# Performance and Exergy Transfer Analysis of Heat Exchangers with Graphene Nanofluids in Seawater Source Marine Heat Pump System

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}heat pump system with graphene nano-fluid refrigerant is experimentally studied, and the influence of related factors on its heat transfer enhancement performance is analyzed. First, the paper describes the transformation of the heat pump system experimental bench, the preparation of six different mass concentrations (0~1 wt.%) of graphene nanofluid and its thermophysical properties. Secondly, this paper defines graphene nanofluids as beneficiary fluids, the heat exchanger gains cold fluid heat exergy increase, and the consumption of hot fluid heat is heat exergy decrease. Based on the heat transfer efficiency and exergy efficiency of the heat exchanger, an exergy transfer model was established for a seawater source of tube heat exchanger. Finally, the article carried out a test of enhanced heat transfer of heat exchangers with different concentrations of graphene nanofluid refrigerants under simulated seawater constant temperature conditions and analyzed the test results using energy and an exergy transfer model. The results show that the enhanced heat transfer effect brought by the low concentration (0~0.1 wt.%) of graphene nanofluid is greater than the effect of its viscosity on the performance and has a good exergy transfer effectiveness. When the concentration of graphene nanofluid is too high, the resistance caused by the increase in viscosity will exceed the enhanced heat transfer gain brought by the nanofluid, which results in a significant decrease in the exergy transfer effectiveness.

## 1. Introduction

_{2}emissions of marine vessels will account for 18% of the global total by 2050 [2]. Most of the ship’s energy consumption and emissions are energy consumption for its cargo storage, personnel production and life. Traditional ship air conditioners generally use exhaust gas or oil-fired boilers to generate saturated steam above 150 °C for heat exchangers. Then, the fan or steam pipeline sends the heat to each cabin, to achieve the purpose of heating and domestic hot water. However, due to the general slowdown of the ship, the steam generated by the exhaust gas boiler cannot meet the needs of the whole ship, and an oil-fired boiler has to be used to assist [3], which will lead to an increase in the operating cost of the whole ship. Data show that the demand for refrigeration air conditioning and hot water for cruise ships accounts for more than 45% of the entire ship’s electricity consumption [4]. These electric power needs to consume a large amount of fuel, which will generate huge additional energy consumption in addition to power navigation, especially when the ship’s power system is not working after the port is docked, and its energy consumption and emissions will be more serious without the main engine energy recovery [5]. In summary, the quality of the air in the ship, as well as the supply of cold and heat, will not only greatly affect the health and efficiency of the crew and passengers, but also bring safety risks to the operation of the cargo and the main and auxiliary equipment of the ship’s operation.

_{2}O-LiBr absorption heat pump as the HVAC system. Yun et al. [13] proposed an automatic cascade heat pump system to overcome the adverse effect of environmental temperature on the efficiency of the CO

_{2}heat pump. The automatic cascade heat pump uses two-stage expansion and CO

_{2}-R32 azeotropic refrigerant. Priarone et al. [14] used a curve fitting method to import measured data from a large number of suppliers into the software, and built models of ground source water heat pumps and air heat pumps, and finally estimated the COP of the heat pump under different temperature operating conditions.

_{2}and R410A heat pumps in zero-energy comprehensive building applications. Combined with experimental data and models, the situation of two hot pumps receiving and generating hot water at the same ambient temperature was analyzed. Aiming at the characteristic that transcritical CO

_{2}is more sensitive to working conditions, an optimization method was developed to improve its performance. The above research content reflects an alternative situation of the current thermal system working fluid. The research hotspots are mainly the application of environmentally friendly new working fluid and the impact of the system.

_{2}O

_{3}nanoparticles increases, the average Nusselt number increases. Qi et al. [34] used a two-step method to prepare stable titanium dioxide-water nanofluids and tested their heat transfer and flow characteristics in triangular and circular tube heat exchanger systems. The fitting formula of the Nusselt number and drag coefficient of nanofluid in the triangular tube is given, and the comprehensive performance of nanofluid in the triangular tube is studied. In recent years, research on related nanometers has been very rapid. Due to its better thermophysical properties, the heat transfer performance of the fluid can be increased. Among many nanofluids, graphene is a leader with higher thermal conductivity and electrical conductivity, and smaller viscosity [35,36,37]. Therefore, it is very promising to study graphene nanofluids as refrigerants to increase the performance of traditional thermal systems.

