# Gas–Liquid Two-Phase Flow and Heat Transfer without Phase Change in Microfluidic Heat Exchanger

^{*}

## Abstract

**:**

## 1. Introduction

^{2}[1] with local hotspots ranging from 1200 to 4500 W/cm

^{2}[2]. Therefore, to keep pace with the current growth trend of microelectronics, efficient cooling methods capable of dissipating large amounts of thermal load from the chip to a surface temperature of less than 125 °C for defense use [3] and less than 85–100 °C for general microelectronics are needed [4].

^{2}. However, the previously developed MFHEs had a problem associated with an uneven temperature distribution over the base (substrate) of the heat exchanger, which adversely affects local overheating. Another disadvantage of heat transfer in single-phase flow microchannels is the low Nusselt number obtained in laminar flow, which is about 4.

^{2}[16], which is 10 times more heat than in a single-phase flow. This advantage of the boiling flow has found application for heat transfer in devices such as oscillating heat pipe [17], microchannel pulsating heat pipe [18] and others. While boiling in a stream is attractive because it provides a high heat flux at a constant phase transition temperature, it can be difficult to control due to backflow and instability. Another disadvantage of boiling flow is that the water in the heat exchanger is the working fluid, and the boiling point of the water is higher than the operating temperature of most electronic devices. There is a solution to use refrigerants as working fluids, since the boiling point is lower than the boiling point of water. However, refrigerants have a lower cooling capacity due to their lower specific heat and heat of vaporization.

## 2. Experimental Part

#### 2.1. Microfluidic Heat Exchanger Design

_{ch}= 1 mm, H

_{ch}= 1 mm), the width of the walls between the channels was also 1 mm (W

_{w}= 1 mm) (see Figure 1c), and the length of the channels was 55 mm (L

_{ch}= 55 mm) (see Figure 1, Table 1).

#### 2.2. Experimental Rig

## 3. Theoretical Part

^{3}/s; $\rho $ is coolant density, kg/m

^{3}; ${T}_{in}$, ${T}_{out}$ is coolant temperature before and after MFHE, K; $Cp$ is specific heat capacity of coolant, J/kg·K, for water $Cp$ = 4190 J/kg·K.

^{2}, since the length of the channels is 55 mm, and the width of six channels is 13 mm (see Figure 1a), ${A}_{h}$ = 715 mm

^{2}.

^{2}and m, respectively.

^{2}⋅K, which is equal to

^{3}; ${\mu}_{c}$ is dynamic viscosity of the continuous phase, Pa·s; ${u}_{f}$, ${u}_{TP}$ is fluid velocity and two-phase flow velocity, m/s, the last of which is calculated as

## 4. Results and Discussion

_{SP}= 0.036–0.54 L/m for a single-phase flow and Q

_{TP}= 0.036–0.45 L/m for a two-phase flow, which corresponds to the Reynolds numbers Re

_{SP}= 100–1500 and Re

_{TP}= 100–1250. It was experimentally found that it takes from a few seconds (for pressure) to one minute (for temperature) to stabilize the readings of pressure, temperature and flow sensors. Therefore, for all the experiments, the recording of the sensor readings was carried out two minutes after setting the appropriate flow rate, to be certain that the flow rates and heat flow to the coolant from the electric heater are stabilized.

#### 4.1. Heat Transfer in Single-Phase Flow in Microchannels

_{SP}= 100 to Re

_{SP}= 1500, which corresponds to the fluid velocity in the channel from ${u}_{f}$ = 0.1 to 1.5 m/s. Taking into account that the thermocouples were installed under the channel at a depth of $dz$ = 0.5 mm, the actual temperature on the channel wall was calculated as

_{SP}= 100, 300 (see Figure 3a), Re

_{SP}= 500, 750 (see Figure 3b), Re

_{SP}= 1000, 1250, 1500 (see Figure 3c). Due to the fact that the maximum temperature measurement error is less than 1%, the error bar will not be visible on the graph. So, the error bar is smaller than the size of the dots.

