DESIGN OF OPEN-HEARTH FURNACES 221
the ordinates are given per cent values to permit their application
to any initial temperature. These curves are computed by a
formula developed from Fourier's conduction equation. They
show that the rate of temperature rise at the center of the brick
will vary according to the square of the thickness of the brick.
These curves apply equally to the cooling period. A curve
showing the complete heating and cooling cycle will resemble the
hysteresis loop, which shows the heating effect of cyclic magnetic
changes upon an iron core.
The firebrick makers in this country list a special checker
brick, 10.5X4.5X4.5 in (265X115X115 mm), and a checker
brick 2.9X2.75X2.75 in (107X70X70 mm), and some designers
use 9-in straights, which give a 2.5-in (63-mm) wall. With a
30-minute period between reversals, the temperature change on
the central plane of these bricks may be approximated as follows:
Assuming that the initial temperature throughout the bricks
is practically uniform, and the surface is heated through any
temperature range for a period of 30 minutes. At the end of this
period the temperature of the central plane will have increased
to 59 per cent, 94 per cent and 96.5 per cent of the surface tempera-
ture, respectively, according to Fig. 153. So that the cooling
cycle starts with an initial drop in temperature on the central
plane of 41, 6 and 3.5 per cent, respectively.
Fig. 153 shows that the period of time required for these
drops will be, respectively, 21, 3 and 2 minutes. During this
period the portion of the brick between the center and the surface
will be transmitting heat both toward the center and the surface
of the brick.
In other words, the thinner the checker brick the higher its
heat-storage capacity as compared with the volume it occupies,
the greater the amount of heating surface for the given weight of
brickwork and the smaller the heat-storage capacity per unit of
surface. When the checker brick are too thin the heat gradient
from top to bottom of the checker becomes a curve instead of a
straight line. The brick, instead of working on the sloping portion
of the curve (Fig. 153) work over on to the flat upper portion of
the curve.
A great many of the formulas covering the heat transfer from
one substance to another contain a factor which covers the
velocity of flow of the gas or liquid which is absorbing or giving