CHEMICAL ENGINEERING

142 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

0.7 m long, per row. They are arranged in-line, with centre-to-centre spacing equal, in
both directions, to one-and-a-half times the pipe diameter. Both inner and outer diameter
may be taken as 12 mm. Air with a mass velocity of 8 kg/m^2 s enters the pipes at 290 K.
The initial gas temperature is 480 K and the total mass flow of the gases crossing the
pipes is the same as the total mass flow of the air through them.
Neglecting gas radiation, estimate the outlet temperature of the air. The physical
constants for the waste gases, assumed the same as for air, are:

Temperature Thermal conductivity Viscosity

(K) (W/m K) (mN s/m^2 )

250 0.022 0.0165

310 0.027 0.0189

370 0.030 0.0214

420 0.033 0.0239

480 0.037 0.0260

Specific heatD 1 .00 kJ/kg K.

Solution

Heat load

The cross area for flow per pipeD
$/ 4
0. 0122 D 0 .000113 m^2 and therefore for
12 ð
20 D240 pipes, the total flow areaD
240 ð 0. 000113 D 0 .027 m^2.

Thus: flow of airD 

8. 0 ð 0. 271 D 0 .217 kg/s

which is also equal to the flow of waste gas.
If the outlet temperatures of the air and waste gas areTaandTwK respectively, then:

QD 

0. 217 ð 1. 0 

Ta 290 kW or 217

Ta 290 W

and: QD
0. 217 ð 1. 0
480 Tw kW

from which: TwD
770 Ta K

Area

Surface area/unit length of pipeD
$ð 0. 012 ð 1. 0 D 0 .0377 m^2 /m.

Total length of pipeD 

240 ð 0. 7 D168 m

and hence the heat transfer area,AD
168 ð 0. 0377 D 6 .34 m^2.

Temperature driving force

 1 D 

480 Ta

 2 D

Tw 1290