CHEMICAL ENGINEERING

HEAT TRANSFER 131

Area required

In equation 9.1,ADQ/UmD
74. 7 ð 103 /
63. 7 ð 180 D 6 .52 m^2.

Area/unit length of tubeD

$/ 4

12 ð 10 ^2 D 9. 43 ð 10 ^3 m^2 /m and hence:

total length of tubing requiredD 6. 52 /
9. 43 ð 10 ^3 D 6. 92 ð 102 m.

The length of each tube is thereforeD 

6. 92 ð 102 /

 20 ð 20 D 1 .73 m

PROBLEM 9.5

A cooling coil, consisting of a single length of tubing through which water is circulated, is
provided in a reaction vessel, the contents of which are kept uniformly at 360 K by means
of a stirrer. The inlet and outlet temperatures of the cooling water are 280 K and 320 K
respectively. What would be the outlet water temperature if the length of the cooling coil
were increased by 5 times? Assume the overall heat transfer coefficient to be constant
over the length of the tube and independent of the water temperature.

Solution

QDUATm (equation 9.1)

whereTmis the logarithmic mean temperature difference. For the initial conditions:

Q 1 D

m 1 ð 4. 18

320  280 DU 1 A 1 [ 

360  280  

360  320 ]/

[ln 

360  280 /

 360  320 ]

or: 167. 2 m 1 DU 1 A 1
80  40 /ln 80/ 40 D 57. 7 U 1 A 1

and:
m 1 /U 1 A 1 D 0. 345

In the second case,m 2 Dm 1 ,U 2 DU 1 ,andA 2 D 5 A 1.

∴ Q 2 D
m 1 ð 4. 18 
T 280 D 5 U 1 A 1 [
360  280 
360 T]/

ln 

360  280 /

 360 T

or: 4. 18
m 1 /U 1 A 1 
T 280 / 5 D
80  360 CT/[ln[80/ 360 T]

Substituting for

m 1 /U 1 A 1 ,

0. 289 

T 280 D

T 280 /[ln 80/

 360 T]

or: ln[80/
360 T]D 3 .467 and TD 357 .5K

PROBLEM 9.6

In an oil cooler, 216 kg/h of hot oil enters a thin metal pipe of diameter 25 mm. An
equal mass of cooling water flows through the annular space between the pipe and a