CHEMICAL ENGINEERING

202 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Taking the density as 1000 kg/m^3 ,

Mass flow of waterD 

1000 ð 0. 00049 D 0 .491 kg/s

and taking the mean specific heat as 4.18 kJ/kg K,

Heat loadD 

0. 491 ð 4. 18

309  293 D 32 .83 kW

With steam at 373 K, T 1 D 

373  293 D80 deg K,

T 2 D 

373  309 D64 deg K

and from equation 9.9,TmD 

80  64 /ln 

80 / 64 D 71 .7degK

Therefore from equation 9.1, the overall coefficient,UD 32. 83 /

 0. 602 ð 71. 7 D

0 .761 kW/m^2 K or 761 W/m^2 K.

From equation 9.201, and neglecting any scale resistance:

1 /UD 1 /hiC 1 /h 0 Cx/k

In this case,hoD8kW/m^2 KD8000 W/m^2 K, kD20 W/mK, xD 3 .2mm or

0.0032 m andhiDKu^0.^8 whereuD1m/sandKis a constant.

∴ 1 / 761 D 1 /K 10.^8 C 

1 / 8000 C 

0. 0032 / 20

0. 00131 D 

1 /KC 

0. 000125 C 0. 00016 andKD 976

ii)When the velocity is 1.3 m/s

Volume flow of waterD 

0. 00049 ð 1. 3 D 0 .000637 m^3 /s

Mass flow of water D 

1000 ð 0. 000637 D 0 .637 kg/s

∴Heat load D 

0. 637 ð 4. 18 

T 293

D 2. 663 

T 293 kW or 2663

T 293 W

The inside coefficient,hiD 976 ð 1. 30.^8 D1204 W/m^2 K

and the overall coefficient,Uis given by:

1 /UD 

1 / 1204 C 1 / 8000 C 0. 0032 / 20

∴ UD 896 .4W/m^2 K

T 1 D 

373  293 D80 deg K andT 2 D 

373 Tdeg K.

Thus, from equation 9.9:

TmD 

80  373 CT/ln[80/

 373 T]D

T 293 /ln[80/

 373 T]degK

andinequation9.1:

2663 

T 293 D 

896. 4 ð 0. 602 

T 293 /ln[80/

 373 T]

ln 80/

 373 TD 0 .2026 and: TD 307 .7K.