_{SP}= 1500 compared to Re

_{SP}= 100, the average wall temperature decreases from ${T}_{SP.w.avg\left(ReSP=\text{}100\right)}$ = 39.2 °C to ${T}_{SP.w.avg\left(ReSP=\text{}1500\right)}$ = 29.0 °C, and fluids with ${T}_{SP.f.avg\left(ReSP=\text{}100\right)}$ = 31.2 °C to ${T}_{SP.f.avg\left(ReSP=\text{}1500\right)}$ = 25.5 °C, which at 1.35 and 1.22 times lower, respectively. Additionally, it can be seen from Figure 3 that temperatures, as expected, increase linearly along the length of the MFHE. In this case, the lower the Reynolds number, the more significant the increase in both the wall temperature and the fluid flow. So, at Re

_{SP}= 100, the temperature for ${T}_{SP.w}$ and ${T}_{SP.f}$ increases along the length by 2.1 and 10.1 °C, respectively, while for Re

_{SP}= 1500 the temperature for ${T}_{SP.w}$ and ${T}_{SP.f}$ increases by only 1.4 and 0.8 °C. Figure 3 also shows that with an increase in the fluid velocity in the channels, and correspondingly with an increase in the Reynolds number, the temperature difference between ${T}_{SP.w}$ and ${T}_{SP.f}$ decreases significantly. For clarity, we plotted the dependence of the temperature difference on the Reynolds number (see Figure 4).

_{SP}= 100, 300 increases with the MFHE length. Additionally, Figure 5 shows that the local Nusselt number becomes rather uniform over the entire heating length starting from Re

_{SP}≥ 750, with the exception of the first two points (x = 7 and 17 mm), which is explained by the influence of the entrance region. In this case, the effect of the entrance area is more significant the higher the Reynolds number, which is caused by the restructuring of the velocity profile. So, from Figure 5, it can be seen that for the first two points $N{u}_{SP.x}$ for Re

_{SP}= 1500 is almost 2 times higher compared to $N{u}_{SP.x}$ for Re

_{SP}= 300 (24 versus 13). Whereas, for the separate points (x = 25–50), the local Nusselt number is fairly uniform. It can be seen that after Re

_{SP}= 300, an increase in the Reynolds number does not give a significant increase in the local Nusselt number, which takes a value equal to about $N{u}_{SP.x}$ = 17 for Re

_{SP}= 300–1500, and the spread $N{u}_{SP.x}$ for x = 27, 37, 47 is only ±1.7, ±1.4 and ±1, respectively.

#### 4.2. Heat Transfer in Two-Phase Flow in Microchannels

_{TP}= 100 to Re

_{TP}= 1250 at a gas content of 10% and for Re

_{TP}= 300 at a gas content of 10 to 40%. As mentioned earlier, segmented flow is widely used in chemical engineering to enhance the mass transfer process. This should accordingly increase the heat transfer due to the same phenomenon of enhanced convection due to the Taylor vortices in liquid slugs. The presence of Taylor vortices in channel requires surface tension to prevail over gravity, which occurs when the Bond number $\rho g{D}_{h}{}^{2}/\sigma $ < 3.368 [22] and the capillary number Ca < 0.707 [23]. In our case, the Bond number is 0.135, and the Ca number is in the range from 0.0014 to 0.0172.

#### 4.2.1. Influence of Reynolds Number on the Heat Transfer Efficiency in MFHE

_{TP}= 100–1250 was plotted (see Figure 6).

_{TP}= 1250, compared with Re

_{TP}= 100, the average wall and liquid temperatures decrease by 1.76 and 1.46 times, respectively, while for a single-phase flow these ratios took the values 1.35 and 1.22. Additionally, it can be seen from Figure 6 that temperatures, as expected, increase linearly along the length of the MFHE. In this case, the lower the Reynolds number, the more significant the increase in both the wall temperature and the fluid flow.

