# Boiling Heat Transfer Characteristics of Porous Microchannel with Pore-Forming Agent

^{*}

## Abstract

**:**

_{2}CO

_{3}, 60–90 μm). Porous microchannels were composed of 23 parallel porous microchannels with 600 μm in width and 1200 μm in depth.The addition of PFA (pore-forming agent) could increase the sample porosity. For Q10 series, sample porosities increase from 20.4% to 52.9% with the PFA percentage change from 0% to 40%, while for the Q30 series they increase from 26.6% to 47.5%. Experimental results showed the boiling heat transfer coefficient (HTC) reached the maximum at the moderate porosity for both Q10 and Q30 series. Too large or too small porosity would degrade boiling heat transfer performance. It demonstrated that there existed an optimal range of PFA content for sintered microchannels. PFA content has a minor effect on the average pressure drop and would not cause the rapid increase in flow resistance. Visual observation disclosed that the sample porosity would affect the pressure instability significantly. The sample with moderate porosity showed periodic pressure fluctuation and could establish rhythmical boiling. Particle size also exerted a certain influence on the boiling heat transfer performance. Q30 series could achieve higher HTC and CHF (Critical heat flux) than Q10 series. This is attributed to the larger ratio of layer-thickness-to-particle-size (δ/d) for Q10-series samples.

## 1. Introduction

^{2}. Multifaceted requirements are considered in the design of a heat dissipation system: high efficiency, miniaturization, low cost, energy saving, etc. Traditional air and single-phase liquid cooling methods are transformed to the phase-change one. Since the 1980s, the microchannel boiling system has attracted extensive attention, as it dissipates the heat by the two-phase flow boiling process. It combines various advantages of high HTC and low working-fluid demand [1,2]. Due to limited space, traditional microchannels need to face flow reversal difficulty in high heat fluxes, which results in large pressure and temperature pulsation [3,4]. In recent years porous microchannels have attracted more interest to provide a new solution to this problem [5,6].

_{2}CO

_{3}as a PFA to produce a kind of micro-nano capillary wick. They found that multiscale structure could reduce the evaporator wall temperature greatly compared with the microchannel/wick evaporator. Small pores (µm scale) provide great capillary force for liquid suction, large pores (10 µm scale) between clusters increase surface area for liquid film evaporation, and microchannels (mm scale) are responsible for vapor venting. Lin [13] applied the two-steps sintering method to build an excellent bi-porous structure: the first step is to form perforated clusters by mixing Nickel powder with the binder, and the second to sinter these packed clusters to complete the bi-disperse wick. Its maximum heat transfer coefficient could reach 23.3 kW/m

^{2}·K, which is approximately 230% of the mono-porous wick at heat load of 400 W. Liu and Kandlikar [14] combined the drop coating and screen-printing technique with the sintering method. Na

_{2}CO

_{3}was added to alter the porosity of the porous layer. Some samples could achieve 303 W/cm

^{2}in CHF in the pool boiling test. The effect of coating thickness on pool boiling performance was also investigated. However, this work did not present detailed porosity and PFA content. Wei and Yang [15] used both the loose sintering (LS) method and cold pressure sintering (CPS) method to investigate the PFA content on LHP evaporator performance. They found that the porosity and average pore size increased with the PFA content, and capillary performance was enhanced due to the improvement in the connectivity of internal pores. The optimal PFA content was suggested to be <10% for loose sintering and <20% for cold press sintering.

## 2. Experimental System

#### 2.1. Experimental System

#### 2.2. Fabrication of Porous Microchannel and Characterization

_{2}CO

_{3}(60–90 μm), as shown in Figure 3. Before the sintering process the copper powder and Na

_{2}CO

_{3}were screened separately, and then mixed with a certain volume ratio. The mixed powder is evenly shaken and filled into the graphite mold. Finally, these samples are sintered under the protection of hydrogen and nitrogen atmosphere. The sintering temperature is 850 °C, which is also the melting temperature of Na

_{2}CO

_{3}. After cooling to room temperature the sintered sample is placed in a water bath for 2 h to dissolve the melted Sodium carbonate.