_{2}heat pump system. The temperature and pressure coupled exergy transfer analysis method is used to specifically evaluate the comprehensive performance of the heat exchanger to guide subsequent optimization and practical design.

## 2. Research Methods and Experiments

#### 2.1. Heat Pump Heat Exchanger Test-Bed

_{2}heat pump system with a seawater source. The original heat pump system is a 1.5 HP transcritical CO

_{2}water source heat pump system test bench for heating energy efficiency of about four, which can supply 80–200 L of hot water at a temperature of 55~60 °C [38,39]. The modified seawater source circulation system is shown in Figure 1. Based on the nano-fluid refrigerant-enhanced heat transfer enhanced seawater source heat pump heat exchanger, a testbed for improving performance, other transcritical CO

_{2}heat pump systems, data measurement acquisition and electrical control systems are constant.

_{1}, x

_{2}, etc. and w

_{1}, w

_{2}, etc. are the independent variables of a measuring result and the uncertainties, respectively.

#### 2.2. Properties of Graphene Nanofluid

## 3. Exergy Transfer Model and Data Reduction

_{p}is specific heat at constant pressure, v is the specific volume of the working medium, T

_{Θ}is the environment temperature. For incompressible fluids, v is considered to be constant in normal physical properties and ${(\frac{\partial v}{\partial T})}_{P}=0$ is brought into Equation (4) to obtain:

_{e}of the heat exchanger is defined as the actual exergy change of the target heat exchange medium compared to its maximum possible exergy change. For the heat exchanger of this study, the target medium is cold fluid, which benefits from the increase of the cold fluid (graphene nanofluid refrigerant) heat exergy and its consumption is the reduction of the hot fluid (seawater) heat exergy. The maximum possible exergy change of the medium is the maximum exergy change in the ideal state of the countercurrent, i.e., the case of the pressure exergy loss of the countercurrent is 0, after that:

## 4. Results and Discussion

#### 4.1. Performance Analysis of Heat Exchanger

#### 4.2. Energy Transfer Efficiency Analysis

## 5. Conclusions

_{2}heat pump system. Firstly, the effect of the enhanced heat transfer and fluid resistance factor in the heat exchanger using different concentrations of graphene nanofluids was studied. Secondly, based on the heat transfer effectiveness and exergy efficiency of the heat exchanger, a heat exchanger exergy transfer model was theoretically established. Finally, exergy transfer was evaluated for various working conditions of the graphene nanofluid heat exchanger with different concentrations. The main conclusions are as follows:

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | area of surface-heat transfer (m^{2}) |

