Page 255 - Mechanical Engineers' Handbook (Volume 4)
P. 255
244 Furnaces
As an illustration, find the time required to heat a steel plate to 2350 F in a furnace at
a uniform temperature of 2400 F. The plate is 0.25 in. thick with a unit weight of 10.2 lb/
2
ft and is to be heated from one side. Overall emissivity–absorptivity is e 0.80. Specific
m
1. MTD is
heat is 0.165. The view factor is F s
(2400 70) (2400 2350)
588 F
ln(2400 70)/(2400 2350)
0.1713 0.80 1[28.6 (28.6 5.88) ]
4
4
H 93.8
r
588
10.2 0.165(2350 70)
t 0.069 hr
1 93.8 588
8.11 Newman Method
For loads heated from two or more perpendicular sides, final maximum temperatures will
be at exposed corners, with minimum temperatures at the center of mass for heating from
all sides, or at the center of the face in contact with the hearth for hearth-supported loads
heated equally from the remaining sides. For surfaces not fully exposed to radiation, the
corrected H factor must be used.
The Newman method can be used to determine final load temperatures with a given
heating time t. To find time required to reach specified maximum and minimum final load
temperatures, trial calculations with several values of t will be needed.
and Y can be found from charts in Figs.
For a selected heating time t, the factors Y s c
, T , H, k, and r—for each
23 and 24 for the appropriate values of the other variables—T s c
, r , and r . If one of these paths is much longer than the
of the heat flow paths involved—r x y z
others, it can be omitted from calculations:
Y Y Y Y cz
c
cx
cy
Y Y Y Y sz
sx
s
sy
For two opposite sides with equal exposure only one is considered. With T known, T s
c
(furnace temperature, T or T ) can be calculated.
and T ƒ g w
As an example, consider a carbon steel ingot, with dimensions 2 ft 4ft 6 ft, being
heated in a direct-fired furnace. The load is supported with one 2 ft 4 ft face in contact
with the refractory hearth and other faces fully exposed to gas and wall radiation. Maximum
final temperature will be at an upper corner, with minimum temperature at the center of the
2ft 4 ft bottom surface. Assuming that the load is a somewhat brittle steel alloy, the
initial heating rate should be suppressed and heating with a constant gas temperature will
be assumed. Heat-transfer factors are then
Flow paths r s 1 ft and r y 2 ft, the contribution of vertical heat flow, on axis r z , will
be small enough to be neglected.
2250 F and T (to be found) about 2300 F, with trial
Desired final temperatures: T c
s
factor t 9hr.
H from gas to load 50
k mean value for load 20 and D 0.25