CHEMICAL ENGINEERING

HEAT TRANSFER 157

PROBLEM 9.25

Toluene is continuously nitrated to mononitrotoluene in a cast-iron vessel 1 m in diameter
fitted with a propeller agitator of 0.3 m diameter driven at 2 Hz. The temperature is
maintained at 310 K by circulating cooling water at 0.5 kg/s through a stainless steel coil
of 25 mm outside diameter and 22 mm inside diameter wound in the form of a helix of
0.81 m diameter. The conditions are such that the reacting material may be considered to
have the same physical properties as 75% sulphuric acid. If the mean water temperature
is 290 K, what is the overall heat transfer coefficient?

Solution

The overall coefficientUobased on the outside area of the coil is given by equation 9.201:

1 /UoD 1 /hoC

xw/kw

do/dw C 

1 /hi

do/di CRoCRi

do/di

wheredwis the mean pipe diameter.

Inside

The coefficient on the water side is given by equations 9.202 and 9.203:

hiD

k/d

 1  3. 5 d/dc 0. 023 

diu/^0.^8 

Cp/k^0.^4

where: uD 0. 5 /[
$/ 4 ð 0. 0222 ]D1315 kg/m^2 s

diD 0 .022 m,dcD 0 .80 m

and for water at 290 K:kD 0 .59 W/m K,D 0 .00108 Ns/m^2 ,andCpD4180 J/kg K.

∴ hiD
0. 59 / 0. 022
1 C 3. 5 ð 0. 22 / 0. 80 ð 0. 023
0. 022 ð 1315 / 0. 001080.^8

ð 

4180 ð 0. 00108 / 0. 590.^4

D 0. 680

26 , 7800.^8

7. 650.^4 D5490 W/m^2 K

Outside

In equation 9.204:

hodv/k

s/^0.^14 D 0. 87 

Cp/k^0.^33 

L^2 N/^0.^62

For 75% sulphuric acid:

kD 0 .40 W/m K,sD 0 .0086 N s/m^2 at 300 K,D 0 .0065 N s/m^2 at 310 K,CpD
1880 J/kg K andD1666 kg/m^3

∴
hoð 1. 0 / 0. 40
0. 0086 / 0. 00650.^14 D 0. 87
1880 ð 0. 0065 / 0. 400.^33

ð 

0. 32 ð 2. 0 ð 1665 / 0. 00650.^62

∴ 2. 5 ho

1. 3230.^14 D 0. 87


2. 550.^33
   46 , 1080.^62

and: hoD
0. 348 ð 3. 09 ð 779 / 1. 04 D 805 .5W/m^2 K