c_{p} | heat capacity (J·kg^{−1}·K^{−1}) |

d | hydraulic diameter (m) |

D | heat capacity ratio |

e | exergy (W) |

ΔE | specific exergy (W) |

f | friction factor |

h | heat transfer coefficient (W·m^{−2}·K^{−1}) |

L | heat transfer length (mm) |

k | thermal conductivity (W·m^{−1}·K^{−1}) |

m | mass flow rate (kg·s^{−1}) |

Nu | Nusselt number |

ΔP | pressure drop (kPa) |

Pe | Peclet number |

Pr | Prandtl number |

q | heat (W) |

Q | heat flux (W) |

Re | Reynolds number |

s | cross-sectional area (m^{2}) |

T | temperature (K) |

U | overall heat transfer coefficient (W·m^{−2}·K^{−1}) |

v | specific volume (m^{3}·kg^{−1}) |

P_{w} | pump power (kW) |

μ | dynamic viscosity (Pa·s) |

u | velocity (m·s^{−1}) |

Greek symbols | |

ε_{E} | exergy transfer effectiveness |

ρ | density (kg·m^{−3}) |

ϕ | volume concentration |

φ | thermal efficiency |

Subscripts | |

bf | base fluid |

exp | experimental |

c, h | cold or hot side |

nf | nanofluid |

i, o | inlet or outlet |

Θ | environment |

Abbreviations | |

EGW | ethylene glycol-water |

GnP | graphene nanoplatelets |

CHTC | convective heat-transfer coefficient |

ID/OD | inner tube/outer tube |

HVAC | heating ventilation air conditioning |

TC | thermocouple |

DP | differential pressure |

HE | heat exchanger |

RMSE | root-mean-square error |

## References

- Han, F.; Wang, Z.; Ji, Y.; Li, W. Energy analysis and multi-objective optimization of waste heat and cold energy recovery process in LNG-fueled vessels based on a triple organic Rankine cycle. Energy Convers. Manag.
**2019**, 195, 561–572. [Google Scholar] [CrossRef] - Trivyza, N.L.; Rentizelas, A.; Theotokatos, G. Impact of carbon pricing on the cruise ship energy systems optimal configuration. Energy
**2019**, 175, 952–966. [Google Scholar] [CrossRef] [Green Version] - Benamara, H.; Hoffmann, J.; Youssef, F. Maritime Transport: The Sustainability Imperative. In Sustainable Shipping; Springer: Cham, Switzerland, 2019; pp. 1–31. [Google Scholar]
- Goldsworthy, B.; Goldsworthy, L. Assigning machinery power values for estimating ship exhaust emissions: Comparison of auxiliary power schemes. Sci. Total Environ.
**2019**, 657, 963–977. [Google Scholar] [CrossRef] [PubMed] - Valencia Ochoa, G.; Acevedo Peñaloza, C.; Duarte Forero, J. Thermoeconomic optimization with PSO Algorithm of waste heat recovery systems based on organic rankine cycle system for a natural gas engine. Energies
**2019**, 12, 4165. [Google Scholar] [CrossRef] [Green Version] - Zhao, Z.; Zhang, Y.; Mi, H.; Zhou, Y.; Zhang, Y. Experimental research of a water-source heat pump water heater system. Energies
**2018**, 11, 1205. [Google Scholar] [CrossRef] [Green Version] - Valarezo, A.S.; Sun, X.Y.; Ge, T.S.; Dai, Y.J.; Wang, R.Z. Experimental investigation on performance of a novel composite desiccant coated heat exchanger in summer and winter seasons. Energy
**2019**, 166, 506–518. [Google Scholar] [CrossRef] - Fossa, M. The temperature penalty approach to the design of borehole heat exchangers for heat pump applications. Energy Build.
**2011**, 43, 1473–1479. [Google Scholar] [CrossRef] - Andrei, P. Study Regarding Marine Heat Pump; Analele Universitatii Maritime Constanta: Constanta, Romania, 2012; Volume 13, pp. 143–146. [Google Scholar]
- Zheng, W.; Zhang, H.; You, S.; Ye, T. Numerical and experimental investigation of a helical coil heat exchanger for seawater-source heat pump in cold region. Int. J. Heat Mass Transf.
