Page 249 - Mechanical Engineers' Handbook (Volume 4)

238 Furnaces

Convection heat transfer from gases to walls and load is also involved, but can be
eliminated from calculations by assuming that gas to wall convection is balanced by wall
losses, and that gas to load convection is equivalent to a slight increase in load surface
absorptivity. Mean effective gas temperature is usually difficult to measure, but can be cal-
culated if other factors are known. For example, carbon steel slabs are being heated to rolling
temperature in a fuel-fired continuous furnace. At any point in the furnace, neglecting con-
vection,
4
4
4
F gw (T T ) F ws (T T )
4
g
s
w
w
where T , T , and T are gas, wall, and load surface temperatures in S.
g
s
w
For a ratio of 2.5 for exposed wall and load surfaces, and a value of 0.17 for gas-to-
wall emissivity, F gw 2.5 0.17 0.425. With wall to load emissitivity equal to F ws
0.89, wall temperature constant at 2350 F (28.1 S), and load temperature increasing from 70
to 2300 F at the heated surface (T 5.3–27.6 S), the mean value of gas temperature (T )
s
g
can be determined:
2280 50
MTD, walls to load 584 F
ln(2280/50)
Mean load surface temperature T sm 2350 584 1766 F (22.26 S)
Q/A per unit of load surface, for reradiation:
2
4
4
4
0.425 0.1713(T 28.1 ) 0.89 0.1713(28.1 22.26 ) 57,622 Btu/hr ft 2
g
T 34.49 S (2989 F)
g
With a net wall emissivity of 0.85, 15% of gas radiation will be reflected to the load,
with the balance being absorbed and reradiated. Direct radiation from gas to load is then
1.15 0.17 0.1713(34.49 22.26 ) 47,389 Btu/hr ft 2
4
4
Total radiation: 57,622 47,389 105,011 Btu/hr ft 2
For comparison, blackbody radiation from walls to load, without gas radiation, would
be 64,743 Btu/hr ft or 62% of the combined total.
2
With practical furnace temperature profiles, in a counterflow, direct-fired continuous
furnace, gas and wall temperatures will be depressed at the load entry end to reduce flue
gas temperature and stack loss. The resulting net heating rates will be considered in Section
8.12.
Overall heat-transfer coefficients have been calculated for constant wall temperature, in
the upper chart in Fig. 21, or for constant gas temperature in the lower chart. Coefficients
vary with mean gas emissivity and with A /A , the ratio of exposed surface for walls and
s
w
load, and are always less than one for overall radiation from gas to load, or greater than one
for wall to load radiation. Curves can be used to find gas, wall, or mean load temperatures
when the other two are known.
8.8 Steady-State Conduction
Heat transfer through opaque solids and motionless layers of liquids or gases is by conduc-
tion. For constant temperature conditions, heat flow is by ‘‘steady-state’’ conduction and does
not vary with time. For objects being heated or cooled, with a continuous change in internal
temperature gradients, conduction is termed ‘‘non-steady-state.’’