CHEMICAL ENGINEERING

192 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

PROBLEM 9.61

A jacketed reaction vessel containing 0.25 m^3 of liquid of density 900 kg/m^3 and specific
heat 3.3 kJ/kg K is heated by means of steam fed to a jacket on the walls. The contents of
the tank are agitated by a stirrer rotating at 3 Hz. The heat transfer area is 2.5m^2 and the
steam temperature is 380 K. The outside film heat transfer coefficient is 1.7kW/m^2 Kand
the 10 mm thick wall of the tank has a thermal conductivity of 6.0 W/m K. The inside
film coefficient was 1.1kW/m^2 K for a stirrer speed of 1.5 Hz and proportional to the
two-thirds power of the speed of rotation. Neglecting heat losses and the heat capacity of
the tank, how long will it take to raise the temperature of the liquid from 295 to 375 K?

Solution

For a stirrer speed of 1.5 Hz,hiD 1 .1kW/m^2 K.

∴ 1. 1 Dk^01. 50.^67 andk^0 D 0. 838

Thus at a stirrer speed of 3 Hz,hiD 

0. 838 ð 3. 00.^67 D 1 .75 kW/m^2 K.

The overall coefficient is given by:

1 /UD 

1 / 1750 C 

0. 010 / 6. 0 C 

1 / 1700 C 0 .00283 (equation 9.201)

and: UD 353 .8W/m^2 K neglecting scale resistances.

The time for heating the liquid is given by:

ln[

TsT 1 /

TsT 2 ]DUAt/mCp (equation 9.209)

In this case:mD
0. 25 ð 900 D225 kg andCpD3300 J/kg K.

∴ ln[
380  295 /
380  375 ]D 353. 8 ð 2. 5 t/
225 ð 3300

2. 833 D 0. 00119 tandtD2381 s 40 min

PROBLEM 9.62

By dimensional analysis, derive a relationship for the heat transfer coefficienthfor natural
convection between a surface and a fluid on the assumption that the coefficient is a function
of the following variables:
kDthermal conductivity of the fluid,CpDspecific heat of the fluid,Ddensity of the
fluid,Dviscosity of the fluid,ˇgDthe product of the coefficient of cubical expansion
of the fluid and the acceleration due to gravity, lDa characteristic dimension of the
surface, andTDthe temperature difference between the fluid and the surface.
Indicate why each of these quantities would be expected to influence the heat transfer
coefficient and explain how the orientation of the surface affects the process.
Under what conditions is heat transfer by natural convection important in Chemical
Engineering?