Page 202 - Design and Operation of Heat Exchangers and their Networks

CHAPTER 5

Optimal design of heat

exchangers

a
b
Wilfried Roetzel , Xing Luo , Dezhen Chen c
a
Institute of Thermodynamics, Helmut Schmidt University/University of the Federal Armed Forces Hamburg,
Hamburg, Germany
b
Institute of Thermodynamics, Gottfried Wilhelm Leibniz University Hannover, Hannover, Germany
c
Institute of Thermal Energy and Environmental Engineering, Tongji University, Shanghai, China

Generally speaking, the heat exchanger design is a design optimization prob-
lem because it deals with many factors, parameters, and requirements. The
heat exchanger design problem involves many variables for geometry and
operating conditions; also, the heat exchanger should be designed for a vari-
ety of applications with different objectives. In addition to the selection of
surfaces on both sides, one also needs to consider a number of design criteria
and constraints in heat exchanger design for a given application. Although
the experiences will help us to make a suitable design, the methodologies for
heat exchanger optimization for different applications and exchanger types
are always expected.
Bergles et al. (1974) performed an evaluation of different objective func-
tions for compact heat exchangers with different heat exchanger surfaces and
improved heat exchanger performance by properly choosing the heat
exchanger surfaces and adjusting two design parameters. Their method
did not include any actual optimization technique, but their results did show
that a great improvement in heat exchanger performance can be achieved.
Fax and Mills (1957) develop a method using Lagrange multipliers to opti-
mize a heat exchanger design under specified constraints. This Lagrange
multiplier technique requires the objective function f(x) and the constraints
that are differentiable throughout the range of interest and can be expressed
in an explicit form. The total number of constraints is less than the total
number of variables, and all constraints are equality constraints. The previous
limitations would be strict with the use of this method to only a limited
number of optimization problems. Thanks to the rapid developments in
computer and computing techniques as well as a large number of software

Design and Operation of Heat Exchangers and their Networks © 2020 Elsevier Inc.
https://doi.org/10.1016/B978-0-12-817894-2.00005-4 All rights reserved. 191