# Use of Nanoparticle Enhanced Phase Change Material for Cooling of Surface Acoustic Wave Sensor

## Abstract

**:**

## 1. Introduction

## 2. Modeling

#### 2.1. Cooling Part

#### 2.2. Surface Acoustic Wave in Electrical Part

## 3. Results

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

C | Constant pressure specific heat (J·kg${}^{-1}$·K${}^{-1}$) |

g | Gravity constant (m·s${}^{-2}$) |

l | Length of the cavity |

H | Height of the cavity |

${H}_{sf}$ | latent heat of melting (J·kg${}^{-1}$) |

k | Coefficient of the thermal conductivity (W·m${}^{-1}$·K${}^{-1}$) |

Nu | Nusselt number |

p | pressure (Pa) |

Pr | Prandtl number |

Ra | Rayleigh number |

Ste | Stefan number |

T | temperature (K) |

u | x-velocity component (m·s${}^{-1}$) |

v | y-velocity component (m·s${}^{-1}$) |

x | x-Cartesian coordinate (m) |

y | y-Cartesian coordinate (m) |

Greek symbols | |

$\mu $ | Dynamic viscosity (kg·s${}^{-1}$m${}^{-1}$) |

$\alpha $ | Coefficient of thermal diffusivity (m${}^{2}$·s${}^{-1}$) |

$\beta $ | Coefficient of thermal expansion (K${}^{-1}$) |

$\varphi $ | Weight ratio of the nanoparticle inside NEPCM |

$\rho $ | Density (kg·m${}^{-3}$) |

Subscript | |

b | Bulk properties |

c | cold surface |

f | base fluid |

h | Hot surface |

## References

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**Figure 1.**Top view of a typical of surface acoustic wave device, including input transducer, output transducer, and piezoelectric subtrace in a design.

**Figure 2.**Geometry of the unit cell of the proposed surface acoustic wave (SAW) unit cell where cooling system is interacted with electrical part.

**Figure 3.**Geometry of the electric part of the proposed SAW unit cell and electrical boundary condition.

**Figure 4.**First six modes of SAW problem with cooling: (

**a**) mode 1, (

**b**) mode 2, (

**c**) mode 3, (

**d**) mode 4, (

**e**) mode 5, (

**f**) mode 6.

**Figure 5.**Electric potential: (

**a**) mode 1, (

**b**) mode 2, (

**c**) mode 3, (

**d**) mode 4, (

**e**) mode 5, (

**f**) mode 6.

**Figure 6.**Comparison of the results of current method with Jamaabadi and Park [18].

**Figure 7.**Temperature distribution in SAW with cooling at the initial steps of applying resonance power.

**Figure 9.**Initial condition of phase change material (PCM) cell: (

**a**) contours of dimensionless temperature, (

**b**) contours of dimensionless pressure, (

**c**) velocity vector, (

**d**) contours of velocity magnitude.

**Figure 10.**Final condition of PCM cell: (

**a**) contours of dimensionless temperature, (

**b**) contours of dimensionless pressure, (

**c**) velocity vector, (

**d**) contours of velocity magnitude.

Nanofluid Property | Formula |
---|---|

$\rho $ | $(1-\alpha ){\rho}_{\mathrm{f}}+\alpha {\rho}_{\mathrm{s}}$ |

$\rho {c}_{\mathrm{p}}$ | $(1-\alpha ){\left(\rho {c}_{\mathrm{p}}\right)}_{\mathrm{f}}+\alpha {\left(\rho {c}_{\mathrm{p}}\right)}_{\mathrm{s}}$ |

$\rho \beta $ | $(1-\alpha ){\left(\rho \beta \right)}_{\mathrm{f}}+\alpha {\left(\rho \beta \right)}_{\mathrm{s}}$ |

$\mu $ | $\frac{{\mu}_{\mathrm{f}}}{{(1-\alpha )}^{2.5}}$ |

k | ${k}_{\mathrm{f}}\frac{{k}_{\mathrm{s}}+2{k}_{\mathrm{f}}-2\alpha ({k}_{\mathrm{f}}-{k}_{\mathrm{s}})}{{k}_{\mathrm{s}}+2{k}_{\mathrm{f}}+\alpha ({k}_{\mathrm{f}}-{k}_{\mathrm{s}})}+C{\left(\rho {c}_{\mathrm{p}}\right)}_{\mathrm{nf}}\sqrt{{u}^{2}+{\nu}^{2}}\alpha {d}_{\mathrm{p}}$ |

$\rho L$ | $(1-\alpha ){\left(\rho L\right)}_{\mathrm{f}}$ |

**Table 2.**Material thermo-physical properties [18].

Material | k | C | $\mathit{\rho}$ | $\mathit{\beta}$ | ${\mathit{H}}_{\mathit{f}}$ | $\mathit{\mu}$ |
---|---|---|---|---|---|---|

