 # Design of Optimal Multistage Heat Exchanger

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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 , , and 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 ºF) of these exchangers are equal to , , and . Assume that the hot and cold fluids have the same flow rate and specific heat , and that Btu/hr ºF.

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We seek the optimal design, which minimizes the overall area or , where is the area of the 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 .

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Contributed by: Housam Binous and Ahmed Bellagi (January 2016)
(King Fahd University of Petroleum & Minerals, KSA; University of Monastir, Tunisia)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

A detailed mathematical formulation of the problem (objective function and inequality constraints) is given in [1, 2].

References

 M. Avriel and A. C. Williams, "An Extension of Geometric Programming with Applications in Engineering Optimization," Journal of Engineering Mathetmatics, 5(2), 1971 pp. 187–194. doi10.1007/BF01535411.

 N. Andrei, Nonlinear Optimization Applications Using the GAMS Technology, New York: Springer, 2013.

## Permanent Citation

Housam Binous and Ahmed Bellagi

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