CHEMICAL ENGINEERING

HEAT TRANSFER 197

If the thickness of the lagging is doubled to 0.100 m, then:

0. 05 ð 8 / 0. 100 

TT 1 D 

10 ð 8 

T 1  293

and: T 1 D
0. 0476 TC 279. 1 K

∴Heat loss to the surroundings D
10 ð 8
0. 0476 TC 279. 1  293

D 

3. 808 T 1112 W

Heat input from the coilD
300 ð 0. 2
393 TD
23580  60 TW

and net heat inputD
23580  60 T
3. 808 T 1112 D 24692  63. 808 T.

∴ mCpdT/dtD
24 , 692  63. 808 T

105442 dT/dtD 

24 , 692  63. 808 T

or: 1652 .5dT/dtD 387 T

Thus, the time taken to heat the contents from 293 to 373 K is:

tD 1652. 5

∫ 373

293

dT/

 387 T

D 1625 .5ln[ 

387  293 /

 387  373 ]D 

1652. 5 ð 1. 904

D3147 s 

0 .87 h

PROBLEM 9.66

A smooth tube in a condenser which is 25 mm internal diameter and 10 m long is carrying
cooling water and the pressure drop over the length of the tube is 2ð 104 N/m^2. If vapour
at a temperature of 353 K is condensing on the outside of the tube and the temperature
of the cooling water rises from 293 K at inlet to 333 K at outlet, what is the value of the
overall heat transfer coefficient based on the inside area of the tube? If the coefficient for
the condensing vapour is 15,000 W/m^2 K, what is the film coefficient for the water? If
the latent heat of vaporisation is 800 kJ/kg, what is the rate of condensation of vapour?

Solution

From equation 3.23:
R/u^2 Re^2 DPfd^3 /
4 l/^2

Taking the viscosity of water as 1 mN s/m^2 0 .001 Ns/m^2 , then:

Pfd^3 /

 4 l/^2 D 20 , 000

0. 02531000 /

 4 ð 10

0. 0012 D 7 , 812 , 500

From Fig. 3.8, for a smooth pipe,ReD 57 , 000

∴ du/D
0. 025 u 1000 / 0. 001 D 57 , 000

and: uD 2 .28 m/s

∴Volume flow of waterD$
0. 0252 / 42. 28 D 0 .00112 m^3 /s