Page 231 - Modelling in Transport Phenomena A Conceptual Approach

7.6. DESIGN OF A SPRAY TOWER 21 1

Substitution of Eqs. (9)-(11) into Eq. (8) and rearrangement gives

Ck dT

Integration gives
T = 298 + 45,000 E (13)
662,000 - 85 E
Now it is possible to evaluate Eq. (6) numerically. The use of Simpson's rule with
n = 8, i.e., Ae = 200, gives

E: [k(2000 - e)(2400 - E)]-' x lo4
(mol/m3) (K)
0 298 248
200 312 121.9
400 326.7 63.3
600 342.2 34.9
800 358.6 20.5
1000 376 12.9
1200 394.4 8.9
1400 414 6.9
1600 434.9 6.5

The application of Eq. (A.8-12) in Appendix A duces Eq. (6) to

200
t = - [248 + 4 (121.9 + 34.9 + 12.9 + 6.9)
3
+ 2 (63.3 + 20.5 + 8.9) + 6.51 x = 7.64min (14)

7.6 DESIGN OF A SPRAY TOWR FOR THE
GRANULATION OF MELT

The purpose of this section is to apply the concepts covered in this chapter to a
practical design problem. A typical tower for melt granulation is shown in Figure
7.3. The dimensions of the tower must be determined such that the largest melt
particles solidify before striking the walls or the floor of the tower. Mathematical
modelling of this tower can be accomplished by considering the unsteady-state
macroscopic energy balances for the melt particles in conjunction with their settling
velocities. This enables one to determine the cooling time and thus, the dimensions
of the tower.