# Local Heat Transfer Analysis in a Single Microchannel with Boiling DI-Water and Correlations with Impedance Local Sensors

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## Abstract

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## 1. Introduction

## 2. Experimental Setup

## 3. Data Reduction

## 4. Results and Discussions

#### 4.1. Single Phase Pressure Drop Validation

#### 4.2. Two Phase Experimental Results

#### 4.3. Local Electrical Sensing

#### Slug Flow Analysis Using Impedance Sensors

## 5. Summary

- It was found that the flow regime in the channels varied considerably between the selected experimental conditions.
- Two different regimes were identified for the value of the heat transfer coefficient with respect to the vapor quality within the investigated mass and heat flux conditions: At the onset of evaporation (0 < x < 0.05), the heat transfer coefficient increases with the vapour quality. At intermediate vapor quality ranges (0.05 < x < 0.5), the heat transfer coefficient shows a “U” shape profile. Since the dry-out did not occur in any of the experiments, the heat transfer coefficient did not decrease to a value typical for gas systems.
- For the heat transfer coefficient, a similar comparison was done using four correlations. It was found that most correlations predicted the correct values for some points but failed in other regimes. The correlation published by Mahmoud and Karayianis [48] showed the best predictive performance over the whole range of experiments. There are relatively big mean absolute error values observed between experimental results and prediction of the selected correlations. We conclude that this is due to the relative unstable and different flow conditions.
- It was affirmed that it is possible to find local information regarding the flow regime using impedance sensors as we presented previously in [35]. In most conditions, slug flow and annular flow regimes were observed in the channel. In the instances when bubbly flow was found, it transformed into slug flow. The application of such sensing system was highlighted in mechanistic models based on flow regime such as the model presented by Falsetti et al. [33].
- The slug passing frequency and duty cycle are critical and usable information that was obtained and cross checked with the synchronized videos. Thus for the case when slug flow is the dominant regime in the channel, the information gleaned form the impedance spectroscopy, namely residence time and bubble frequency at the sensor location is very useful.
- Since it has been found that the flow regime is of paramount importance regarding the heat transfer, the information gained from impedance spectroscopy is a useful tool to use the correct correlations for a given set of experimental conditions.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | cross-section area | (${\mathrm{mm}}^{2}$) |

${c}_{p}$ | heat capacity | ($\mathrm{J}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{kg}}^{-1}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{K}}^{-1}$) |

${D}_{h}$ | hydraulic diameter | ($\mathsf{\mu}\mathrm{m}$) |

f | friction factor | (-) |

G | mass flux | ($\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$) |

h | heat transfer coefficient | ($\mathrm{W}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{K}}^{-1}$) |

${h}_{lv}$ | latent heat of vaporization | ($\mathrm{j}.{\mathrm{kg}}^{-1}$) |

${h}_{ch}$ | channel height | ($\mathsf{\mu}\mathrm{m}$) |

I | electrical current | ($\mathrm{A}$) |

k | thermal conductivity | ($\mathrm{W}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-1}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{K}}^{-1}$) |

K | pressure loss coefficient | (-) |

L | channel length | ($\mathrm{mm}$) |

${q}^{\u2033}$ | heat flux | ($\mathrm{W}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}$) |

$\dot{Q}$ | power | ($\mathrm{Watt}$) |

t | time | ($\mathrm{s}$) |

T | temperature | (${}^{\circ}\mathrm{C}$) |

V | electrical voltage | ($\mathrm{V}$) |

${W}_{ch}$ | channel width | ($\mathsf{\mu}\mathrm{m}$) |

x | vapor quality, $\frac{{\dot{m}}_{vapor}}{{\dot{m}}_{total}}$ | (-) |

$\alpha $ | void fraction | (-) |

$\beta $ | channel aspect ratio | (-) |

$\delta $ | liquid film thickness | ($\mathsf{\mu}\mathrm{m}$) |

$\mu $ | dynamic viscosity | ($\mathrm{Pa}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\mathrm{s}$) |

$\rho $ | density | ($\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-3}$) |

$\tau $ | time period | ($\mathrm{s}$) |

$\Phi $ | two phase multiplier | (-) |

Dimensionless numbers | ||

$Bl$ | Boiling number $Bl={q}^{\u2033}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{h}_{lv}^{-1}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\dot{m}$ | |

