CHEMICAL ENGINEERING

HEAT TRANSFER 127

From (iii), NDB 2 ex

p

p/DH (^) D (^0) p (^1) ekppwherekDx/pD
H
The Laplace transform ofp^1 ek
pp
Derfck/ 2
p
t(from Volume 1, Appendix).
and: D^0 t> 0
xD 0
erfc

[

x

2

p

DHt

]

(v)

WhenxD 0 .45 m,D
470  290 D180 deg K, and hence in (v), withDHD 4. 2 ð
10 ^7 m^2 /s,

180 / 580 Derfcf[0. 45 /

 6. 481 ð 10 ^4 ][1/

 2

p

t]gD 0. 31

∴
0. 45 / 6. 481 ð 10 ^4 / 2

p

tD 0. 73

and: tD 2. 26 ð 105 sor 0.226 Ms
62 .8h

As an alternative method of solution, Schmidt’s method is used with the construc-
tion shown in Fig. 9a. In this casexD 0 .1 m and it is seen that atxD 0 .45 m, the
temperature is 470 K after a time 20t.
In equation 9.43:tD
0. 12 /
2 ð 4. 2 ð 10 ^7 D 1. 191 ð 104 s
and hence the required time,tD
20 ð 1. 191 ð 104 D 2. 38 ð 105 sD 0 .238 Ms
66 .1h

The difference here is due to inaccuracies resulting from the coarse increments ofx.

1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

300

400

500

600

700

800

(^900870)
470
290
Temperature (K)
Distance from hot face (m)
(^97)
5 3 1 2 3 4
9 10 119 6 5
11 10
1315
1719
7
(^108)
12
1416
1820
7
9
11
13
15
1719
6
8
10
(^1412)
1618
20
5
7
9
(^1311)
(^1715)
19
4
6
8
1012
(^1614)
Figure 9a.
PROBLEM 9.3
Benzene vapour, at atmospheric pressure, condenses on a plane surface 2 m long and
1 m wide maintained at 300 K and inclined at an angle of 45°to the horizontal. Plot the
thickness of the condensate film and the point heat transfer coefficient against distance
from the top of the surface.