## 3. Data Processing and Error Analysis

#### 3.1. HTC Calculation

_{base}is the top surface area of the copper block, W and L are the width and length of the microchannel sample, respectively, and Q

_{eff}is the effective heat input.

_{total}is the total input heating power. Q

_{loss}is the heat loss between heat sink and environment.

_{sp}is the total length of the microchannel, m; T

_{sat}and T

_{in}are saturation enthalpy and inlet temperature of water, KkJ/kg, respectively. qis effective heat quantity, W/cm

^{2}.

_{eff}is the effective heat flux, W/cm

^{2}; y

_{cop}is the distance between the temperature measuring hole and upper surface of the copper plate; λ

_{cop}is the thermal conductivity of copper block, W/m·K.

_{avg}) is calculated by the weighted average of the single-phase HTC (hsp) and the two-phase boiling HTC (h

_{tp}) [16]:

#### 3.2. Error Analysis and Heat Loss

_{in}= 60 °C, G = 142 kg/(m

^{2}·s), the fitting curve of heat loss is as follows:

_{ave}represents the average pressure of microchannel inlet and outlet (kPa).

## 4. Results and Discussion

#### 4.1. Boiling Curves and Heat Transfer Coefficients

^{2}·s. During the experiment, three-point temperatures along the microchannel direction are measured. The average temperature is selected to calculate the wall superheat degree. The ONB can be identified at the point with a radical change in slope of the boiling curve. At low heat fluxes lower than 20 W/cm

^{2}, all curves almost coincide in single-phase state. When the heat flux is over 40 W/cm

^{2}boiling curves begin to differ greatly. Q10-20% presents the lowest wall superheats and the highest CHF of 160 W/cm

^{2}of all samples, showing excellent boiling performance. Other samples reach only about 120 W/cm

^{2}. It indicates that too large or small porosity would degrade the boiling performance. Figure 7b shows boiling curves of Q30 series samples. Incipient wall superheats of all samples are less than 3.0 K. Q30-20% displays the lowest wall superheats and highest CHF of 160 W/cm

^{2}of all samples. Comparatively, the sample without PLA and larger percent PLA could not give full play to the best performance. Although sample Q30-10% can reach higher CHF, its wall superheats relatively more.

^{2}, HTCs show an almost constant single-phase state. After initiation, HTCs increase rapidly with heat fluxes. Q10-20%, with moderate PFA content, achieves a higher HTC level. The maximum HTC of Q10-20% reaches up to 112.4 kW/(m

^{2}·K). However, for the sample without PLA, HTCs would decrease after moderate heat fluxes.

^{2}·K). Comparatively, the maximum HTC of Q30-40% is only 98 kW/(m

^{2}·K).

#### 4.2. Average Pressure Drop

^{2}all porous microchannels stay in the single-phase flow state. The pressure drop increases slightly with increasing heat flux. After the boiling incipience the average pressure drop is almost proportional to the heat flux. Q10-10% shows slightly higher pressure drop in each series. In general, the addition of PLA has a minor impact on the average pressure drop and would not cause a significant increase in the two-phase pressure drop.

#### 4.3. Pressure Instability and Boiling Pattern of Sintered Microchannels Containing PLA

^{2}. Inlet and outlet pressure presents an unstable large-amplitude, low-frequency oscillation type (LALF), superposed by small-amplitude, high-frequency type (SAHF). This is a typical pressure-oscillation mode found in porous microchannels sintered with small-sized copper particles (d ≤ 50 μm) [6]. Maximum amplitude of LALF oscillations yields 17.0 kPa and those of SAHF ones 2.0 kPa. One typical event is visually shown in Figure 11, selected from one range of pressure fluctuation curve in Figure 10. At t = t

