Design of Optimal Multistage Heat Exchanger

temperature of hot fluid entering the heat exchangers (ºF)

first

300

second

400

third

600

heat exchanger

diagram

areas

Consider a three-stage heat exchanger optimal design problem [1, 2]. A cold fluid is heated from 100 °F to 500 °F by passing through three heat exchangers in series (labeled

HX

1

,

HX

2

, and

HX

3

in the diagram). At each stage, the cold stream is heated by a hot fluid. You can set the temperatures (expressed in °F) of the hot fluids entering the three heat exchangers. The overall heat transfer coefficients (expressed in Btu/hr

2

ft

ºF) of these exchangers are equal to

U

1

=120

,

U

2

=80

, and

U

3

=40

. Assume that the hot and cold fluids have the same flow rate

W

and specific heat

C

P

, and that

W×

C

P

=

5

10

Btu/hr ºF.

We seek the optimal design, which minimizes the overall area or

A

total

=

A

1

+

A

2

+

A

3

, where

A

i

is the area of the

th

i

heat exchanger. The Demonstration computes all the unknown temperatures (expressed in °F and shown in magenta in the diagram). In addition, if you select the "area" tab, you will find the computed values of the areas of the three heat exchangers that minimize

A

total

.