**2016**, 96, 1–10. [Google Scholar] [CrossRef] - Liu, L.; Wang, M.; Chen, Y. A practical research on capillaries used as a front-end heat exchanger of seawater-source heat pump. Energy
**2019**, 171, 170–179. [Google Scholar] [CrossRef] - Ezgi, C.; Girgin, I. Design and thermodynamic analysis of a steam ejector refrigeration/heat pump system for naval surface ship applications. Entropy
**2015**, 17, 8152–8173. [Google Scholar] [CrossRef] [Green Version] - Yun, S.K. Study on the performance characteristics of a new CO
_{2}auto-cascade heat pump system. J. Korean Soc. Mar. Eng.**2017**, 41, 191–196. [Google Scholar] [CrossRef] - Priarone, A.; Silenzi, F.; Fossa, M. Modelling Heat Pumps with Variable EER and COP in EnergyPlus: A Case Study Applied to Ground Source and Heat Recovery Heat Pump Systems. Energies
**2020**, 13, 794. [Google Scholar] [CrossRef] [Green Version] - Hafner, I.A.; Gabrielii, C.H.; Widell, K. Refrigeration Units in Marine Vessels: Alternatives to HCFCs and High GWP HFCs; Nordic Council of Ministers: Copenhagen, Denmark, 2019; pp. 1–90.
- Chen, X.; Li, Z.; Zhao, Y.; Jiang, H.; Liang, K.; Chen, J. Modelling of refrigerant distribution in an oil-free refrigeration system using R134a. Energies
**2019**, 12, 4792. [Google Scholar] [CrossRef] [Green Version] - Bobbo, S.; Fedele, L.; Curcio, M.; Bet, A.; De Carli, M.; Emmi, G.; Poletto, F.; Tarabotti, A.; Mendrinos, D.; Mezzasalma, G.; et al. Energetic and exergetic analysis of low global warming potential refrigerants as substitutes for R410A in ground source heat pumps. Energies
**2019**, 12, 3538. [Google Scholar] [CrossRef] [Green Version] - López Paniagua, I.; Jiménez Álvaro, Á.; Rodríguez Martín, J.; González Fernández, C.; Nieto Carlier, R. Comparison of transcritical CO
_{2}and conventional refrigerant heat pump water heaters for domestic applications. Energies**2019**, 12, 479. [Google Scholar] [CrossRef] [Green Version] - Wang, Z.; Li, Y. Layer pattern thermal design and optimization for multistream plate-fin heat exchangers—A review. Renew. Sustain. Energy Rev.
**2016**, 53, 500–514. [Google Scholar] [CrossRef] - Zhao, Z.; Zhou, Y.; Ma, X.; Chen, X.; Li, S.; Yang, S. Effect of different zigzag channel shapes of PCHEs on heat transfer performance of supercritical LNG. Energies
**2019**, 12, 2085. [Google Scholar] [CrossRef] [Green Version] - Pons, M. Exergy Analysis and process optimization with variable environment temperature. Energies
**2019**, 12, 4655. [Google Scholar] [CrossRef] [Green Version] - Lillo, G.; Mastrullo, R.; Mauro, A.W.; Trinchieri, R.; Viscito, L. Thermo-economic analysis of a hybrid ejector refrigerating system based on a low grade heat source. Energies
**2020**, 13, 562. [Google Scholar] [CrossRef] [Green Version] - Bejan, A.; Lorente, S. Constructal theory of generation of configuration in nature and engineering. J. Appl. Phys.
**2006**, 100, 041301. [Google Scholar] [CrossRef] [Green Version] - Alic, F. Entransy dissipation analysis and new irreversibility dimension ratio of nanofluid flow through adaptive heating elements. Energies
**2020**, 13, 114. [Google Scholar] [CrossRef] [Green Version] - Sun, Y.; Wang, X.; Long, R.; Yuan, F.; Yang, K. Numerical Investigation and Optimization on Shell Side Performance of a Shell and Tube Heat Exchanger with Inclined Trefoil-Hole Baffles. Energies
**2019**, 12, 4138. [Google Scholar] [CrossRef] [Green Version] - Shen, S.; Qian, Z.; Ji, B. Numerical Analysis of Mechanical Energy Dissipation for an Axial-Flow Pump Based on Entropy Generation Theory. Energies
**2019**, 12, 4162. [Google Scholar] [CrossRef] [Green Version] - Preißinger, M.; Brüggemann, D. Thermoeconomic evaluation of modular organic Rankine cycles for waste heat recovery over a broad range of heat source temperatures and capacities. Energies
**2017**, 10, 269. [Google Scholar] [CrossRef] [Green Version] - Wu, Z.; You, S.; Zhang, H.; Fan, M. Mathematical Modeling and Performance Analysis of Seawater Heat Exchanger in Closed-Loop Seawater-Source Heat Pump System. J. Energy Eng.
