CHEMICAL ENGINEERING

196 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The change in temperature is then given by:
∫T

368

dT/

 293 TD 

1 / 1425

∫ 1800

0

dt

ln 



293  368 /

 293 TD 

1800 / 1425 D 1 .263 andTD 311 .8K.

PROBLEM 9.65

The contents of a reaction vessel are heated by means of steam at 393 K supplied to a
heating coil which is totally immersed in the liquid. When the vessel has a layer of lagging
50 mm thick on its outer surfaces, it takes one hour to heat the liquid from 293 to 373 K.
How long will it take if the thickness of lagging is doubled? Outside temperatureD293 K.
Thermal conductivity of laggingD 0 .05 W/mK. Coefficient for heat loss by radiation and
convection from outside surface of vesselD10 W/m^2 K. Outside area of vesselD8m^2.
Coil areaD 0 .2m^2. Overall heat transfer coefficient for steam coilD300 W/m^2 K.

Solution

IfTK is the temperature of the liquid at timetsandT 1 Kthe temperature at the outside
surface of the vessel, then heat flowing through the insulation is equal to the heat lost by
convection and radiation to the surroundings or:

kA/x

TT 1 DhcA

T 1 T 0

wherehcis the coefficient for heat loss,Athe outside surface area of the vessel andT 0
the ambient temperature. Thus:

0. 05 ð 8 / 0. 050 

TT 1 D 

10 ð 8 

T 1  293

and: T 1 D
0. 0909 TC 266. 4 K

∴Heat loss to the surroundings D
10 ð 8
0. 0909 TC 266. 4  293

D 

7. 272 T 2128 W

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

and net heat inputD
23580  60 T
7. 272 T 2128 D 25708  67. 3 TW

which is equal to:QDmCpdT/dt

or: mCpdT/dtD 25708  67. 3 T

and: 0. 0149 mCpdT/dtD 382 T

It takestD3600 s to heat the contents from 293 to 373 K, or:

3600 D 0. 0149 mCp

∫ 373

293

dT/

 382 T

∴ 241610 DmCpln

382  293 /
382  373 D 2. 291 mCp

and: mCpD105442 J/K