# Experimental Observation of Natural Convection Heat Transfer Performance of a Rectangular Thermosyphon

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}); the temperature in the cooling section is 30, 40, or 50 °C; and the potential difference between the hot and cold sections is 5, 11, or 18 for the cooling section lengths of 60, 45, and 30 cm, respectively. The results indicate that the value of the dimensionless heat transfer coefficient, the Nusselt number, is generally between 5 and 10. The heating power is the main factor affecting the natural convection intensity of the thermosyphon.

## 1. Introduction

_{g}to modify the Gr, crafting a prediction model that was applicable in four different heating and cooling modes. Thomas and Sobhan [15] experimentally studied the stability and transient performance of a vertical heater–cooler natural circulation loop with metal oxide nanoparticles. Their results indicate that nanofluids containing aluminum oxide and copper oxide have superior heat transfer performances than pure water as the working fluid.

## 2. Materials and Methods

#### 2.1. Scenarios and Test Cell Development

#### 2.2. Experimental Test Cell

#### 2.2.1. The Rectangular Loop

#### 2.2.2. Heating Section

#### 2.2.3. Cooling Section

#### 2.2.4. Insulation Materials

#### 2.3. Experimental Apparatus

#### 2.3.1. Power Supply System

#### 2.3.2. Thermoregulated Bath

#### 2.3.3. Liquid Flow Meter

#### 2.3.4. Thermocouples

#### 2.4. Parameters

- The input power ${q}_{h}=\mathrm{VI}$ can be obtained from the voltage V and the current I supplied by the power supply. Thus, the heat flux ${q}_{flux}$ is ${q}_{h}$/A. During the experiment, the heating from the power supply is not completely transferred to the fluid in the heating section. A small amount of heat enters the cooling section via axial heat conduction ${q}_{a}$ in the loop body or escapes into the environment, so the axial heat transfer ${q}_{a}$ must be deducted from the input thermal power first. Therefore, the corrected actual input thermal power is ${q}_{in}={q}_{h}-{q}_{a}$.
- Modified Rayleigh number, Ra*$$R{a}^{*}=\frac{g\beta \left(\frac{{q}_{in}}{A}\frac{{R}_{i}}{k}\right){L}_{y}{D}_{i}{}^{2}}{\alpha \nu}$$
- Parameters of the working fluid
- (1)
- Flow rate of the working fluid ($\dot{V}$)The temperature of the fluid in the rectangular loop increases in the heating section, causing the fluid to flow to the cooling section by convection. The flow rate of this flow varies depending on the amount of thermal power input to the heating section and the cooling conditions in the cooling section. In this experiment, the input heat power (${q}_{in}$) and temperature difference ($\Delta T={T}_{3}-{T}_{1}$) were used to determine the fluid flow rate in the tube.$$\dot{V}=\frac{{q}_{in}}{\rho {C}_{p}A\Delta T}$$
- (2)
- Reynolds number, Re$$\mathrm{Re}=\frac{\dot{V}\left(2{R}_{i}\right)}{\nu}$$

- Nusselt number
- (1)
- The average heat transfer coefficient of the cooling end is:$$\overline{h}=\frac{{q}_{c}/A}{\overline{{T}_{w}}-\overline{{T}_{c}}}$$
- (2)
- The calculation of the Nu is as follows:$$\overline{\mathrm{Nu}}=\frac{\overline{h}\left(2{R}_{i}\right)}{k}$$

#### 2.5. Experimental Uncertainty

## 3. Results and Discussion

^{2}); Tc is 30, 40, or 50 °C, and ΔZ is 5, 11, or 18 (Lc = 60, 45, or 30 cm, respectively).