**2019**, 4, 04019012. [Google Scholar] [CrossRef] - Alam, T.; Kim, M.H. A comprehensive review on single phase heat transfer enhancement techniques in heat exchanger applications. Renew. Sustain. Energy Rev.
**2018**, 81, 813–839. [Google Scholar] [CrossRef] - Sun, X.H.; Yan, H.; Massoudi, M.; Chen, Z.H.; Wu, W.T. Numerical simulation of nanofluid suspensions in a geothermal heat exchanger. Energies
**2018**, 11, 919. [Google Scholar] [CrossRef] [Green Version] - Aprea, C.; Greco, A.; Maiorino, A.; Masselli, C. Enhancing the heat transfer in an active barocaloric cooling system using ethylene-glycol based nanofluids as secondary medium. Energies
**2019**, 12, 2902. [Google Scholar] [CrossRef] [Green Version] - Kristiawan, B.; Wijayanta, A.T.; Enoki, K.; Miyazaki, T.; Aziz, M. Heat Transfer Enhancement of TiO2/water nanofluids flowing inside a square minichannel with a microfin structure: A numerical investigation. Energies
**2019**, 12, 3041. [Google Scholar] [CrossRef] [Green Version] - Ramirez-Tijerina, R.; Rivera-Solorio, C.; Singh, J.; Nigam, K.D.P. Numerical study of heat transfer enhancement for laminar nanofluids flow. Appl. Sci.
**2018**, 8, 2661. [Google Scholar] [CrossRef] [Green Version] - Qi, C.; Liu, M.; Wang, G.; Pan, Y.; Liang, L. Experimental research on stabilities, thermophysical properties and heat transfer enhancement of nanofluids in heat exchanger systems. Chin. J. Chem. Eng.
**2018**, 26, 2420–2430. [Google Scholar] [CrossRef] - Ghozatloo, A.; Rashidi, A.; Shariaty-Niassar, M. Convective heat transfer enhancement of graphene nanofluids in shell and tube heat exchanger. Exp. Therm. Fluid Sci.
**2014**, 53, 136–141. [Google Scholar] [CrossRef] - Sadeghinezhad, E.; Mehrali, M.; Saidur, R.; Mehrali, M.; Latibari, S.T.; Akhiani, A.R.; Metselaar, H.S.C. A comprehensive review on graphene nanofluids: Recent research, development and applications. Energy Convers. Manag.
**2016**, 111, 466–487. [Google Scholar] [CrossRef] - Arshad, A.; Jabbal, M.; Yan, Y.; Reay, D. A review on graphene based nanofluids: Preparation, characterization and applications. J. Mol. Liq.
**2019**, 279, 444–484. [Google Scholar] [CrossRef] - Wang, Z.; Gong, Y.; Wu, X.H.; Lu, Y. Thermodynamic analysis and experimental research of transcritical CO
_{2}cycle with internal heat exchanger and dual expansion. Int. J. Air Cond. Refrig.**2013**, 21, 1350005. [Google Scholar] [CrossRef] - Wang, Z.; Han, F.; Sundén, B. Parametric evaluation and performance comparison of a modified CO
_{2}transcritical refrigeration cycle in air-conditioning applications. Chem. Eng. Res. Des.**2018**, 131, 617–625. [Google Scholar] [CrossRef] - Wu, Z.; Wang, L.; Sunden, B. Pressure drop and convective heat transfer of water and nanofluids in a double-pipe helical heat exchanger. Appl. Therm. Eng.
**2013**, 60, 266–274. [Google Scholar] [CrossRef] - Wang, Z.; Wu, Z.; Han, F.; Wadsö, L.; Sundén, B. Experimental comparative evaluation of a graphene nanofluid coolant in miniature plate heat exchanger. Int. J. Therm. Sci.
**2018**, 130, 148–156. [Google Scholar] [CrossRef] - Tariq, R.; Zhan, C.; Ahmed Sheikh, N.; Zhao, X. Thermal performance enhancement of a cross-flow-type Maisotsenko heat and mass exchanger using various nanofluids. Energies
**2018**, 11, 2656. [Google Scholar] [CrossRef] [Green Version] - Wang, Z.; Li, Y. Irreversibility analysis for optimization design of plate fin heat exchangers using a multi-objective cuckoo search algorithm. Energy Convers. Manag.
**2015**, 101, 126–135. [Google Scholar] [CrossRef]