_{TP}on the growth of $N{u}_{TP.x}$ is noticeably more significant. However, the most important conclusion, from the point of view of heat transfer efficiency, which can be drawn from the analysis of the graphs in Figure 5 and Figure 7, is that the segmented flow significantly increases the local $N{u}_{TP.x}$ and, therefore, leads to an increase and averaged dimensionless heat transfer coefficient $N{u}_{TP.avg}$.

_{TP}, Re

_{SP}= 1250, the Nusselt number for two-phase and single-phase flows is $N{u}_{TP.avg}$ = 34.3 and $N{u}_{SP.avg}$ = 20.5, respectively. Figure 8 also shows that for a single-phase flow at Re

_{SP}= 500, the average Nusselt number is $N{u}_{SP.avg}=18.5$, and a further increase in the flow rate does not significantly affect $N{u}_{SP.avg}$. In this case, for a two-phase flow, an increase in $N{u}_{TP.avg}$ from Re

_{TP}is observed over the entire investigated range (see Figure 8). For Reynolds tending to zero, the average Nusselt number tends to the fully developed value in the square channels of 3.61 (see Figure 8) [25]. It should also be mentioned that the ratio of the Nusselt number to that of the liquid-only flow obtained in this work is comparable with the data of other researchers. Thus, the $N{u}_{TP.avg}$/$N{u}_{SP.avg}$ ratio obtained by the authors lies in the range from 1.63 to 2.88 and from 1.9 to 3.3 obtained experimentally [26,27] and by CFD simulation [28], respectively.

_{SP}= 500, but a further increase in the Reynolds number practically does not affect the R

_{th}and r

_{th}. In the case of a two-phase flow, a decrease in R

_{th}, r

_{th}is observed over the entire investigated range (see Figure 9).

#### 4.2.2. Influence of Gas Hold-Up on the Heat Transfer Efficiency in MFHE

_{TP}= 300. Figure 10 shows the dependence of the averaged Nusselt number on the volumetric gas content at Re

_{TP}= 300. It can be seen from the graph that the injection of gas in the amount of φ = 10% makes it possible to increase $N{u}_{avg}$ by 38% (from 14.76 to 20.43). At a gas content above 10%, the intensification of heat transfer due to a segmented flow of air bubbles rapidly decreases, and at φ = 40%, the value of $N{u}_{avg}$ turns out to be lower than for a single-phase flow. It is possible to understand the reason for the obtained dependence by analyzing photographs of flow regimes in microchannels. A visualization of these flow regimes can be seen in Table 2.

_{B}= 1.68 mm at φ = 10% to L

_{B}= 2.61 mm at φ = 30%). The fact is that the effect of liquid circulation in slugs is offset by a large fraction of gas, the contribution of which to heat exchange is insignificant, since the heat capacity of the bubbles is much lower than that of the liquid phase.

#### 4.3. Single-Phase and Two-Phase Flow Hydrodynamics

## 5. Conclusions

_{SP}= 100–1500 and Re

_{TP}= 100–1250, respectively.

_{TP}= 300). When the gas content is higher than 10%, the heat transfer intensification due to the segmented flow of air bubbles decreases rapidly, and at φ = 40%, the value of $N{u}_{avg}$ is lower than for a single-phase flow. Internal recirculations within the liquid slugs have been shown to explain the heat transfer enhancement.

^{2}in the case of single-phase and 120 W/cm

^{2}in the case of two-phase flows. At the same time, MCHE is able to maintain the maximum surface temperature below 85 °C required for general microelectronics [4]. The obtained heat flow for the Taylor flow demonstrates comparable results with the boiling flow in the vapor compression refrigeration flow loop and boiling incipience in pin fin heat sink [16,29]. Therefore, the use of a two-phase gas–liquid flow without a phase transition can be recommended as an alternative to a boiling (vapor–liquid) flow. In addition, it is known that the efficiency of heat transfer in a boiling flow can be significantly increased by reducing the channels hydraulic diameter and using offset strip-fin geometry (the heat transfer coefficient reaches 130,000 W/m

^{2}·°C and higher) [16]. It can be assumed that the use of similar methods for intensifying thermal characteristics in the case of a two-phase Taylor flow will provide an effective solution for cooling with large heat fluxes.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Dependence of the wall temperature on the axial arrangement of thermocouples in the MFHE at zero phase flow.

