CHEMICAL ENGINEERING

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