## 4. Conclusions

- The outer wall of the end of the heating section has the highest wall temperature. Due to the influence of axial heat transfer through the thermosyphon wall, the wall temperature of the outer tube decreases slightly after exiting the heating section (entering the upper adiabatic section); similarly, after exiting the cooling section, the wall temperature of the adiabatic section increases slightly.
- A higher heating power or a larger height difference between the hot and cold ends can increase the fluid flow in the loop, whereas the cooling temperature has little influence.
- Overall, the Nu is approximately 5–10. If one wants to increase the natural convection effect of the fluid in the loop, in addition to increasing the heating power, the height difference between the hot and cold ends is also one of the controllable factors.
- With a height difference of ΔZ = 5 and a heating power of 40 W, the temperature of the fluid in the middle heating section oscillates, and an increase in the heating power also increases the oscillations. For ΔZ = 11, the temperature oscillations in the middle heating section are reduced. For ΔZ = 18, fluid temperature oscillations are observed at the exits of both the heating and cooling sections; however, the water temperature in the middle heating section does not oscillate. The oscillation phenomenon may result from the mixing of fluid with different temperatures, which is caused by the growth of temperature boundary layers and turning of the flow at the loop elbows after the fluid is heated or cooled.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | heating (or cooling) area (m^{2}) |

AR | aspect ratio (=${\mathrm{L}}_{\mathrm{y}}/{\mathrm{L}}_{\mathrm{x}}$) |

Ch. | position of the thermocouple |

${C}_{p}$ | specific heat capacity (kJ/kg K) |

${\mathrm{D}}_{\mathrm{i}}$ | inner diameter of the loop tube (m) |

g | acceleration due to gravity (m/s) |

$\overline{h}$ | average heat convection coefficient at the cooling end (W/m^{2} °C) |

I | electric current (A) |

k | thermal conductivity of the working fluid (W/m) |

${\mathrm{L}}_{\mathrm{c}}$ | length of the cooling end (m) |

${\mathrm{L}}_{\mathrm{x}}$ | width of the test cell (200 mm) |

${\mathrm{L}}_{\mathrm{y}}$ | height of the test cell (=length of the heating end) (700 mm) |

Nu | Nusselt number |

${q}_{a}$ | axial heat conduction along the loop wall (W) |

${q}_{c}$ | heat transfer rate at the cooling section (W) |

${q}_{flux}$ | heat flux at the heating section ($={q}_{h}$/A) |

${q}_{h}$ | heating power (W) |

${q}_{in}$ | actual heating power (W) |

Ra* | modified Rayleigh number |

Re | Reynolds number |

${R}_{i}$ | inner radius of the loop tube |

T | temperature (°C) |

${T}_{c}$ | temperature at the cooling section (°C) |

${\overline{T}}_{c}$ | average fluid temperature at the cooling section (°C) |

${\overline{T}}_{w}$ | average wall temperature at the cooling section (°C) |

$\Delta \mathrm{T}$ | temperature difference between the exit and inlet at the heating section (°C) |

V | electric voltage (Volt) |

$\dot{V}$ | velocity of the loop working fluid (m/s) |

$\Delta \mathrm{Z}$ | potential difference ($=\frac{1}{2}\left(\frac{{\mathrm{L}}_{\mathrm{y}}-{\mathrm{L}}_{\mathrm{c}}}{{\mathrm{D}}_{\mathrm{i}}}\right)$) |

