Page 235 - Modelling in Transport Phenomena A Conceptual Approach

7.6. DESIGN OF A SPRAY TOWER 215

where ml and m, represent the liquid and solidified portions of the particle,
respectively. Therefore, Eq. (7.58) reduces to

- dm,
rD;(h)(T, - (T,)) = X - (7.6- 12)
dt

Integration of Eq. (7.612) gives the time required for solidification, t2, as

(7.6-13)

Therefore, the total time, t, in Eq. (7.64) is

t = tl + t2 (7.6-14)

Example 7.10 Determine the dimensions of the spray cooling tower for the
following conditions:
Production rate = 3000 kg/ h
Dp = 2mm
pm = 1700 kg/ m3
v, = 2m/s
(Ta)an 10°C
=
(Ta)out = 20°C
(Tm)in = 110°C
T, = 70°C
= 186 kJ/ kg
Cpm = 1.46 kJ/ kg. K

Solution

Physical properties

The average air temperature is (10 + 20)/2 = 15°C.
p = 1.2 kg/ m3
p = 17.93 x kg/ m. s
For air at 15 "C (288 K) : k = 25.22 x low3 W/ m. K
Cp = 1.004
Pr = 0.714