$Bo$ | Bond number $Bo=({\rho}_{l}-{\rho}_{g})g{D}_{h}^{2}{\sigma}^{-1}$ | |

C | Chisholm parameter | |

$\chi $ | Martinelli parameter | |

$Fr$ | Froude number, $Fr=u\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{(g\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}L)}^{-0.5}$ | |

$Nu$ | Nusselt number | |

$Pe$ | Peclet number, $Pe=Re\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}Pr$ | |

$Pr$ | Prandtl number, $Pr=\mathsf{\mu}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{c}_{p}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{k}^{-1}$ | |

$Re$ | Reynolds number, $Re=G\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{D}_{h}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathsf{\mu}}^{-1}$ | |

$We$ | Webber number, $We=\frac{{G}^{2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{D}_{h}}{(\rho \phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\sigma )}$ | |

Subscripts | ||

$acc$ | acceleration | |

$amb$ | ambient | |

$base$ | base | |

$ch$ | channel | |

$exp$ | expansion | |

$eff$ | effective | |

$fl$ | fluid | |

$ftp$ | footprint | |

v | vapor | |

$in$ | inlet | |

l | liquid | |

$loc$ | local | |

$loss$ | heat loss | |

$out$ | outlet | |

$sat$ | saturation | |

$sp$ | single phase | |

$tp$ | two phase | |

w | wall | |

$sc$ | sudden contraction | |

$se$ | sudden expansion | |

${90}^{\circ}$ | corner |

## Appendix A. Single Phase Pressure Drop

## Appendix B. Boiling Heat Transfer Coefficient Correlations

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**Figure 3.**Thermal path with implemented sensors of the boiling liquid in the housing. Light blue is the liquid path inside the housing and red is liquid path inside the channel plate. (

**a**). Cropped zoom of the cross section with temperature sensors in the channel plate, heater block, and housing. (

**b**). Top view of the housing assembly with heater block, channel plate, and glass lid. (

**c**). A-A cross section of the housing assembly.

**Figure 4.**Example of raw data using a heating power of 25 $\mathrm{W}$ and a flow of 1 mL/min (22.17 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$) water acquired by test setup. (

**a**). Time domain recorded temperatures of thermocouples located in heater block. (

**b**). Time domain recorded temperatures of thermocouples located in channel block. (

**c**). Mean value of the recorded temperature in each sensor. (

**d**). Time domain recorded pressure drop in the channel. (

**e**). Power spectrum of the Fast Fourier Transformation of pressure drop.

**Figure 5.**Schematic of the single microchannel evaporator. (

**a**) isometric view of channel plate. (

**b**) cross section of the channel plate.

**Figure 6.**Single phase pressure drop. Shah and London model from [42] and Muzychka and Yovanovich model from [43]. (

**a**) Fanning friction of channel with 1.050 mm × 0.5 mm cross section. (

**b**) pressure drop of channel with 1.050 mm × 0.5 mm cross section compared with predictive models. (

**c**) Fanning friction of channel with 1.500 mm × 0.5 mm cross section. (

**d**) pressure drop of channel with 1.500 mm × 0.5 mm cross section compared with predictive models.

**Figure 7.**Example of differential pressure drop in different wall heat flux with a constant mass flux of G = 22.17 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}$ in channel with ${D}_{h}=$ 750 $\mathsf{\mu}$m. the black line indicates pressure drop in single phase in room temperature with the same mass flux. (

**a**). ${q}^{\u2033}=14.7$ $\mathrm{kW}.{\mathrm{m}}^{-2}$. (

**b**). ${q}^{\u2033}=38.3$ $\mathrm{kW}.{\mathrm{m}}^{-2}$. (

**c**). ${q}^{\u2033}=59.2$ $\mathrm{kW}.{\mathrm{m}}^{-2}$. (

**d**). ${q}^{\u2033}=93.9$ $\mathrm{kW}.{\mathrm{m}}^{-2}$.

**Figure 8.**Heat transfer coefficient versus heat flux. (

**a**). Mean heat transfer coefficient for both single and two phase regions versus mean heat flux. (

**b**). Mean heat transfer coefficient of two phase regions versus mean heat flux.

**Figure 9.**Local boiling heat transfer coefficient vs. vapor quality for channel 1 with fixed mass flux in each subplot for channel 1.5 mm × 0.5 mm (${D}_{h}$ = 750 $\mathsf{\mu}$m). (

