CHEMICAL ENGINEERING

HEAT TRANSFER 161

and cross-sectional area for flowD
$/ 4
0. 01482 D 0 .000172 m^2 per tube or:

0. 000172 ð 162 D 0 .0279 m^2 per pass.

∴ G^0 D
37. 5 / 0. 0279 D1346 kg/m^2 s

In equation 9.61:

hið 0. 0148 / 0. 136 D 0. 023

0. 0148 ð 1346 / 0. 00290.^8

1986 ð 0. 0029 / 0. 1360.^4

hiD 0. 211

68690.^8

42. 40.^4 D1110 W/m^2 K

or, based on the outside area,hioD
1110 ð 0. 0148 / 0. 019 D865 W/m^2 K

or: hioD 0 .865 kW/m^2 K.

Overall coefficient

Neglecting the wall and scale resistance, the clean overall coefficient is:

1 /UcD 

1 / 1. 02 C 

1 / 0. 865 D 2 .136 m^2 K/kW

The area available isAD
324 ð 3. 65 ð$ð 0. 019 D 70 .7m^2 and hence the minimum
value of the design coefficient is:

1 /UDDAm/Q

 1 D 

420  330 D90 deg K, 2 D 

380  295 D85 deg K

and: mD
90  85 /ln
90 / 85 D 87 .5deg K

∴ 1 /UDD
70. 7 ð 87. 5 / 2607 D 2 .37 m^2 K/kW

The maximum allowable scale resistance is then:

RD 

1 /UD  

1 /Uc D 

2. 37  2. 136 D 0 .234 m^2 K/kW

This value is very low as seen from Table 9.16, and the exchanger would not give the
required temperatures without frequent cleaning.

PROBLEM 9.28

A 150 mm internal diameter steam pipe, carrying steam at 444 K, is lagged with 50 mm
of 85% magnesia. What will be the heat loss to the air at 294 K?

Solution

In this case:diD 0 .150 m,doD 0 .168 m anddwD 0. 5
0. 150 C 0. 168 D 0 .159 m.

dsD
0. 168 ð 2 ð 0. 050 D 0 .268 m anddm(the logarithmic mean ofdoandds) D
0 .215 m.