Page 320 - Dust Explosions in the Process Industries

Propagation of Flames in Dust Clouds 289

Figure 4.21 Physical model forming the basis of the one-dimensional Nomura and Tanaka (1978)
theory for laminar flame propagation through dust clouds of monosized particles.

direction, while the cross section L2normal to the x axis is maintained constant. During
this plug flow expansion, the whole chain of subsequentgas elements are pushed to the
right along the x axis. The unburned particles are assumed to follow their respective gas
elements completely during this process.
When calculating the temperature profile due to combustion of particle no. 1, a one-
dimensionalmodel is used, correspondingto the particle being a plane of sizeL2,normal
to the x axis rather than a sphere. The correspondingthermal diffusion equation is

(4.39)

where Tis the gas temperature at distance x at time t and a is the thermal diffusivity. If
the boundary condition at x = 0 is T = Tf,that is, a constant flame temperature, and T =
Toat x = 00,the solution of equation (4.39) is

(4.40)

A dynamic heat balance for each particle is obtained by consideringthe heat transfer from
the burning particle no. n, to the unburned particle no. (n+ 1)as given in equation (4.41):

;n 7CD;
-D3p c s=hzD;(TgL-TdL)+-(apefFoTf4 +apeGoT:)-;nD;EpoTL (4.41)
6 p p p dt 2
The notation not already explained is as follows:
cpis the specific heat of particle (J/gK);
TdLis the temperature of particle no. (n + 1) (K);
TgLis the temperature of gas surrounding particle no. (n + 1) (K);
TGis the temperature of hot gas sphere surrounding particle after burning (K);
h is the heat transfer coefficient (J/(cm2sK));
apis the absorptivity of particle (-);
efis the emissivity of flame (-);
eGis the emissivity of hot gas surrounding particle after burning (-);
ePis the emissivity of the particle (-);
F is the particle shape factor (-);
ois the Stefan-Boltzmannconstant (= 5.66 J/(sm2K4)).