Page 259 - Mechanical Engineers' Handbook (Volume 4)

248 Furnaces

demand in a continuous furnace, contemporary designs are based on operation with a variable
temperature profile from end to end, with furnace wall temperature reduced at the load charge
and flue gas discharge end, to improve available heat of fuel, and at the load discharge end,
to balance the desired maximum and minimum load temperatures. Any loss in capacity can
be recovered by operating the intermediate firing zones at a somewhat elevated temperature.
Consider a furnace designed to heat carbon steel slabs, 6 in. thick, from the top only
to final temperatures of 2300 F at top and 2250 F at the bottom. To hold exit flue gas
temperature to about 2000 F, wall temperature at the charge end will be about 1400 F. The
furnace will be fired in four zones of length, each 25 ft long for an effective total length of
100 ft. The preheat zone will be unfired, with a wall temperature tapering up to 2400 Fat
the load discharge end. That temperature will be held through the next two firing zones and
dropped to 2333 F to balance final load temperatures in the fourth or soak zone. With overall
heating capacity equal to the integral of units of length times their absolute temperatures,
effective heat input will be about 87% of that for a uniform temperature of 2400 F for the
entire length.
Heat transfer from combustion gases to load will be by direct radiation from gas to
load, including reflection of incident radiation from walls, and by radiation from gas to walls,
absorbed and reradiated from walls to load. Assuming that wall losses will be balanced by
convection heat transfer from gases, gas radiation to walls will equal solid-state radiation
from walls to load:
4
4
4
4
A /A 0.1713 e (T T ) e ws 0.1713(T T )
g
w
gm
s
w
w
s
where A /A exposed area ratio for walls and load
w
s
e gm emissivity–absorptivity, gas to walls
e ws emissivity–absorptivity, walls to load
At the midpoint in the heating cycle, MTD 708 F and mean load surface tempera-
ture T sm 1698 F.
With a 0.85 for refractory walls, 15% of gas radiation will be reflected to load, and
s
total gas to load radiation will be:
4
4
1.15 e gm 0.1713(T T )
s
g
For A /A 2.5, e gm 0.17, and e ws 0.89 from walls to load, the mean gas
w
s
2
temperature T 3108 F, net radiation, gas to load 47,042 Btu/hr ft and gas to
g
2
walls walls to load 69,305 Btu/hr ft for a total of 116,347 Btu/hr ft . This illustrates
2
the relation shown in Fig. 21, since blackbody radiation from walls to load, without gas
2
radiation, would be 77,871 Btu/hr ft . Assuming black-body radiation with a uniform wall
temperature from end to end, compared to combined radiation with the assumed wall tem-
perature, overall heat transfer ratio will be
(0.87 116,347)/77,871 1.30
As shown in Fig. 26, this ratio will vary with gas emissivity and wall to load areas
exposed. For the range of possible values for these factors, and for preliminary estimates of
heating times, the chart in Fig. 26 can be used to indicate a conservative heating time as a
function of final load temperature differential and depth of heat penetration, for a furnace
temperature profile depressed at either end.
Radiation factors will determine the mean coefficient of wall to load radiation, and the
corresponding non-steady-state conduction values. For black-body radiation alone, H is
r
about 77,871/708 110. For combined gas and solid-state radiation, in the above example,