# Ultrasounds Used as Promoters of Heat-Transfer Enhancement of Natural Convection in Dielectric Fluids for the Thermal Control of Electronic Equipment

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## Abstract

**:**

## 1. Introduction

_{sat}): in optimal conditions, and the value of ΔT

_{sat}was of the order of 30 K.

## 2. The Use of Ultrasound for Heat Transfer Enhancement: Fundamental Physical Elements

- Acoustic streaming: consists in the alteration of the trajectories of the fluid flow, with its consequent mixing which alters heat transfer;
- Acoustic alteration of the boundary layer: the oscillation of the velocity component perpendicular to the portion of the wall affected by the exchange determines alternating compression and expansion phases of the thermal boundary layer which determines an overall increase of the heat transfer;
- Acoustic cavitation: the phenomenon causes temperature and pressure oscillations due to the propagation of the acoustic waves, which can be quite large, the fluid locally reaches, during the rarefaction phase, the steam condition. Steam bubbles then form: after a certain period of time, they implode violently, causing shock waves and jets of fluid. If the collapse of the bubbles occurs near the thermal boundary layer, it produces strong internal mixing, with consequent variation of the local heat-transfer coefficient.

#### 2.1. Sound and Acoustic Cavitation

#### 2.2. The Mechanisms of Action of Ultrasonic Waves for Heat-Transfer Enhancement

- -
- the fluid and its phase (gas, liquid or two-phase);
- -
- the operating conditions of the fluid (such as temperature and pressure);
- -
- the ultrasonic frequency of the generator, f;
- -
- the power of the ultrasound generator, P
_{gen}; - -
- the geometry of the system;
- -
- the characteristics of the surfaces;
- -
- the material of the surface and the possible formation of chemical substances.

^{2}and is directly proportional to the frequency (that is, the higher the frequency, the greater the intensity necessary to lead to unstable cavitation).

_{0}is the ambient pressure, p

_{v}is the water vapor pressure, ρ the fluid density and w the velocity of the liquid. In order for cavitation to occur, a substrate is needed that acts as a nucleation center: this may be the surface of a container, impurities present in the liquid or other irregularities. The temperature has a considerable influence on cavitation, since it modifies the vapor pressure.

## 3. Experimental Studies on Heat-Transfer Enhancement: General Elements

- Difficulty in modifying the acoustic parameters: the frequency is almost always fixed and often the power cannot be varied; geometry and fluid dynamics influence the actual power released by the generator. It would be useful to modify the generators in such a way that they always supply the set power;
- With the exception of some particular cases, the acoustic generation leads to high P
_{US}/∆P_{th}ratios, where P_{US}is the total power given with the ultrasounds and ΔP_{th}represents the heat-transfer enhancement. This occurs because a large part of the acoustic energy is dissipated in the fluid before reaching the exchange surface and before altering it. The possibility could be assessed case by case to switch to mechanical generation or to bring the exchange surface as close as possible to the generation area.

## 4. Definition of the Experimental Setup and Measurement System

#### 4.1. Experimental Setup

#### 4.2. Measurement Strategy and Control System

_{T}and that of the fluid T

_{f}remain constant. The printed circuit board with the power transistors is held horizontal with the transistors facing down. The acoustic field in the dielectric fluid has been measured with a Bruel and Kjaer meter, obtaining value around 0.5 bar.

_{r}= 1.75, which thus does not raise stray capacitance values significantly with respect to operation in air, a thermal conductivity of 0.057 W/(m K), a critical temperature of 176 °C, a critical pressure of 1.83 × 10

^{6}Pa, an electrical resistivity of 10

^{13}Ω m, and a breakdown field of 15 MV/m. It would not be possible to use water for example, because of its conductivity (even deionized water would lose its insulating properties in the presence of any contaminant) and its very large relative permittivity.

## 5. Measurements for the Electronic Equipment Validation and Heat-Transfer Analysis

#### 5.1. Preliminary Operation

#### 5.2. Thermal Measurements and Data Analysis

_{sub}variable between 12 and 28 K, being the saturation temperature of FC72 at atmospheric pressure equal to 56 °C.

_{sub}meaning the temperature difference between the saturation temperature and the operating temperature of the fluid.

_{US}and the value obtained without ultrasounds, h, for the same hydrodynamic configuration. In an equivalent way, it is possible to define the ratio of the enhanced value of the heat-transfer coefficient and the basic value obtained without ultrasounds. The two enhancement factors are defined, respectively as:

_{T}is an average temperature measured on the nine transistors and T

_{f}the temperature of the fluid.

_{sub}). Obviously, the action of the ultrasounds allows increasing the operating power of the devices (i.e. the thermal power removed by the bath) at a given temperature difference between the devices and the coolant. In the third and in the fourth columns of Table 1 the average value of the enhancement factor and of the relative increase of the heat-transfer coefficient, obtained considering the results of the experiments reported in Figure 5 and Figure 6, are reported, according to the definitions given in Equations (3) and (4).

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Block diagram of the experimental apparatus with the interaction among all the different components.

**Figure 4.**Plot of the temperature transient with respect to time at switch-on (

**a**) and temperature vs. time in “steady state conduction” (

**b**).

**Figure 5.**Heat flux removed as a function of the temperature without ultrasound action (results of five different experiments).

**Figure 6.**Heat flux removed as a function of the temperature of the fluid with ultrasound action (result of five different experiments corresponding of those of Figure 5).

**Figure 7.**Plot based on the parameters shown in Table 1.

**Table 1.**Average dissipated power in each transistor and computed relative variation of the heat-transfer coefficient for different subcooling values.

ΔT_{sub} [K] | P_{t} [W] | EF | Δh/h |
---|---|---|---|

12 | 1.89 | 3.476 | 2.476 |

16 | 2.43 | 2.223 | 1.123 |

20 | 2.52 | 2.260 | 1.160 |

24 | 3.00 | 1.907 | 0.907 |

28 | 3.97 | 1.848 | 0.848 |

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**MDPI and ACS Style**

Bartoli, C.; Franco, A.; Macucci, M.
Ultrasounds Used as Promoters of Heat-Transfer Enhancement of Natural Convection in Dielectric Fluids for the Thermal Control of Electronic Equipment. *Acoustics* **2020**, *2*, 279-292.
https://doi.org/10.3390/acoustics2020017

**AMA Style**

Bartoli C, Franco A, Macucci M.
Ultrasounds Used as Promoters of Heat-Transfer Enhancement of Natural Convection in Dielectric Fluids for the Thermal Control of Electronic Equipment. *Acoustics*. 2020; 2(2):279-292.
https://doi.org/10.3390/acoustics2020017

**Chicago/Turabian Style**

Bartoli, Carlo, Alessandro Franco, and Massimo Macucci.
2020. "Ultrasounds Used as Promoters of Heat-Transfer Enhancement of Natural Convection in Dielectric Fluids for the Thermal Control of Electronic Equipment" *Acoustics* 2, no. 2: 279-292.
https://doi.org/10.3390/acoustics2020017