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Edited by: Uwe Schröder, Technische Universitat Braunschweig, Germany

Reviewed by: Claudio Tenreiro, University of Talca, Chile; Khalil Ur Rahman, Pakistan Nuclear Regulatory Authority (PNRA), Pakistan

This article was submitted to Nuclear Energy, a section of the journal Frontiers in Energy Research

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

In this paper, water and CuO-water nanofluids are selected as working fluids. The characteristics of fluid flow and heat transfer in a heat transfer tube are analyzed by means of numerical simulation. The effect of nanofluid concentration on the flow and heat transfer characteristics of the flat tube under the condition with a Reynolds number of 6,000~10,000 is analyzed and compared with that of the circular tube. The results show that the addition of nanoparticles in the nanofluid has little effect on the velocity and temperature distribution in the flow channel. With the increase of nanofluid concentration, the heat transfer coefficient and flow resistance of the fluid increased. And the comprehensive evaluation factor was 2.51~3.29, which had the effect of enhancing heat exchange. There is a similar trend in the same concentration with different Reynolds numbers. Compared with the circular tube, the nanofluid has a better ability to enhance heat transfer when it flows in the flat tube. Under conditions with the same fluid concentration, the effect of the application of the nanofluids on the flat tube is better.

Nanoparticles are particles in the 1–100 nm, between the microscopic system and macroscopic system, and consist of a group of few atoms or molecules (Choi,

In recent years, various aspects of nanotechnology have been described as emphasizing applications in energy systems, such as nuclear energy, geothermal energy, and solar energy (Banerjee,

In order to analyze the comprehensive heat transfer capacity of flat tube, the geometrical model of flat tube and circular tube is established, and its cross-section is shown in Figure

Schematic diagram.

Calculation model.

Geometrical parameters of heat transfer tube.

Circular tube | 1,000 | 1 | 53.41 | – | – | 17 |

Flat tube | 1,000 | 1 | 53.41 | 7 | 15.7 | 11.12 |

In this paper, the Workbench software is used to divide the hexahedral structured grids by sweep division. The three-stage fluid parts have the same setting. The minimum mesh size of the source surface is 0.8 mm, and the boundary layer grid is refined, and the solid wall surface is set to 5 nodes 4-layer grid. The final grid form is shown in Figure

Grid partition.

Grid quality measurement method is skewness, in general, the value <0.7 is acceptable. As shown in Figure

Grid quality.

In this paper, the correlation between the heat transfer coefficient and the friction coefficient is also verified. The heat transfer coefficient is derived from analog data, and the calculation formula of friction coefficient is as follows:

Type: Δ

As shown in Figure

Grids Independent verification.

In the setting of boundary conditions, the inlet of the heat transfer tube adopts the velocity boundary, and the size is determined by Reynolds number at the temperature of 293 K. The outlet is provided with a pressure exit border of 0 Pa, which is discharged into the vacuum. The tube wall is provided with no slip boundary condition, and the heating wall is provided with constant wall temperature boundary of 400 K. At the same time, the fluid surface of the stable section and the end surface of the tube are adiabatic conditions, and the SST model is chosen.

It is known from the literature (Rao et al.,

Water and concentration of nanofluids physical parameters (Sun et al.,

^{2}O |
||||
---|---|---|---|---|

Density ^{−3} |
997.1 | 1272. 2 | 1547.4 | 1822.5 |

Specific heat at constant pressure c_{p}/J⋅(kg⋅K)^{−1} |
4179 | 3250 | 2650 | 2232 |

Coefficient of thermal conductivity ^{−1} |
0.613 | 0.658 | 0.692 | 0.716 |

Thermal expansion coefficient ^{−1} × 10^{5} |
21 | 15.85 | 12.54 | 10.22 |

Dynamic viscosity ^{3} |
0.894 | 1.016 | 1.163 | 1.342 |

The change of heat transfer coefficient with Reynolds number in the tube is shown in Figure

Therefore, under the same section circumference of the heat transfer tube, the equivalent diameter of the flat tube is smaller, that is, the thickness of the flow boundary layer is thinner and the heat transfer effect is stronger under the same Reynolds number.

Change of heat transfer coefficient with Reynolds number.

Figure

Change of heat transfer coefficient increase with Reynolds number.