**a**) G = 22.17 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ (

**b**) G = 44.35 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ (

**c**) G = 66.53 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ (

**d**). G = 88.68 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$.

**Figure 10.**Local boiling heat transfer coefficient vs. vapor quality for channel 2 with fixed mass flux in each subplot for channel 1.05 mm × 0.5 mm (${D}_{h}$ = 677 $\mathsf{\mu}$m). (

**a**) G = 23.76 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ (

**b**) G = 47.52 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ (

**c**) G = 71.28 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ (

**d**). G = 95.04 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$.

**Figure 11.**Pressure drop vs. vapor. (

**a**) channel cross Section 1.50 mm × 0.5 mm. (

**b**) channel cross Section 1.050 mm × 0.5 mm.

**Figure 13.**Location of the sensors center with respect to the channel inlet center located along the channel.

**Figure 16.**Example of impedance measurements and high speed videos. (

**a**). An example of annular flow impedance measurement and high-speed pictures. (

**b**). An example of slug flow with high speed videos.

**Figure 18.**Example of synchronized recorded photos and impedance amplitude measurement. The green and red vertical lines are derived from signal post processing.

**Figure 19.**(

**a**) Representation of slugs in updated 3-zone-model passing in microchannel boiling [8]. (

**b**) Impedance measurements signal using implemented sensors [36]. (

**c**) Slug flow impedance signal for 5 s. The red arrow shows an example of a slug that has lower impedance level comparing to the other slugs impedance amplitude.

**Figure 20.**Example of electrical sensing for slug flow. The green vertical lines show the beginning and of the slug and red vertical lines denote end of passing slug. (

**a**) impedance amplitude with total power 30 $\mathrm{W}$ and flow rate 2 mL/min (44.35 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$) ( in S1 location. (

**b**) impedance amplitude with total power 30 $\mathrm{W}$ and flow rate 3 mL/min (66.53 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$) in S3 location. (

**c**) impedance amplitude with total power 25 $\mathrm{W}$ and flow rate 2 mL/min (44.35 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$) in S1 location. (

**d**) pulse width and pulse period with impedance amplitude with total power 30 $\mathrm{W}$ and flow rate 2 mL/min (44.35 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$) in S1 location. (

**e**) pulse width and pulse period with impedance amplitude with total power 30 $\mathrm{W}$ and flow rate 3 ml/m in S3 location. (

**f**). pulse width and pulse period with impedance amplitude with total power 30 $\mathrm{W}$ and flow rate 2 mL/min (44.35 $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$) in S1 location.

Property | Unit | Value or Range | Uncertainty |
---|---|---|---|

Channel hydraulic diameter | $\mathsf{\mu}\mathrm{m}$ | 750 & 1050 | |

Flow rate | $\mathrm{mL}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{min}}^{-1}$ | 0.5–4 | |

Temperature | ${}^{\circ}\mathrm{C}$ | 60–140 | ±0.5 |

Total heaters applied power | $\mathrm{Watt}$ | 7–30 | |

measurement excitation freq. | $\mathrm{kHz}$ | 50 | less than 0.01% = 5 Hz |

measurement sampling freq. | $\mathrm{kHz}$ | 13.7 | |

Reynolds number @ 90 ${}^{\circ}\mathrm{C}$ | - | 25–206 | |

differential pressure sensing | $\mathrm{mbar}$ | 0–350 | 0.35 |

absolute inlet pressure sensing | $\mathrm{mbar}$ | 0 to 40,000 | 40 |

input power | $\mathrm{Watt}$ | 7–33 |

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## Share and Cite

**MDPI and ACS Style**

Talebi, M.; Sadir, S.; Kraut, M.; Dittmeyer, R.; Woias, P.
Local Heat Transfer Analysis in a Single Microchannel with Boiling DI-Water and Correlations with Impedance Local Sensors. *Energies* **2020**, *13*, 6473.
https://doi.org/10.3390/en13236473

**AMA Style**

Talebi M, Sadir S, Kraut M, Dittmeyer R, Woias P.
Local Heat Transfer Analysis in a Single Microchannel with Boiling DI-Water and Correlations with Impedance Local Sensors. *Energies*. 2020; 13(23):6473.
https://doi.org/10.3390/en13236473

**Chicago/Turabian Style**

Talebi, Mohammadmahdi, Sahba Sadir, Manfred Kraut, Roland Dittmeyer, and Peter Woias.
2020. "Local Heat Transfer Analysis in a Single Microchannel with Boiling DI-Water and Correlations with Impedance Local Sensors" *Energies* 13, no. 23: 6473.
https://doi.org/10.3390/en13236473