CHEMICAL ENGINEERING

180 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Solution

Use is made of equation 9.209:

ln[

TsT 1 ]/

TsT 2 DUAt/GCp

∴ ln[
390  290 /
390  360 ]D 600 ð 1. 0 t/
1000 ð 3. 8 ð 103

or: ln 3. 33 D 0. 000158 tandtD7620 s
2 .12 h

The heat lost from the vessel:QLDhAv

TTa ,whereTais the ambient temperature.

∴ QLD 8. 5 ð 10. 0
T 290 D
85. 0 T 24650 W

Heat from the steamDheat to the reactantsCheat losses

∴ UA
TsTDGCpdT/dtC 85. 0 T 24650

600 ð 1. 0

390 TD 

1000 ð 3. 8 ð 103 dT/dtC 85. 0 T 24650

∫t

0

dtD 5548

∫T 2

T 1

dT/

 3777. 6 T

∴ tD5548 ln[
377. 6 T 1 /
337. 6 T 2 ]

D5548 ln[ 

377. 6  290 /

 377. 6  360 ]D8904 s 

2 .47 h

The maximum temperature of the reactants is attained when the heat transferred from
the steam is equal to the heat losses, or:

UA

TsTDhAv

TTa

Thus: 600 C 1. 0
390 TD 8. 5 ð 10. 0
T 290 andTD378 K

The heating-up time could be reduced by improving the rate of heat transfer to the
fluid, by agitation of the fluid for example, and by reducing heat losses from the vessel
by insulation. In the case of a large vessel there is a limit to the degree of agitation and
circulation of the fluid through an external heat exchanger is an attractive alternative.

PROBLEM 9.49

What do you understand by the terms “black body” and “grey body” when applied to
radiant heat transfer?
Two large parallel plates with grey surfaces are situated 75 mm apart; one has an
emissivity of 0.8 and is at a temperature of 350 K and the other has an emissivity of 0.4
and is at a temperature of 300 K. Calculate the net rate of heat exchange by radiation
per square metre taking the Stefan – Boltzmann constant as 5. 67 ð 10 ^8 W/m^2 K^4 .Any
formula (other than Stefan’s law) which you use must be proved.