CHEMICAL ENGINEERING

154 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

No. of tube passes Total tubes Outlet water temperature Tube length

Nn T(K) (m)

19.42G 308.6 3.05

2 18.84G 327.2 3.99

4 37.68G 364.4 —

6 56.52G 401.6 —

Arrangements with 4 and 6 tube side passes require water outlet temperatures in excess
of the condensing temperature and are clearly not possible. With 2 tube side passes,
TD 327 .2 K at which severe scaling would result and hence the proposed unit would
consist of one tube side pass and a tube length of 3.05 m.

The outlet water temperature would be 308.6K.

PROBLEM 9.21

A heat exchanger is required to cool continuously 20 kg/s of water from 360 K to 335 K
by means of 25 kg/s of cold water, inlet temperature 300 K. Assuming that the water
velocities are such as to give an overall coefficient of heat transfer of 2 kW/m^2 K, assumed
constant, calculate the total area of surface required (a) in a counterflow heat exchanger,
i.e. one in which the hot and cold fluids flow in opposite directions, and (b) in a multi-
pass heat exchanger, with the cold water making two passes through the tubes, and the
hot water making one pass along the outside of the tubes. In case (b) assume that the
hot-water flows in the same direction as the inlet cold water, and that its temperature over
any cross-section is uniform.

Solution

The heat load,QD 20 ð 4. 18
360  335 D2090 kW

and the outlet cold water temperature is given by: 2090D
25 ð 4. 18 
T 2  300 orT 2 D
320 K

Case (a)

 1 D 

360  320 D40 deg K, 2 D 

335  300 D35 deg K

and in equation 9.9:

mD 

40  35 /ln 

40 / 35 D 37 .4deg K

As the flow is true counter-flow, no correction factor is necessary andFD 1 .0. Therefore
in equation 9.150:

ADQ/UFmD 2090 /

 2. 0 ð 1. 0 ð 37. 4 D 27 .94 m^2