Page 183 - Modelling in Transport Phenomena A Conceptual Approach

6.3. CONSERVATION OF ENERGY 163

It should be remembered that the quantities CA, and JA must be evaluated at T,,
whereas p~, epB, Pig and SCB must be evaluated at Tf = (T, + T,)/2. Since
T, is unknown, a trial-and-emr procedure will be used in order to detennine T,
as follows:
Step 1: Assume T, = 15°C

Step 2: Determine the physical properties:
Prt = 0.01703 bar
For water at 15°C (288K) :
i~ 18 = 44,388 kJ/ kmol
x
2466
=
The saturation concentration is

- 0.01703 = 7.11 x kmol/ m3
-
(8.314 x 10-2)(15 + 273)

The fiZm temperature is Tf = (35 + 15)/2 = 25°C.
f p = 1.1845 kg/ m3
v = 15.54 x m2/ s
For air at 25 "C (298K) :
Cp = 1.005 kJ/ kg. K
Pr = 0.712
The diffusion coeficient of water in air is
DAB = (2.88 x E ( 3'2 = 2.68 x m2/ s
!
)

The Schmidt number is
Y
sc = -
DAB
- 15.54 x low6 = 0.58
-
2.68 x 10-5

Step 3: Substitute the values into Eq. (7) and check whether the right and left
sides are equal to each other:

2/3 (7.11 x 10-4)(44,388) 0.712 2/3
(1.1845)(1.005) (058) = 30.4

Since the left- and right-hand sides of Eq. (7) are quite different from each other,
another value of T, should be assumed,