# Operation and Multi-Objective Design Optimization of a Plate Heat Exchanger with Zigzag Flow Channel Geometry

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Model and Experimental Setup

#### 2.2. Optimization of Operation Conditions by the Taguchi Method and Analysis of Variance (ANOVA)

_{9}(3

^{3}) orthogonal array with 9 cases can be constructed, as shown in Table 3.

#### 2.3. Schematic of the PHE Model

#### 2.4. Theoretical Model and Numerical Simulation

_{p}is the specific heat of water, and T is the temperature. The heat diffusion equation in the solid regions is:

#### 2.5. Genetic Algorithm for Multi-Objective Optimization

_{i}is the objective function, g

_{j}is the equality constraint, h

_{k}is the inequality constraint, and x is the design variable (geometrical parameter or working condition). The subscripts i, j, and k represent the number of the state variable.

## 3. Results and Discussion

#### 3.1. Operating Factor Analysis by the Taguchi Method

#### 3.2. ANOVA Analysis

#### 3.3. Effect of Geometric Parameters of the Zigzag Flow Channel

#### 3.4. Optimization of Flow Channel Geometry by NSGA-II

^{2}) value for this equation is 0.91. In fact, any point on the Pareto optimal front is the optimal design point. The choice of the design point is based on the consideration of the relative importance of the two objective functions. Then the corresponding optimal geometric design of the zigzag flow channel can be determined.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The photos and dimensions of (

**a**) the PHE, (

**b**) the flow channel plate, and (

**c**) the PCM plate.

**Figure 2.**(

**a**) The directions of cold/hot water flows in the flow channel plates, and (

**b**) the structure of the PHE.

**Figure 4.**The simplified model of PHE with zigzag flow channels. The boundary conditions are adiabatic on the lateral surfaces and periodic on the top and bottom surfaces.

**Figure 9.**(

**a**) Effectiveness and (

**b**) S/N ratio for the nine cases in the orthogonal array, and (

**c**) mean S/N ratio variations for factors A, B, and C with three levels.

**Figure 10.**(

**a**) Radar chart for Taguchi factor influences; and (

**b**) correlation of Taguchi experimental design influence value and ANOVA p-values.

**Figure 11.**Effects of (

**a**) the entrance length, (

**b**) the bending angle, and (

**c**) the fillet radius on the effectiveness and pressure drop of the PHE.

**Figure 13.**The variations of the pressure drop with the effectiveness at the three typical design points A′, B′, and C′ as marked in the Pareto optimal front (Figure 11) by adjusting (

**a**) entrance length, (

**b**) bending angle, and (

**c**) fillet radius.

**Figure 14.**Simulation results at optimal design points A′ and C′ in Figure 12; (

**a**) the axial velocity magnitude along the hot water channels, and (

**b**) the profiles of axial velocity magnitude and streamline pattern at the turning locations of the flow channels.

Heat Exchanger | Working Fluid | Objective Function | Ref. |
---|---|---|---|

Plate-fin heat exchanger | Air | Maximize: Colburn factor Minimize: friction factor | [16] |

Plate heat exchanger | R134a and water | Maximize: heat transfer surface area Minimize: pressure drop | [17] |

Shell and tube heat exchanger | Oil and water | Maximize: effectiveness Minimize: pressure drop, cost, and entropy generation | [18] |

Plate-fin heat exchanger | Air | Maximize: effectiveness Minimize: total annual cost | [19] |

Fin-and-tube heat exchanger | Air and water | Minimize: total weight Minimize: total annual cost | [20] |

Printed circuit heat exchanger | CO_{2} | Maximize: temperature rise Minimize: pressure drop | [21] |

Factor | Control Parameter | Level | ||
---|---|---|---|---|

1 | 2 | 3 | ||

A | Inlet temperature of hot water (°C) | 75 | 85 | 95 |

B | Inlet temperature of cold water (°C) | 10 | 20 | 30 |

C | Flow rate ratio of cold/hot water flows * | 0.25 | 0.5 | 1 |

^{−1}(LPM).

Case | Factor | ||
---|---|---|---|

A | B | C | |

1 | 1 | 1 | 1 |

2 | 1 | 2 | 2 |

3 | 1 | 3 | 3 |

4 | 2 | 1 | 2 |

5 | 2 | 2 | 3 |

6 | 2 | 3 | 1 |

7 | 3 | 1 | 3 |

8 | 3 | 2 | 1 |

9 | 3 | 3 | 2 |

Factor | DF | Adj SS | Adj MS | F-Value | p-Value |
---|---|---|---|---|---|

A | 2 | 4.9371 | 2.4686 | 10.73 | 0.085 |

B | 2 | 0.7832 | 0.3916 | 1.70 | 0.370 |

C | 2 | 63.8308 | 31.9154 | 138.74 | 0.007 |

Residual Error | 2 | 0.4601 | 0.2300 | ||

Total | 8 |

Design Point | Geometric Parameters | Objective Function | |||
---|---|---|---|---|---|

Entrance Length (mm) | Bending Angle (degree) | Fillet Radius (mm) | Effectiveness | Pressure Drop (Pa) | |

A′ | 10 | 100.1 | 6.18 | 0.955 | 529 |

B′ | 10 | 117.2 | 6.17 | 0.953 | 492 |

C′ | 10 | 144.0 | 6.09 | 0.948 | 454 |

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**MDPI and ACS Style**

Chen, W.-H.; Li, Y.-W.; Chang, M.-H.; Chueh, C.-C.; Ashokkumar, V.; Saw, L.H.
Operation and Multi-Objective Design Optimization of a Plate Heat Exchanger with Zigzag Flow Channel Geometry. *Energies* **2022**, *15*, 8205.
https://doi.org/10.3390/en15218205

**AMA Style**

Chen W-H, Li Y-W, Chang M-H, Chueh C-C, Ashokkumar V, Saw LH.
Operation and Multi-Objective Design Optimization of a Plate Heat Exchanger with Zigzag Flow Channel Geometry. *Energies*. 2022; 15(21):8205.
https://doi.org/10.3390/en15218205

**Chicago/Turabian Style**

Chen, Wei-Hsin, Yi-Wei Li, Min-Hsing Chang, Chih-Che Chueh, Veeramuthu Ashokkumar, and Lip Huat Saw.
2022. "Operation and Multi-Objective Design Optimization of a Plate Heat Exchanger with Zigzag Flow Channel Geometry" *Energies* 15, no. 21: 8205.
https://doi.org/10.3390/en15218205