Page 251 - Mechanical Engineers' Handbook (Volume 4)

240 Furnaces

preliminary temperature profile for the composite wall. Overall resistance will include the
effects of radiation and conduction between the outer wall surface and its surroundings.
A chart showing heat loss from walls to ambient surrounding at 70 F, combining radi-
ation and convection for vertical walls, is shown in Fig. 7. The corresponding thermal re-
sistance is included in the overall heat-transfer coefficient shown in Fig. 8 as a function of
net thermal resistance of the wall structure and inside face temperature.
As an example of application, assume a furnace wall constructed as follows:
Material r k r/k

9 in. firebrick 0.75 0.83 0.90
1
4 ⁄2 in. 2000 F insulation 0.375 0.13 2.88
1
2 ⁄2 in. ceramic fiber block 0.208 0.067 3.10
Total R for solid wall 6.88
With an inside surface temperature of 2000 F, the heat loss from Fig. 7 is about 265
2
Btu/ft hr . The corresponding surface temperature from Fig. 8 is about 200 F, assuming an
ambient temperature of 70 F.
Although not a factor affecting wall heat transfer, the possibility of vapor condensation
in the wall structure must be considered by the furnace designer, particularly if the furnace
is fired with a sulfur-bearing fuel. As the sulfur dioxide content of fuel gases is increased,
condensation temperatures increase to what may exceed the temperature of the steel furnace
casing in normal operation. Resulting condensation at the outer wall can result in rapid
corrosion of the steel structure.
Condensation problems can be avoided by providing a continuous membrane of alu-
minum or stainless steel between layers of the wall structure, at a point where operating
temperatures will always exceed condensation temperatures.

8.9 Non-Steady-State Conduction
Heat transfer in furnace loads during heating or cooling is by transient or non-steady-state
conduction, with temperature profiles within loads varying with time. With loads of low
internal thermal resistance, heating time can be calculated for the desired load surface tem-
perature and a selected time–temperature profile for furnace temperature. With loads of
appreciable thermal resistance from surface to center, or from hot to colder sides, heating
time will usually be determined by a specified final load temperature differential, and a
selected furnace temperature profile for the heating cycle.
For the case of a slab-type load being heated on a furnace hearth, with only one side
exposed, and with the load entering the furnace at ambient temperature, the initial gradient
from the heated to the unheated surface will be zero. The heated surface will heat more
rapidly until the opposite surface starts to heat, after which the temperature differential
between surfaces will taper off with time until the desired final differential is achieved.
In Fig. 22 the temperatures of heated and unheated surface or core temperature are
shown as a function of time. In the lower chart temperatures are plotted directly as a function
of time. In the upper chart the logarithm of the temperature ratio (Y load temperature/
source temperature) is plotted as a function of time for a constant source temperature. After
a short initial heating time, during which the unheated surface or core temperature reaches
its maximum rate of increase, the two curves in the upper diagram become parallel straight
lines.
Factors considered in non-steady-state conduction and their identifying symbols are
listed in Table 6.