Page 430 - Dust Explosions in the Process Industries

lgnition of Dust Clouds and Dust Deposits 397

It seems that a generally applicabletheory for reliable estimation of heat conductivi-
ties of powder deposits does not exist. Therefore, one must rely on experimental deter-
mination, such as by the method developed by John and Hensel(1989).

5.2.3
FURTHER THEORETICAL WORK

5.2.3.1
The Bid Number

The dimensionless Biot number is an important parameter in the theoiy of self-heating
and self-ignition of dust deposits. It is defined as
Bi = hrl A. (5.16)
where h is the heat transfer coefficient at the boundary between the dust deposit and its
environment; r is half the thickness, or the radius, of the dust deposit; and ilis its ther-
mal conductivity.The Biot number expresses the ease with which heat flows though the
interface between the powder deposit and its surroundings, in relation to the ease with
which heat is conductedthrough the powder.A Biot number of 0 means that the heat con-
ductivity in the powder is infinite and the temperature distribution uniform at any time.
Bi = ~0 implies that the resistance to heat flow across the boundary is negligible com-
pared to the conductiveresistance within the powder.
As pointed out by Bowes (1981) and Hensel(l989), the classical work of Semenov
(1935) rests on the assumptionthat Bi =0, whereas Frank-Kamenetzkiiassumed Bi = a.
Thomas (1958) derived steady-statesolutionsof the basic partial differentialheat balance
equation for finite plane slabs, cylinders and spheres from which the Frank-Kamenetzkii
parameter (equation (5.1I)) could be calculated for Biot numbers 0 < Bi < 00.
Liang and Tanaka (1987) found that the fairly complex approximate relationships
between the critical condition for ignition and the Biot number originally proposed by
Thomas could be replaced by much simpler formulas based on the Frank-Kamenetzkii
approximatesteady-statetheory. Improved accuracy was obtainedby adjusting the formulas
to closer agreement with the more-exact generalnumerical solutions for a nonsteady state.

5.2.3.2
Further Theoretical Analysis of Self-Ignition Processes: Computer Simulatioii Models

Liang andTanaka (1987b, 1988)used the experimentalresults of Leuschke (1980,1981)
from ignition of cylindrical cork dust samples under isoperibolic conditions as a refer-
ence for comprehensivecomputer simulationof the self-heatingprocess in such a system.
They assumed that heat did not flow in the axial direction, only radially, and arrived at
the following partial differential equation for the heat balance, considering heat gener-
ation by zero-order chemical reaction and heat dissipationby radial conduction:

(5.17)

,where