Page 236 - Modelling in Transport Phenomena A Conceptual Approach

216 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

Analysis
The mass flow rate of air, ma, is calculated from Eq. (7.6-2) as

mrn { ~p,,, [(Trn)i, - T~I i}
+

The use of Eq. (7.63) gives the tower diameter as

(4)(73,028) = 3.3m
r( 1.2) (2) (3600)

The use of Eq. (4.3-6) gives the Archimedes number as

D;gPa(Prn - Pa)
Ar=
P2
- (2 x 10-3)3(9.8)(1.2)(1700 - 1.2) = 4.97
- 105
(17.93 x 10-6)2
Hence, the Reynolds number and the relative velocity are
Ar
Rep = - [1+ 0.0579 Ar0.412] -le214
18
-
- 4'97 lo5 [1+ 0.0579 (4.97 x 105)0.412]-'214 = 1134
18

- (17.93 x 10-6)(1134)
- = 8.5m/s
(1.2)(2 x 10-3)
Therefore, the terminal velocity of the particle is
vt = v, - va = 8.5 - 2 = 6.5m/s

The we of the Whitaker correlation, Eq. (7.6-11), with pao/pw M 1, gives
Nu = 2 + (0.4Rei12 +0.06 ReZ3) (p,/pw)'14

= 2 + [0.4 (1134)'12 + 0.06 (1134)~/~] (0.714)0.4 = 19.5