CHEMICAL ENGINEERING

174 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Solution

IfTandT^0 are the liquid and thermometer temperatures respectively after timets, then:

dT/dtD 0 .05 K/s and hence TD 290 C 0. 05 t

WhentD600 s,
TT^0 D1.

∴ TD 290 C
600 ð 0. 05 D320 K and T^0 D319 K

Balancing:GtCtdT^0 /dtDUA

TT^0

∴
30 / 10004 .18 dT^0 /dtDUA
290 C 0. 05 tCT^0

∴ dT^0 /dtC 7. 98 UAT^0 D 2312 UA
1 C 0. 000173 t

∴ e^7.^98 UAtT^0 D 2312 UA

{

1 C 0. 000173 t

e^7.^98 UAt

7. 98 UA



∫

0. 000173

e^7.^98 UAt

7. 98 UA

dt

}

D 290

1 C 0. 000173 te^7.^98 UAt 0. 050

e^7.^98 UAt

7. 98 UA

Ck

WhentD0,T^0 D290 K and kD 0. 00627 /UA.

∴ T^0 D 290
1 C 0. 000173 t
0. 00627 /UA
1 e^7.^98 UAt

WhentD600 s,T^0 D319 K.

∴ 319 D 320 C
0. 00627 /UA
1 e^4789 UA

∴  4789 UADln
1  159. 5 UA

and: UAD 0 .000209 ln
1  159. 5 UA

Solving by trial and error:UAD 0 .00627 kW/K.

AD 0 .01 m^2 and hence:UD 0 .627 kW/m^2 K or 627 W/m^2 K

∴ 627 D 735 u^0.^8 and uD 0 .82 m/s

PROBLEM 9.43

In a shell-and-tube type of heat exchanger with horizontal tubes 25 mm external diameter
and 22 mm internal diameter, benzene is condensed on the outside of the tubes by means
of water flowing through the tubes at the rate of 0.03 m^3 /s. If the water enters at 290 K
and leaves at 300 K and the heat transfer coefficient on the water side is 850 W/m^2 K,
what total length of tubing will be required?

Solution

Mass flow of waterD
0. 03 ð 1000 D30 kg/s