Page 254 - Mechanical Engineers' Handbook (Volume 4)

8 Heat Transfer 243

Figure 24 The ratio Y s /Y c plotted as a function of R. 1

ln 0.0429
X 0.1 1.95 tD/r 2
1.7
With D 0.25, from Section 7,
Xr 2 1.95 0.67 2
t 3.50 hr
D 0.25
Slabs or plates heated from two sides are usually supported in the furnace in a horizontal
position on spaced conveyor rolls or rails. Support members may be uncooled, in which case
radiation to the bottom surface will be reduced by the net view factor. If supports are water
cooled, the additional heat input needed to balance heat loss from load to supports can be
balanced by a higher furnace temperature on the bottom side. In either case, heating times
will be greater than for a uniform input from both sides.
Furnace temperatures are normally limited to a fraction above final load temperatures,
to avoid local overheating during operating delays. Without losses to water cooling, top and
bottom furnace temperature will accordingly be about equal.

8.10 Heat Transfer with Negligible Load Thermal Resistance

When heating thin plates or small-diameter rods, with internal thermal resistance low enough
to allow heating rates unlimited by specified final temperature differential, the non-steady-
state-conduction limits on heating rates can be neglected. Heating time then becomes

W C (T T )
t s 0
A H MTD
The heat-transfer coefficient for radiation heating can be approximated from the chart
in Fig. 13 or calculated as follows:
4
4
0.1713eF [T (T MTD) ]
H m s ƒ ƒ
r
MTD A s