# Impact of Microgroove Shape on Flat Miniature Heat Pipe Efficiency

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}in the horizontal orientation and 150 W/cm

^{2}in the vertical orientation. Khrustalev and Faghri [12] developed a one-dimensional mathematical model for heat transfer during liquid evaporation in a porous structure at high heat flux. The model characterizes evaporation heat transfer and the location of the liquid–vapor interface. Suh [13] analyzed liquid and vapor flows in trapezoidal and sinusoidal microgrooves taking into account the shear stress effect along the liquid–vapor interface. A modified correlation for liquid friction is proposed for trapezoidal and sinusoidal microgrooves.

## 2. Heat Pipe Analytical Model

_{v}and h

_{v}, respectively. The geometrical parameters for triangular, rectangular, and trapezoidal microgrooves are shown in Figure 3. The microgrooves’ top width and depth are designated 2W

_{t}and h

_{g}, respectively. For trapezoidal microgrooves, 2W

_{b}is the bottom width.

#### 2.1. Meniscus Radius Expressions

#### 2.2. Capillary Limit

#### 2.2.1. Liquid Flow Pressure Loss

#### 2.2.2. Vapor Flow Pressure Loss

_{v}and h

_{v}are the vapor width and depth defined as

#### 2.3. Heat Pipe Effective Length and Maximum Heat

#### 2.4. Solution Procedures

**Step 1**: The input parameters are imposed, and the working fluid thermophysical properties are calculated. The saturation temperature is deduced from the pressure and the heat pipe size and orientation;**Step 2**: An initial value of the heat flux is given;**Step 3**: Selection of the microgroove number;**Step 4**: Calculation of the maximum heat flux;**Step 5**: Calculation of the heat transport limits;**Step 6**: Calculation of the hydraulic limits;**Step 7**: Calculation of the fluid velocities;**Step 8**: Calculation of the pressure differences;**Step 9**: Calculation of the boiling limitation;**Step 10**: Check the convergence criterion calculations. If this criterion is not satisfied, a new value will be estimated by the secant method, taking into account the difference obtained on the estimation of the new value of the heat flux and the value imposed at Step 2;**Step 11**: The calculation loop is repeated until the error is less than the imposed criterion.

## 3. Results

#### 3.1. Determination of the Heat Pipe Design

#### 3.1.1. Flat Heat Pipe with Rectangular Microgrooves

_{t}, where the capillary pressure decreases (Figure 6a). This figure presents the heat pipe working zone where the maximum capillary pressure is greater than the sum of the liquid and vapor pressure drops. It shows that the maximum heat flux decreases gradually by increasing the groove width, where the total pressure decreases slightly and becomes greater than the maximum capillary pressure, as shown by Figure 6b.

#### 3.1.2. Flat Heat Pipe with Trapezoidal Microgrooves

_{g}> 800 $\mathsf{\mu}\mathrm{m}$) where the variation of the liquid section is more influenced by the variation of $\beta $. For the same $\beta $, it can be seen that the maximum heat is increased from 10 to 60 W for heat pipe microgroove depth varying from 400 to 1200 $\mathsf{\mu}\mathrm{m}$.

#### 3.1.3. Influence of the Microgroove Shape on the Maximum Heat Flux

^{2}; (ii) isosceles triangular microgroove where the remaining side is 280 µm and the triangle height is 1600 µm; and (iii) trapezoidal microgrooves with a height of 1600 µm, top width of 280 µm, and angle β of 4°.

#### 3.1.4. Influence of the Heat Pipe Length

#### 3.1.5. Heat Pipe Heat Transport Limitations

_{v}is the cross-sectional area of the vapor flow, ${\rho}_{v}$ is the vapor density, P

_{v}is the vapor pressure, ${h}_{lv}$ is the latent heat, and $\gamma $ is the heat capacity ratio at constant pressure and volume.

_{m}is the average capillary radius.

_{m}is the capillary radius; and ${R}_{b}$ is the bubble radius, strongly dependent on the experimental conditions on the heat pipe (presence of non-condensable gas, surface state at the solid–liquid interface, etc.).

^{3}–2.10

^{4}W and the entrainment limitation is 10

^{3}–5.10

^{3}W. For n-pentane, the sonic limitation is increased to 6.10

^{3}–3.10

^{4}W and the entrainment limitation is 800–1200 W. In the operating range, the maximum heat of the studied flat heat pipe is defined as a function of the flow temperature. For the operating temperature of 55 °C, the maximum heat is about 80 W when using n-pentane as working fluid and 200 W when using water. The maximum heat is approximately two times higher for water than for n-pentane due to the water latent heat, which is 7 times higher than that of n-pentane.