_{0,}both inlet and outlet pressure reach a peak value. A large vapor mass is found near the entrance. Inlet liquid could not flow into the channels and some regions have become drought. At t = t

_{0}+ 24 ms, inlet pressure has been released and some liquid begins to rewet upper-side channels. Intense evaporation takes place in these channels. An explosive boiling emerges in the middle region and induces a small pressure spike in the pressure curve. At t = t

_{0}+ 164 ms, liquid inlets change from upper side to low side. Due to strong evaporation the inflow liquid is rapidly transformed into water vapor, and the formed vapor mass at upper-side channels is rapidly expanded towards upstream. The inlet and outlet pressure drops to almost the lowest value. At t = t

_{0}+ 235 ms, a violent explosive boiling occurs abruptly near the upstream region due to the high wall superheat (ΔT = 19.2 K). Its extensive influence hinders liquid inflow completely and disrupts the rhythmical flow pattern.

^{2}·s) and q = 121.2 W/cm

^{2}. Distinct from that of Q10-0%, the pressure curve of Q10-20% presents a quasi-periodicity. The addition of PLA with a volume ratio of 20% improves the flow instability. The corresponding visual observation is shown in Figure 13. At t = t

_{0}, the inlet and outlet pressure reach the highest value, and inlet region is completely covered by a large vapor mass produced by evaporation, difficult for liquid to enter. At t = t

_{0}+ 135 ms, the inlet liquid reenters those downside microchannels and rewets the relevant region. Both inlet and outlet pressure also fall to the trough. After t = t

_{0}+ 198 ms, the liquid front has migrated to the middle region. Almost in the meantime, a new vapor pocket is growing up near the entrance, which leads to a new climb of inlet pressure. When t = t

_{0}+ 305 ms the vapor pocket is completely formed. The inlet pressure reaches the crest and the inlet liquid was blocked outside.

#### 4.4. Existence of Optimal PFA Content on CHF and Discussion

^{2}. Figure 15b shows the measured CHF values of Q30 series. Both Q30-10% and Q30-20% show a higher CHF of 160 W/cm

^{2}. For both series, samples of 40% PFA content present a great decrease in CHF. This demonstrates that too large porosity is not conducive to the promotion of CHF.

## 5. Conclusions

- (1)
- For sintered parallel microchannels, the addition of PFA increases the sample porosity. Too large or too small content of PFA would degrade boiling heat transfer performance greatly. There exists an optimal range of PFA content for sintered microchannels. At the moderate PFA content, the boiling HTC of sintering microchannel reaches the maximum;
- (2)
- PFA content has little effect on the average pressure drop and would not cause the rapid increase in flow resistance;
- (3)
- According to the visual observation, the sample with moderate porosity is helpful to establish the rhythmic boiling and reduce the occurrence of explosive boiling. Larger porosity results in more rapid evaporation-rewetting cycle;
- (4)
- Particle size also has a great influence on boiling curves and HTC ones. Q30 series could achieve better performance than Q10 series. This is attributed to larger ratio of layer thickness to particle size (δ/d) for Q10-series samples.

^{2}. Figure 14b shows the measured CHF values of Q30 series. Both Q30-10% and Q30-20% show a high CHF of 160 W/cm

^{2}. For both series, samples of 40% PFA content present a great decrease in CHF. This demonstrates that too large porosity is not conducive to the promotion of CHF.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A_{base} | top surface area of copper block, cm^{2} | PFA | pore-forming agent |

CHF | critical heat flux, W/cm^{2} | q_{eff} | effective heat flux, W/cm^{2} |

d | particle diameter, mm | Q_{eff} | effective input heat power, W |

G | mass flux, kg/m^{2}·s | Q_{loss} | heat loss, W |

HTC | heat transfer coefficient | Q_{total} | input heat power, W |

h_{avg} | average heat transfer coefficient, kW/(m^{2}·K) | T_{w} | wall temperature, K |

h_{sp} | single-phase heat transfer coefficient, kW/(m^{2}·K) | T_{in} | inlet temperature, K |

h_{tp} | two-phase heat transfer coefficient, kW/(m^{2}·K) | T_{s} | saturation temperature, K |