**Figure 9.**Effects of nanofluids mass fraction on exergy transfer effectiveness at different heat capacity ratios.

Items | Coaxial Tube Heat Exchanger |
---|---|

Structure tube ID/OD | Double-pipe 16 single row 9.5 mm/16 mm |

Total heat exchange area | 1.9 m^{2} |

Material ID/OD | Stainless steel/Nickel cupronickel |

Items | Units | Measuring Range | Accuracy |
---|---|---|---|

Temperature | °C | −35.0–200.0 | ±0.2 |

Pressure | bar | 0–100 | ±1.0% |

Pressure drop | bar | 0–10 | ±1.0% |

Sea water flow rate | m^{3}/h | 0–5 | ±0.5% |

Refrigerant mass flow rate | kg/s | 0–0.5 | ±0.5% |

Pump power | kW | 0–10 | ±0.5% |

Item | |||||
---|---|---|---|---|---|

Mass fraction | 0.01 | 0.05 | 0.1 | 0.5 | 1.0 |

Volume fraction | 0.0048% | 0.024% | 0.048% | 0.24% | 0.48% |

k_{nf}/k_{bf} | 1.017 | 1.019 | 1.021 | 1.102 | 1.211 |

µ_{nf}/µ_{bf} | 1.001 | 1.034 | 1.058 | 1.488 | 3.0 |

NO. | Items | Note |
---|---|---|

1 | $d=\frac{4s}{L}$ | Equivalent diameter: |

2 | $Q=\frac{({q}_{h}+{q}_{c})}{2}$ | Heat flux |

3 | $\mathrm{LMTD}=\frac{({T}_{h,i}+{T}_{c,o})-({T}_{h,o}+{T}_{c,i})}{\mathrm{ln}[({T}_{h,i}-{T}_{c,o})/({T}_{h,o}-{T}_{c,i})]}$ | Logarithmic mean temperature difference |

4 | $h=\frac{Q}{A\mathrm{LMTD}}$ | Convective heat transfer coefficient |

5 | $\phi =\frac{Ah\mathrm{LMTD}}{{(m{c}_{p})}_{min}({T}_{h,i}-{T}_{c,i})}$ | Thermal efficiency of heat exchanger |

6 | ${P}_{w}=\frac{m\Delta P}{\rho}$ | Pump power |

7 | $\mathrm{Nu}=\frac{hd}{k}$ | Nusselt number |

8 | $\mathrm{Re}=\frac{\rho ud}{\mu}$ | Reynolds number |

9 | $\mathrm{Pr}=\frac{\mu {c}_{p}}{k}$ | Prandtl number |

10 | $\mathrm{Pe}=\frac{\rho {c}_{p}Lu}{k}$ | Peclet number |

11 | $\mathrm{NTU}=\frac{KA}{{(m{c}_{p})}_{min}}$ | Number of Transfer Units |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, Z.; Han, F.; Ji, Y.; Li, W.
Performance and Exergy Transfer Analysis of Heat Exchangers with Graphene Nanofluids in Seawater Source Marine Heat Pump System. *Energies* **2020**, *13*, 1762.
https://doi.org/10.3390/en13071762

**AMA Style**

Wang Z, Han F, Ji Y, Li W.
Performance and Exergy Transfer Analysis of Heat Exchangers with Graphene Nanofluids in Seawater Source Marine Heat Pump System. *Energies*. 2020; 13(7):1762.
https://doi.org/10.3390/en13071762

**Chicago/Turabian Style**

Wang, Zhe, Fenghui Han, Yulong Ji, and Wenhua Li.
2020. "Performance and Exergy Transfer Analysis of Heat Exchangers with Graphene Nanofluids in Seawater Source Marine Heat Pump System" *Energies* 13, no. 7: 1762.
https://doi.org/10.3390/en13071762