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SCIENCE CHINA Technological Sciences, Volume 59 , Issue 7 : 1071-1079(2016) https://doi.org/10.1007/s11431-016-6076-4

Differences and relations of objectives, constraints, and decision parameters in the optimization of individual heat exchangers and thermal systems

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  • ReceivedFeb 25, 2016
  • AcceptedApr 24, 2016
  • PublishedJun 20, 2016

Abstract

Performance improvement of heat exchangers and the corresponding thermal systems benefits energy conservation, which is a multi-parameters, multi-objectives and multi-levels optimization problem. However, the optimized results of heat exchangers with improper decision parameters or objectives do not contribute and even against thermal system performance improvement. After deducing the inherent overall relations between the decision parameters and designing requirements for a typical heat exchanger network and by applying the Lagrange multiplier method, several different optimization equation sets are derived, the solutions of which offer the optimal decision parameters corresponding to different specific optimization objectives, respectively. Comparison of the optimized results clarifies that it should take the whole system, rather than individual heat exchangers, into account to optimize the fluid heat capacity rates and the heat transfer areas to minimize the total heat transfer area, the total heat capacity rate or the total entropy generation rate, while increasing the heat transfer coefficients of individual heat exchangers with different given heat capacity rates benefits the system performance. Besides, different objectives result in different optimization results due to their different intentions, and thus the optimization objectives should be chosen reasonably based on practical applications, where the inherent overall physical constraints of decision parameters are necessary and essential to be built in advance.


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51422603, 51356001 & 51321002), and the National Basic Research Program of China (“973” Project) (Grant No. 2013CB228301).

Supporting Information

The supporting information is available online at tech.scichina.com and www.springerlink.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.


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  • Figure 1

    (Color online) The sketch of a heat exchanger network with three heat exchangers.

  • Figure 2

    (Color online) The equivalent thermal circuit diagram of the HXN.

  • Figure 3

    (Color online) The optimized total heat transfer areas versus the heat transfer coefficient of HE1.

  • Table 1   The optimal heat capacity rates of each fluid and the corresponding heat transfer areas with prescribed total heat capacity rate for different optimization objectives

    Min

    Heat capacity rate (W K-1)

    Area (m2)

    Ch,1

    Ch,2

    Cc,1

    Cc,2

    Cc,3

    A1

    A2

    A3

    At

    At

    60.40

    143.05

    60.38

    63.75

    72.42

    0.0185

    0.0193

    0.0220

    0.0598

    Sg,t

    66.43

    116.25

    81.61

    72.23

    63.47

    0.0182

    0.0196

    0.0224

    0.0603

    A1

    238.65

    37.20

    21.01

    54.88

    48.26

    0.0173

    0.0225

    0.0273

    0.0670

    A2

    5.00

    170.82

    4.29

    170.79

    49.11

    0.7466

    0.0188

    0.0222

    0.7876

    A3

    4.38

    258.02

    4.21

    4.58

    128.80

    0.4694

    0.1899

    0.0211

    0.6803

    Sg,1

    168.89

    11.15

    205.48

    4.59

    9.90

    0.0175

    0.1908

    1.3120

    1.5203

    Sg,2

    77.47

    147.13

    77.47

    4.68

    93.26

    0.0181

    0.0749

    0.0218

    0.1148

    Sg,3

    90.11

    92.37

    41.78

    27.80

    147.93

    0.0195

    0.0216

    0.0223

    0.0634

  • Table 2   The optimal heat transfer areas and the corresponding heat capacity rates of each fluid with prescribed total heat transfer area for different optimization objectives

    Min

    Area (m2)

    Heat capacity rate (W K-1)

    A1

    A2

    A3

    Ch,1

    Ch,2

    Cc,1

    Cc,2

    Cc,3

    Ct

    Ct

    0.375

    0.135

    0.490

    4.49

    11.77

    4.49

    4.62

    9.56

    34.93

    Sg,t

    0.272

    0.240

    0.492

    5.47

    10.66

    4.46

    5.79

    8.98

    35.35

    C1

    0.479

    0.256

    0.265

    4.73

    15.50

    4.29

    4.59

    25.20

    54.31

    C2

    0.202

    0.336

    0.559

    18.54

    4.29

    26.44

    5.76

    9.80

    64.83

    C3

    0.252

    0.123

    0.629

    15.18

    7.23

    7.13

    31.99

    5.37

    66.90

    Sg,1

    0.366

    0.306

    0.329

    6.83

    11.50

    5.51

    6.79

    13.92

    44.55

    Sg,2

    0.109

    0.353

    0.536

    20.43

    4.49

    23.34

    5.78

    15.61

    69.64

    Sg,3

    0.345

    0.128

    0.529

    3.93

    8.30

    5.29

    14.27

    13.83

    45.62

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