#### 3.2. Experimental Tests on the Optimal Flat Heat Pipe

_{adia}

_{1}, T

_{adia}

_{2}, T

_{adia}

_{3}, T

_{adia}

_{4}) are used to measure the temperatures in the adiabatic zone between the evaporator and condenser. The lowest temperatures in the heat pipe are measured at the condenser zone by the thermocouples T

_{cond}

_{1}and T

_{cond}

_{2}. Only one thermocouple is located in a position to measure the evaporator temperature (T

_{evap}). Temperatures measured along the adiabatic zone are approximately equivalent because the heat loss to the ambient surroundings is negligible. Figure 14b shows the evaporator, adiabatic zone, and condenser. The transient adiabatic temperature is the average value of T

_{adia}

_{1}, T

_{adia}

_{2}, T

_{adia}

_{3}, and T

_{adia}

_{4}. The transient condenser temperature is the average response of the thermocouples T

_{cond}

_{1}and T

_{cond}

_{2}. Moreover, all the measured temperatures increase over time due to the continuous heating source. During the transient step, the measured temperatures are variable against time because the mass flow rate coming from the evaporator to the condenser is lower than that leaving the condenser. At t = 3000 s, the two-phase flow in the heat pipe tends to be stable and reaches a steady state where the liquid mass flow rate becomes equivalent to the vapor mass flow rate. The wall temperatures and, consequently, the heat pipe pressures become stable over time.

## 4. Conclusions

- (a)
- The effect of microgroove width and depth for a flat heat pipe was investigated. It can be seen that increasing microgroove width increases the maximum heat for low values of width and decreases it for high width values. An optimal width and depth were defined for the highest maximum heat.
- (b)
- For the flat heat pipe with trapezoidal microgrooves, the impact of the inclination angle ($\beta $) of the groove side slope was analyzed for different heat pipe depths. The maximum heat is influenced by $\beta $ for low values of the microgroove depth. For high values of h
_{g}(>800 $\mathsf{\mu}\mathrm{m}$), the angle $\beta $ has no effect on the maximum heat flux. - (c)
- The influence of microgroove shape on the heat pipe efficiency is highlighted by studying different architecture of grooves respecting the same cross-sectional area or the same hydraulic diameter. For the same microgroove cross sections, the lowest heat transfer was obtained by microgrooves with a triangular cross section. The highest maximum heat was obtained for the rectangular microgroove cross section. For the same hydraulic diameter, the best configuration is the trapezoidal cross section, for which the highest maximum heat was obtained.
- (d)
- Heat transport limitations were studied versus operating temperature, taking into account the hydrodynamic and thermal processes inside the heat pipe. Respecting the capillary limit, entrainment and boiling limits delimited the operating domain. The maximum heat is approximately 2 times higher for water than for n-pentane due to the water latent heat, which is 7 times higher than that of n-pentane.
- (e)
- Experiments were conducted using a flat heat pipe respecting the optimal geometrical parameters defined by the analytical model. DI water was used as the working fluid. Measurements of thermal resistances and temperatures were in accordance with the performance predicted by the model.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 9.**Comparison of heat pipe efficiency for: (

**a**) the same cross-sectional area; (

**b**) the same hydraulic diameter.

**Figure 10.**Capillary pressure, differences in liquid pressure, vapor, and maximum heat versus the adiabatic length.

Parameters | Values |
---|---|

Hydraulic vapor diameter, ${D}_{hv}$ | $1.62\hspace{1em}{10}^{-2}\text{}\mathrm{m}$ |

Effective length, ${L}_{eff}$ | $4.15\hspace{1em}{10}^{-2}\text{}\mathrm{m}$ |

Capillary radius, ${R}_{m}$ | $2.86\hspace{1em}{10}^{-4}$$\mathrm{m}$ |

Nucleation radius, ${R}_{b}$ [18] | $5\hspace{1em}{10}^{-4}\text{}\mathrm{m}$ |

Vapor flow cross section, ${A}_{v}$ | $6\hspace{1em}{10}^{-5}\text{}\mathrm{m}$^{2} |

Width of vapor cross section, ${W}_{v}$ | ${10}^{-2}$ m |

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**MDPI and ACS Style**

Ternet, F.; Louahlia-Gualous, H.; Le Masson, S.
Impact of Microgroove Shape on Flat Miniature Heat Pipe Efficiency. *Entropy* **2018**, *20*, 44.
https://doi.org/10.3390/e20010044

**AMA Style**

Ternet F, Louahlia-Gualous H, Le Masson S.
Impact of Microgroove Shape on Flat Miniature Heat Pipe Efficiency. *Entropy*. 2018; 20(1):44.
https://doi.org/10.3390/e20010044

**Chicago/Turabian Style**

Ternet, François, Hasna Louahlia-Gualous, and Stéphane Le Masson.
2018. "Impact of Microgroove Shape on Flat Miniature Heat Pipe Efficiency" *Entropy* 20, no. 1: 44.
https://doi.org/10.3390/e20010044