194 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
Assume that the film heat transfer coefficient for the liquid in the tubes is proportional
to the 0.8 power of the velocity, that the transfer coefficient for the condensing steam
remains constant at 3.4kW/m^2 K and that the resistance of the tube wall and scale can
be neglected.
Solution
i) For a flow of 1. 75 ð 10 ^4 m^3 /s:
Density of the liquidD1100 kg/m^3
Mass flow D
1. 75 ð 10 ^4 ð 1100 D 0 .1925 kg/s.
Heat load D 0. 1925 ð 4. 0
373 295 D 61 .6kW
1 D
395 295 D100 deg K, 2 D
395 375 D20 deg K
andinequation9.9:
mD
100 20 /ln
100 / 20 D 49 .7degK
Thus, in equation 9.1:
U 1 AD
61. 6 / 49. 7 D 1 .239 kW/K
ii)For a flow of 3. 25 ð 10 ^4 m^3 /s:
Mass flowD
3. 25 ð 10 ^4 ð 1100 D 0 .3575 kg/s
Heat load D 0. 3575 ð 4. 0
370 295 D 107 .3kW
1 D
395 295 D100 deg K, 2 D
395 370 D25 deg K
andinequation9.9:
mD
100 25 /ln
100 / 25 D 54 .1degK
Thus in equation 9.1:
U 2 AD
107. 3 / 54. 1 D 1 .983 kW/K
∴ U 2 /U 1 D
1. 983 / 1. 239 D 1. 60
The velocity in the tubes is proportional to the volumetric flowrate,vcm^3 /sand
hence
hi/v^0.^8 orhiDk^0 v^0.^8 ,wherek^0 is a constant.
Neglecting scale and wall resistances:
1 /UD 1 /h 0 C 1 /hi
D
1 / 3. 4 C
1 /k^0 v^0.^8
and: UD 3. 4 k^0 v^0.^8 /
3. 4 Ck^0 v^0.^8