Page 184 - Modelling in Transport Phenomena A Conceptual Approach

164 CHAPTER 6. STEADY-STATE MACROSCOPIC BALANCES

Assume T, = 11 "C
For water at 11°C (284K) : { rA
sat = 0.01308 bar
XA = 2475.4 x 18 = 44,557 kJ/ km01
The saturation concentration is

psat
=- A
CAW RT,
-
- 0.01308 = 5.54 x kmol/ m3
(8.314 x 10-2)(11 + 273)

The film temperature is Tf = (35 + 11)/2 = 23°C.
p = 1.1926 kg/ m3
u = 15.36 x m2/ s
For air at 23°C (296K) :
Cp = 1.005 kJ/ kg. K
Pr = 0.713

The diffusion coeficient of water in air is

312
DAB = (2.88 x (E) = 2.65 x 10-5 rn2/

The Schmidt number is

U
sc = -
DAB
- 15.36 x low6 = 0.58
-
2.65 x 10-5
The left- and right-hand sides of Eq. (7) now become

T, - T, = 35 - 11 24
2/3 (5.54 x 10-4)(44,557) 0.713 2/3
(1.1926) (1.005) (m) = 23*6

Therefore, the steady-state temperature is 11 "C.

Comment: Whenever a gas flows over a liquid, the temperature of the liquid
decreases as a result of evaporation. This process is known as evaporative cooling.
The multing steady-state temperature, on the other hand, k called the wet-bulb
temperature.