L | length of microchannel (or sample), cm | y_{cop} | distance, mm |

L_{sp} | two-phase length of microchannel, cm | ||

L_{tp} | single-phase length of microchannel, cm | Greek symbols | |

$\dot{m}$ | mass flow rate, kg/s | ΔP | pressure drop, kPa |

N | microchannel number | λ_{cop} | thermal conductivity, W/(m·K) |

ONB | onset of nucleate boiling | δ | bottom layer thickness, mm |

P_{ave} | average pressure, kPa | ||

P_{in} | inlet pressure, kPa | ||

P_{out} | outlet pressure, kPa |

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**Figure 3.**Microchannel test section: (

**a**) Microchannel test section; (

**b**) Copper block; (

**c**) Porous microchannel.

**Figure 5.**Electron micrographs of porous microchannels with pore-forming agent. Green dotted circle represent large void created by PFA.

**Figure 6.**Electron micrographs of porous microchannels with pore-forming agent. Green dotted circle represent large void created by PFA.

**Figure 7.**Boiling curves of porous-microchannel samples with different PFA contents. (

**a**) Q10-series; (

**b**) Q30-series.

**Figure 8.**HTC curves of porous-microchannel samples with different PFA contents. (

**a**) Q10-series; (

**b**) Q30-series.

**Figure 9.**Average pressure drop curves of samples with different PFA contents. Dotted line represent boundary from single-phase to two-phase state. (

**a**) Q10-series; (

**b**) Q30-series.

**Figure 11.**Visual picture of sample Q10-0% (q

_{eff}= 121.2 W/cm

^{2}). Circle region: explosive boiling; Arrow: flow direction; blue line: vapor mass boundary.

**Figure 13.**Visual images of sample Q10-20% (q

_{eff}= 121.2 W/cm

^{2)}. Circle region: explosive boiling; Arrow: flow direction; blue line: vapor mass boundary.

**Figure 15.**The relationship between PFA content and CHF for Q10 series and Q30 one. (

**a**) Q10-series; (

**b**) Q30-series.

Width (μm) | Depth (μm) | Layer Thickness (μm) | Inter-Rib Width (μm) | Channel Number |
---|---|---|---|---|

600 | 1200 | 200 | 600 | 23 |

Particle Size | 10 μm | |||
---|---|---|---|---|

specification | Q10-0% | Q10-10% | Q10-20% | Q10-40% |

volume content | 0% | 10% | 20% | 40% |

porosity | 20.4% | 29.6% | 39.1% | 52.9% |

Particle Size | 30 μm | |||
---|---|---|---|---|

specification | Q30-0% | Q30-10% | Q30-20% | Q30-40% |

volume content | 0% | 10% | 20% | 40% |

porosity | 26.4% | 33.2% | 40.4% | 47.5% |

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## Share and Cite

**MDPI and ACS Style**

Lei, Q.; Zhang, D.; Feng, L.; Mao, J.; Chen, D.
Boiling Heat Transfer Characteristics of Porous Microchannel with Pore-Forming Agent. *Processes* **2023**, *11*, 617.
https://doi.org/10.3390/pr11020617

**AMA Style**

Lei Q, Zhang D, Feng L, Mao J, Chen D.
Boiling Heat Transfer Characteristics of Porous Microchannel with Pore-Forming Agent. *Processes*. 2023; 11(2):617.
https://doi.org/10.3390/pr11020617

**Chicago/Turabian Style**

Lei, Qinhui, Donghui Zhang, Lei Feng, Jijin Mao, and Daifen Chen.
2023. "Boiling Heat Transfer Characteristics of Porous Microchannel with Pore-Forming Agent" *Processes* 11, no. 2: 617.
https://doi.org/10.3390/pr11020617