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**Figure 1.**Microfluidic heat exchanger (MFHE) top view (

**a**), side view with the thermocouples location (

**b**), cross-section of MFHE (

**c**). All dimensions are in millimeters.

**Figure 2.**Schematic diagram of the experimental setup to study hydrodynamics and heat transfer in single- and two-phase flow in microfluidic heat exchanger (MFHE).

**Figure 3.**Dependence of the wall temperature and fluid flow along the length of the MFHE channel for a single-phase flow at (

**a**) Re

_{SP}= 100, 300, (

**b**) Re

_{SP}= 500, 750, (

**c**) Re

_{SP}= 1000, 1250, 1500.

**Figure 4.**Dependence of the temperature difference between the wall and fluid temperatures along the length of the MFHE channel for a single-phase flow at Re

_{SP}= 100–1500.

**Figure 5.**Dependence of the local Nusselt number on MFHE axial location for single phase flow at Re

_{SP}= 100–1500.

**Figure 6.**Dependence of wall temperature and fluid flow along the length of the MFHE channel for two-phase flow at φ = 10% for (

**a**) Re

_{TP}= 100, 300, (

**b**) Re

_{TP}= 500, 750, (

**c**) Re

_{TP}= 1000, 1250.

**Figure 7.**Dependence of the local Nusselt number on MFHE axial location for two-phase flow at Re

_{TP}= 100–1250, φ = 10%.

**Figure 8.**Dependence of the average Nusselt number on the Reynolds number (Re

_{SP}= 100–1250 for single phase flow and Re

_{TP}= 100–1500 for two-phase flow, φ = 10%).

**Figure 10.**Dependence of the average Nusselt number on the gas hold-up at Re

_{TP}= 300. Bubbly, slug and annular flows (experimental data).

**Figure 13.**Dependence of the average Nusselt number on the pressure drop for single phase and two-phase flow.

**Figure 14.**Dependence of the thermal performance criteria η on the Reynolds number (Re

_{SP}, Re

_{TP}= 100–1250, at φ = 10% for two-phase flow).

Parameter | L_{ch}, mm | W_{ch}, mm | W_{w}, mm | H_{ch}, mm |
---|---|---|---|---|

Value | 55 | 1 | 1 | 1 |

Case | (a) | (b) | (c) | (d) |
---|---|---|---|---|

Gas hold-up (%) | 10 | 20 | 30 | 40 |

Flow regime | slug | slug | slug | annular |

Average length L_{B} (mm) | 1.68 | 2.36 | 2.61 | – |

Average length L_{S} (mm) | 2.31 | 2.81 | 1.22 | – |

Average length L_{UC} (mm) | 3.99 | 4.17 | 3.83 | – |

(a) | (c) | |||

(b) | (d) |

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**MDPI and ACS Style**

Vasilev, M.P.; Abiev, R.S.
Gas–Liquid Two-Phase Flow and Heat Transfer without Phase Change in Microfluidic Heat Exchanger. *Fluids* **2021**, *6*, 150.
https://doi.org/10.3390/fluids6040150

**AMA Style**

Vasilev MP, Abiev RS.
Gas–Liquid Two-Phase Flow and Heat Transfer without Phase Change in Microfluidic Heat Exchanger. *Fluids*. 2021; 6(4):150.
https://doi.org/10.3390/fluids6040150

**Chicago/Turabian Style**

Vasilev, Maksim P., and Rufat Sh. Abiev.
2021. "Gas–Liquid Two-Phase Flow and Heat Transfer without Phase Change in Microfluidic Heat Exchanger" *Fluids* 6, no. 4: 150.
https://doi.org/10.3390/fluids6040150