CHEMICAL ENGINEERING

HEAT TRANSFER 139

PROBLEM 9.11

A condenser consists of 30 rows of parallel pipes of outer diameter 230 mm and thickness
1.3 mm with 40 pipes, each 2 m long in each row. Water, at an inlet temperature of 283 K,
flows through the pipes at 1 m/s and steam at 372 K condenses on the outside of the pipes.
There is a layer of scale 0.25 mm thick of thermal conductivity 2.1 W/m K on the inside
of the pipes. Taking the coefficients of heat transfer on the water side as 4.0 and on the
steam side as 8.5kW/m^2 K, calculate the water outlet temperature and the total mass
flow of steam condensed. The latent heat of steam at 372 K is 2250 kJ/kg. The density
of water is 1000 kg/m^3.

Solution

Overall coefficient

1

U

D

1

hi

C

1

ho

C

xw

kw

C

xr

kr

(equation 9.201)

wherexrandkrare the thickness and thermal conductivity of the scale respectively.
Considering these in turn,hiD4000 W/m^2 K.

The inside diameter,diD 230  

2 ð 1. 3 D 227 .4 mm or 0.2274m.

Therefore basing the coefficient on the outside diameter:

hioD 

4000 ð 0. 2274 / 0. 230 D3955W/m^3 K

For conduction through the wall,xwD 1 .3 mm, and from Table 9.1,kwD45 W/m K
for steel and
kw/xw D
45 / 0. 0013 D34615 W/m^2 K

The mean wall diameterD
0. 230 C 0. 2274 / 2 D 0 .2287 m and hence the coefficient
equivalent to the wall resistance based on the tube o.d. is:
34615 ð 0. 2287 / 0. 230 D
34419 W/m^2 /K

For conduction through the scale,xrD
0. 25 ð 10 ^3 m,krD 2 .1 W/m K and hence:

kr/xrD 

2. 1 / 0. 25 ð 10 ^3 D8400 W/m^2 K

The mean scale diameterD
227. 4  0. 25 D 227 .15 mm or 0.2272 m and hence the
coefficient equivalent to the scale resistance based on the tube o.d. is:

8400 ð 0. 2272 / 0. 230 D8298 W/m^2 K

∴ 1 /UD
1 / 3955 C 1 / 8500 C 1 / 34419 C 1 / 8298 D 5. 201 ð 10 ^4

and: UD1923 W/m^2 K

Temperature driving force

If water leaves the unit atTK:

 1 D 

372  283 D89 deg K, 2 D 

372 T