CHEMICAL ENGINEERING

132 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

larger concentric pipe; the oil and water moving in opposite directions. The oil enters at
420 K and is to be cooled to 320 K. If the water enters at 290 K, what length of pipe
will be required? Take coefficients of 1.6kW/m^2 K on the oil side and 3.6kW/m^2 Kon
the water side and 2.0 kJ/kg K for the specific heat of the oil.

Solution

Heat load

Mass flow of oilD 6. 0 ð 10 ^2 kg/s.

and hence,QD
6. 0 ð 10 ^2 ð 2. 0
420  320 D12 kW

Thus the water outlet temperature is given by:

12 D 

6. 0 ð 10 ^2 ð 4. 18 

T 290 orTD338 K

Logarithmic mean temperature driving force

In equation 9.9:

 1 D 

420  338 D82 deg K, 2 D 

320  290 D30 deg K

and: mD
82  30 /ln
82 / 30 D 51 .7deg K

Overal coefficient

The pipe wall is thin and hence its thermal resistance may be neglected.
Thus in equation 9.8:

1 /UD 1 /hoC 1 /hiD 

1 / 1. 6 C 1 / 3. 6 and UD 1 .108 kW/m^2 K

Area

In equation 9.1,ADQ/UmD 12 /

1. 108 ð 51. 7 D 0 .210 m^2

Tube diameterD 25 ð 10 ^3 m (assuming a mean value)

area/unit lengthD
$ð 25 ð 10 ^3 ð 1. 0 D 7. 85 ð 10 ^2 m^2 /m

and the tube length requiredD 0. 210 /
7. 85 ð 10 ^2 D 2 .67 m

PROBLEM 9.7

The walls of a furnace are built of a 150 mm thickness of a refractory of thermal conduc-
tivity 1.5 W/m K. The surface temperatures of the inner and outer faces of the refractory
are 1400 K and 540 K respectively. If a layer of insulating material 25 mm thick of