CHEMICAL ENGINEERING

190 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The heat flux is:

1. 511 ð 78 D 117 .9kW/m^2.
   For a small length of tube, say 0.001 m, the area for heat transferD
   $ð 0. 025 ð


2. 001 D 7. 854 ð 10 ^5 m^2

and the heat transfer rateD
117. 9 ð 7. 854 ð 10 ^5 ð 1000 D 9 .27 W.
In the small length (0.001 m) of tube, mass of materialD
0. 000491 ð 0. 001 ð 800 D
3. 93 ð 10 ^4 kg and hence temperature riseD[9. 27 /
3. 93 ð 10 ^4 ð 1. 7 ð 103 ]
D 13 .9degK/s

PROBLEM 9.58

Water passes at a velocity of 1.2 m/s through a series of 25 mm diameter tubes 5 m
long maintained at 320 K. If the inlet temperature is 290 K, at what temperature would
it leave?

Solution

Assuming an outlet water temperature ofTK, the mean water temperature is therefore:

D 0. 5 

TC 290 D 

0. 5 TC 145 K.

The coefficient may be calculated from:

hD 4280

0. 00488 T 1 u^0.^8 /d^0.^2 (equation 9.221)

D4280[0. 00488

0. 5 TC 145 1]1. 20.^8 / 0. 0250.^2

D 

25. 28 T 3028. 1 W/m^2 K

Area for heat transferD

$ð 0. 025 ð 5. 0 D 0 .393 m^2

and the heat load,QD[1. 2
$/ 40. 0252 ð 1000 ð 4. 18 ð 103
T 290 ]

D 

2462 T 714 , 045 W

Therefore neglecting any scale resistance:

2462 T 714 , 045 D 

25. 28 T 3028. 10 .393[320 

0. 5 TC 145 ]

from which: T^2 C 25. 98 T 101 , 851 D 0

and: TD 306 .4K

[An alternative approach is as follows:

The heat transferred per unit time in length dLof pipe,

Dhð$ð 0 .025dL

 320 Tk W

whereTkis the water temperature atLm from the inlet.
The rate of increase in the heat content of the water is:

$/ 4 ð 0. 0252 ð 1. 2 ð 1000 ð 4. 18 ð 103 dTD2462 dT