiation, B.t.u./hour
Se = equivalent "effective" heating surface, sq. ft.
C = an empirical coefficient depending on the temperature used for
Tg
Tg = exit gas or theoretical flame temperature, °F. + 460
Ts = temperature of cold surface, °F. + 460.
In contrast to DeBaufre, however, he evaluates Se as a function of
the "fraction cold" of the furnace. An approximate graphical method
is used for solving the DeBaufre type of equation. No cognizance is
taken of the effect of PL on the heat transferred, and furnaces
having the same geometric shape but widely different volumes are
presumed to have the same fractional heat absorbtion. The effect of
excess air on flame emissivity is likewise neglected.
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