CHEMICAL ENGINEERING

184 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Outside:
For condensation on vertical tubes:

ho

^2 /k^3 ^2 g^0.^33 D 1. 47

 4M/^0.^33 (equation 9.174)

The wall temperature is approximately 0. 5
353 C 297. 5 D325 K, and the benzene
film temperature will be taken as 0. 5
353 C 325 D339 K.
At 339 K:kD 0 .15 W/m K,D880 kg/m^3 ,andD 0. 35 ð 10 ^3 Ns/m^2.
With 60 tubes, the mass flow of benzene per tube,G^0 D

1. 25 / 60 D 0 .0208 kg/s.
   For vertical tubes,MDG^0 /$doD 0. 0208 /
   $ð 0. 025 D 0 .265 kg/ms

∴ ho[
0. 35 ð 10 ^32 / 0. 152 ð 8802 ð 9 .8]^0.^33 D 1 .47[4ð 0. 0208 /
0. 35 ð 10 ^3 ]^0.^33

∴ 1. 699 ð 10 ^4 hoD

1. 47 ð 1. 62 ð 10 ^1

and: hoD1399 W/m^2 Kor1.40 kW/m^2 K

Overall:
Neglecting scale resistances:

1 /UD 1 /hioCx/kC 1 /hoD 0. 265 C 0. 036 C 0. 714 D 1 .015 m^2 K/kW

and: UD 0 .985 kW/m^2 K

This is in excess of the value required and would allow for a reasonable scale resistance.
If this were negligible, the water throughput could be reduced.
On the basis of these calculations, 60 tubes are required.

PROBLEM 9.53

One end of a metal bar 25 mm in diameter and 0.3 m long is maintained at 375 K and heat
is dissipated from the whole length of the bar to surroundings at 295 K. If the coefficient
of heat transfer from the surface is 10 W/m^2 K, what is the rate of loss of heat? Take the
thermal conductivity of the metal as 85 W/m K.

Solution

Use is made of equation 9.254:

QfD

√

hbkA 1 tanhmL

where the coefficient of heat transfer from the surface, hD10 W/m^2 K; the
perimeter,bD
$ð 0. 025 C 0 .0785 m; the cross-sectional area,AD
$/ 4 ð 0. 0252 D
0 .000491 m^2 ; the thermal conductivity of the metal,kD85 W/m K; the temperature
difference at the root,  1 D
375  295 D80 deg K; the value of mD

p
p
hb/kAD
[
10 ð 0. 0785 /
85 ð 0. 000491 ]D 4 .337, and the length of the rod,LD 0 .3m.

∴ QfD

√

10 ð 0. 0785 ð 85 ð 0. 000491 [80 tanh 

4. 337 ð 0. 3 ]