In order to understand the temperature change in the heat transfer tube, the axial and radial temperature distributions have been analyzed, and the temperature distributions of the average temperature along the axial and radial directions of each section of the two heat transfer tubes are given. As shown in Figure

Temperature comparison of two tubes along axial section.

As shown in Figure

Comparison of the radial temperature along the section of two tubes.

As shown in Figure

Comparison of pressure drop between flat tube and circular tube flow channel.

Due to the addition of nanoparticles in traditional fluids, their heat transfer capacity is enhanced, and the flow resistance is increased. Therefore, according to the literature (Qing and Zou,

Where:_{0}, _{0}, _{0} is the Nusselt number, the resistance coefficient and the equivalent diameter of the water and the concentration nanometer fluid in the circular tube respectively.

Where:

Where: Δ_{i} is the equivalent diameter of the heat tube; ρ is the fluid density;

As shown in Table

Comprehensive evaluation factors of fluid in flat tube and circular tube at different Reynolds number and concentration.

η | ||||
---|---|---|---|---|

6,000 | 2.80 | 2.57 | 2.52 | 2.51 |

7,000 | 2.92 | 2.72 | 2.67 | 2.66 |

8,000 | 3.04 | 2.86 | 2.81 | 2.79 |

9,000 | 3.17 | 2.99 | 2.94 | 2.92 |

10,000 | 3.29 | 3.12 | 3.06 | 3.05 |

In this paper, the numerical simulation method is used to compare the flow and heat transfer characteristics of the water and the nanofluids in the two heat transfer tubes, and the following conclusions are drawn:

The greater the concentration of the nanoparticles in the fluid, the greater the average heat transfer coefficient, and the maximum is reached at 0.15. Compared with the circular tube, the nanofluid has a higher heat transfer coefficient when it flows in the flat tube, but it is better to improve the heat transfer coefficient when it is applied to the tube.

The axial and radial temperature trends of each concentration of nanofluids are basically the same, and the concentration of nanoparticles in fluids has little effect on the temperature distribution. In conditions with the same Reynolds number and concentration, the average temperature along the axial cross-section of the flat tube is higher than the corresponding circular tube.

With the same Reynolds number, the resistance of the flat tube runner is higher than that of the circular tube, and with the increase of concentration, the growth rate of the flow channel pressure drop of the two heat transfer tubes increases gradually, and the growth rate of the flat tube is always greater than that of the tube.

Under the same Reynolds number, the comprehensive heat transfer capacity of the flat tube is better than that of the circular tube. However, with the increase of the concentration of nanofluids, the increase of the resistance caused by fluid viscosity is greater than that of the fluid heat transfer enhancement, resulting in the gradual decrease of the comprehensive evaluation factor.

For the same fluid, the comprehensive evaluation factor of the flat tube relative to the circular tube increases with the increase of Reynolds number, that is, the larger the Reynolds number, the better the effect of applying the nanometer fluid to the flat tube.

In the course of the completion of this thesis, all authors have substantial contributions to design of the work, GF provided the research direction of the subject, LS determined the research method and specific processes. LS carried out numerical simulation and obtained, collated and analyzed the data, in the process, GF has been instructed and helped. LS wrote the first draft of the paper and corrected it by GF also gave some suggestions. All authors approve the final version to be published. All authors agree to be responsible for all aspects of the work.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

I would like to extend my sincere gratitude to my supervisor for his instructive advice and useful suggestions on my thesis. I am deeply grateful for her help in the completion of this thesis. This work is supported by Key Supported Discipline of Guizhou Provence (Qian Xuewei He Zi ZDXK [2016]24), 2011 Collaborative Innovation Center of Guizhou Province (Qian Jiao he xietongchuangxin zi [2016]02).

_{2}O

_{3}nanofluids in fully developed laminar flow regime

_{2}-water nanofluid flow and heat transfer characteristics in a multiport minichannel flat tube

_{2}O

_{3}-water nanofluids in a flat tube

_{p}

Specific heat at constant pressure, J·(kg·K)^{−1}

equivalent diameter of the heat tube, m

resistance coefficient

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

test section length, m

Nusselt number

pressure drop, Pa

Reynolds number

fluid velocity, m/s

fluid density, ^{3}

thermal expansion coefficient

^{−1}

μdynamic viscosity, Pa·s.