Greek symbols | |

$\alpha $ | thermal diffusion coefficient (m^{2}/s) |

$\beta $ | thermal expansion coefficient (K^{−1}) |

$\rho $ | density (kg/m^{3}) |

ν | kinematic viscosity (m^{2}/s) |

## References

- Garrity, P.T.; Klausner, J.F.; Mei, R. Instability phenomena in a two-phase microchannel thermosyphon. Int. J. Heat Mass Transf.
**2009**, 52, 1701–1708. [Google Scholar] [CrossRef] - Vijayan, P.K.; Sharma, M.; Pilkhwal, D.S.; Saha, D.; Sinha, R.K. A comparative study of single-phase, two-phase, and supercritical natural circulation in a rectangular loop. J. Eng. Gas Turb. Power
**2010**, 132, 102913. [Google Scholar] [CrossRef] - Misale, M.; Garibaldi, P.; Tarozzi, L.; Barozzi, G.S. Influence of thermal boundary conditions on the dynamic behaviour of a rectangular single-phase natural circulation loop. Int. J. Heat Fluid Flow
**2011**, 32, 413–423. [Google Scholar] [CrossRef] - Lai, C.-M.; Chen, R.-H.; Huang, C.S. Development and thermal performance of a wall heat collection prototype. Build. Environ.
**2012**, 57, 156–164. [Google Scholar] [CrossRef] - Delgado, M.; Lázaro, A.; Mazo, J.; Zalba, B. Review on phase change material emulsions and microencapsulated phase change material slurries: Materials, heat transfer studies and applications. Renew. Sustain. Energy Rev.
**2012**, 16, 253–273. [Google Scholar] [CrossRef] - Desrayaud, G.; Fichera, A.; Lauriat, G. Two-dimensional numerical analysis of a rectangular closed-loop thermosiphon. Appl. Therm. Eng.
**2013**, 50, 187–196. [Google Scholar] [CrossRef] - Buschmann, M.H. Nanofluids in thermosyphons and heat pipes: Overview of recent experiments and modelling approaches. Int. J. Therm. Sci.
**2013**, 72, 1–17. [Google Scholar] [CrossRef] - Huminic, G.; Huminic, A. Numerical study on heat transfer characteristics of thermosyphon heat pipes using nanofluids. Energy Conversat. Manag.
**2013**, 76, 393–399. [Google Scholar] [CrossRef] - Sureshkumar, R.; Mohideen, S.T.; Nethaji, N. Heat transfer characteristics of nanofluids in heat pipes: A review. Renew. Sustain. Energy Rev.
**2013**, 20, 397–410. [Google Scholar] [CrossRef] - Gupta, N.K.; Tiwari, A.K.; Ghosh, S.K. Heat transfer mechanisms in heat pipes using nanofluids—A review. Exp. Therm. Fluid Sci.
**2018**, 90, 84–100. [Google Scholar] [CrossRef] - Ho, C.J.; Chiou, S.P.; Hu, C.S. Heat transfer characteristics of a rectangular natural circulation loop containing water near its density extreme. Int. J. Heat Mass Transf.
**1997**, 40, 3553–3558. [Google Scholar] [CrossRef] - Vijayan, P.K.; Sharma, M.; Saha, D. Steady state and stability characteristics of single-phase natural circulation in a rectangular loop with different heater and cooler orientations. Exp. Therm. Fluid Sci.
**2007**, 31, 925–945. [Google Scholar] [CrossRef] - Misale, M.; Garibaldi, P.; Passos, J.C.; de Bitencourt, G.G. Experiments in a single-phase natural circulation mini-loop. Exp. Therm. Fluid Sci.
**2007**, 31, 1111–1120. [Google Scholar] [CrossRef] - Swapnalee, B.T.; Vijayan, P.K. A generalized flow equation for single phase natural circulation loops obeying multiple friction laws. Int. J. Heat Mass Transf.
**2011**, 54, 2618–2629. [Google Scholar] [CrossRef] - Thomas, S.; Sobhan, C.B. Stability and transient performance of vertical heater vertical cooler natural circulation loops with metal oxide nanoparticle suspensions. J. Heat Transf. Eng.
**2018**, 39, 861–873. [Google Scholar] [CrossRef] - Moffat, R.J. Using uncertainty analysis in the planning of an experiment. J. Fluid Eng.
**1985**, 107, 173–178. [Google Scholar] [CrossRef]

**Figure 3.**Fluid temperature variation along the loop as a function of the heating power (AR = 3.5, Tc = 40 °C, ΔZ = 5, 11, and 18).

**Figure 5.**The relationship between the Nusselt number of loop flow and the modified Rayleigh number.

© 2019 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**

Huang, C.S.; Yu, C.-W.; Chen, R.H.; Tzeng, C.-T.; Lai, C.-M.
Experimental Observation of Natural Convection Heat Transfer Performance of a Rectangular Thermosyphon. *Energies* **2019**, *12*, 1702.
https://doi.org/10.3390/en12091702

**AMA Style**

Huang CS, Yu C-W, Chen RH, Tzeng C-T, Lai C-M.
Experimental Observation of Natural Convection Heat Transfer Performance of a Rectangular Thermosyphon. *Energies*. 2019; 12(9):1702.
https://doi.org/10.3390/en12091702

**Chicago/Turabian Style**

Huang, C. S., Chia-Wang Yu, R. H. Chen, Chun-Ta Tzeng, and Chi-Ming Lai.
2019. "Experimental Observation of Natural Convection Heat Transfer Performance of a Rectangular Thermosyphon" *Energies* 12, no. 9: 1702.
https://doi.org/10.3390/en12091702