The investigation (see parts I to III) of the spontaneous ignition of gaseous diethyl peroxide as a thermal explosion is concluded by a series of experiments mainly in a cylindrical vessel, and including diluted mixtures. A very fine thermocouple (25
µ
m diameter) has been used to probe the temperature distributions between the axis and the wall both in systems reacting subcritically and in systems on the verge of ignition. A multijunction thermocouple has also been employed to obtain instantaneous readings of distributed temperature in a spherical vessel. It is found that self heating is always present. In accordance with a conductive theory of heat losses, temperatures are not uniform throughout the reactant, but depend on the fractional distance (
z
=
r
/
r
0
) from the vessel axis, being greatest at the axis and least at the walls. For the cylinder, the form of the profiles expected in a stationary state is (
T
-
T
a
)/(
RT
a
2
/
E
) = 2 ln (1 +
G
)/(1 +
Gz
2
) and good agreement is found between theory and experiment. (The significance of
G
is discussed in the text.) This agreement, the symmetry of the profiles, and the absence of any temperature step at the walls confirm the absence of convection at the pressures concerned. A critical centre temperature rise exists above which ignition is inevitable. The greatest value of this increment is 23.3 K ; for simple theory, the predicted value is 19 K (1.39
RT
a
2
/
E
). Any temperature dependence of this critical increment lies beyond the discrimination of the present apparatus. Similar agreement is found between ‘measured’ and theoretically expected values for Frank-Kamenetskii’s
δ
. At criticality, the measured values average 2.25 against a theoretical value (uncorrected for finite vessel size or finite reaction rate) of 2 exactly. ‘Measured’ values for
δ
in subcritical systems are also in satisfactory accord with expectation. Other ‘indirect’ tests of thermal theory are also satisfied. Thus the curvature of the critical pressure limit (boundary on the
p
—
T
diagram between explosive and slow reaction) exactly corresponds to the activation energy measured in isothermal decomposition. Similar temperature-position profiles are found in diluted mixtures below criticality, and although critical explosion pressures depend on the degree of dilution, the critical temperature rise for ignition does not. The average value found is 19.0 K. Nor does the critical temperature gradient at the vessel boundary vary from the value ( — 2 exactly) predicted for any dilution of vessel geometry. There are the same influences on criticality as in the spherical vessel: in accord with stationary state conductive theory, thermal conductivity is the principal factor but its influence is distorted to varying degrees, first by the occurrence of dynamic heating accompanying gas entry, secondly by the rate of dissipation of this heating, which is governed by the thermal diffusivity, and thirdly by the departures from stationary state behaviour largely governed by the specific heat of the diluent. These influences explain an otherwise erratic dependence of critical ignition pressures on thermal conductivity.
Mathematical model of coal self-heating in a stack