W/m·K | kJ/kg·K | kg/m${}^{\mathbf{3}}$ | (K${}^{-\mathbf{1}}$) | J/kg | ||

fluid TH29 | 0.53 | 2.2 | 1530 | 2 $\times {10}^{-4}$ | 187 | 5.33 $\times {10}^{-3}$ |

solid TH29 | 1.09 | 1.4 | 1719 | 187 | ||

Cu | 400 | 0.383 | 8954 | $1.67\times {10}^{-5}$ |

Parameter | Expression | Explanation |
---|---|---|

T | 25 [${}^{\xb0}$C] | Environment temperature |

${\rho}_{PIB}$ | 0.918 [g/cm${}^{3}$] | Density of polyisobutylene |

${E}_{PIB}$ | 10 [GPa] | Young’s modulus of polyisobutylene |

${\nu}_{PIB}$ | 0.48 | Poisson’s ratio of polyisobutylene |

${\u03f5}_{PIB}$ | 2.2 | Relative permittivity of polyisobutylene |

${v}_{Rayleigh}$ | 3488 [m/s] | Rayleigh wave velocity |

W | 4 $\left[\mathsf{\mu}\mathrm{m}\right]$ | Width of unit cell |

${f}_{0}$ | $\frac{{v}_{Rayleigh}}{W}$ | Estimated SAW frequency |

${t}_{PIB}$ | 0.5 $\left[\mathsf{\mu}\mathrm{m}\right]$ | polyisobutylene thickness |

Property | Units | Value |
---|---|---|

Eigenfrequency | Hz | 2.4664 $\times {10}^{8}$ |

Participation factor, normalized, X-translation | - | −2.4946 $\times {10}^{-4}$ |

Participation factor, normalized, Y-translation | - | 7.0013 $\times {10}^{-6}$ |

Participation factor, normalized, Z-rotation | - | 1.4234 $\times {10}^{-10}$ |

Effective modal mass, X-translation Effective modal mass | kg | 6.2228 $\times {10}^{-8}$ |

Y-translation (kg) Effective modal mass | kg | 4.9018 $\times {10}^{-11}$ |

Effective modal mass, Z-rotation | kg·m${}^{2}$ | 2.0260 $\times {10}^{-20}$ |

Eigenfrequency | Hz | 4.0749 $\times {10}^{8}$ |

Participation factor, normalized, X-translation | - | −6.9887 $\times {10}^{-6}$ |

Participation factor, normalized, Y-translation | - | −2.4954 $\times {10}^{-4}$ |

Participation factor, normalized, Z-rotation | - | 4.0343 $\times {10}^{-12}$ |

Effective modal mass, X-translation Effective modal mass | kg | 4.8841 $\times {10}^{-11}$ |

Y-translation (kg) Effective modal mass | kg | 6.2272 $\times {10}^{-8}$ |

Effective modal mass, Z-rotation | kg·m${}^{2}$ | 1.6275 $\times {10}^{-23}$ |

Eigenfrequency | Hz | 7.3261 $\times {10}^{8}$ |

Participation factor, normalized, X-translation | - | −8.2315 $\times {10}^{-5}$ |

Participation factor, normalized, Y-translation | - | −2.1961 $\times {10}^{-6}$ |

Participation factor, normalized, Z-rotation | - | 2.4716 $\times {10}^{-10}$ |

Effective modal mass, X-translation Effective modal mass | kg | 6.7758 $\times {10}^{-9}$ |

Y-translation (kg) Effective modal mass | kg | 4.8227 $\times {10}^{-12}$ |

Effective modal mass, Z-rotation | kg·m${}^{2}$ | 6.1090 $\times {10}^{-20}$ |

Eigenfrequency | Hz | 8.7055 $\times {10}^{8}$ |

Participation factor, normalized, X-translation | - | 1.0546 $\times {10}^{-11}$ |

Participation factor, normalized, Y-translation | - | −7.1771 $\times {10}^{-13}$ |

Participation factor, normalized, Z-rotation | - | −1.9653 $\times {10}^{-10}$ |

Effective modal mass, X-translation Effective modal mass | kg | 1.1122 $\times {10}^{-22}$ |

Y-translation (kg) Effective modal mass | kg | 5.1511 $\times {10}^{-25}$ |

Effective modal mass, Z-rotation | kg·m${}^{2}$ | 3.8625 $\times {10}^{-20}$ |

Eigenfrequency | Hz | 8.7667 $\times {10}^{8}$ |

Participation factor, normalized, X-translation | - | −3.5058 $\times {10}^{-12}$ |

Participation factor, normalized, Y-translation | - | −4.8362 $\times {10}^{-13}$ |

Participation factor, normalized, Z-rotation | - | 4.8769 $\times {10}^{-11}$ |

Effective modal mass, X-translation Effective modal mass | kg | 1.2291 $\times {10}^{-23}$ |

Y-translation (kg) Effective modal mass | kg | 2.3389 $\times {10}^{-25}$ |

Effective modal mass, Z-rotation | kg·m${}^{2}$ | 2.3784 $\times {10}^{-21}$ |

Eigenfrequency | Hz | 1.1328 $\times {10}^{9}$ |

Participation factor, normalized, X-translation | - | −3.9139 $\times {10}^{-5}$ |

Participation factor, normalized, Y-translation | - | 3.1356 $\times {10}^{-6}$ |

Participation factor, normalized, Z-rotation | - | −5.0336 $\times {10}^{-11}$ |

Effective modal mass, X-translation Effective modal mass | kg | 1.5319 $\times {10}^{-9}$ |

Y-translation (kg) Effective modal mass | kg | 9.8321 $\times {10}^{-12}$ |

Effective modal mass, Z-rotation | kg·m${}^{2}$ | 2.5337 $\times {10}^{-21}$ |

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**MDPI and ACS Style**

Abdollahzadeh Jamalabadi, M.Y.
Use of Nanoparticle Enhanced Phase Change Material for Cooling of Surface Acoustic Wave Sensor. *Fluids* **2021**, *6*, 31.
https://doi.org/10.3390/fluids6010031

**AMA Style**

Abdollahzadeh Jamalabadi MY.
Use of Nanoparticle Enhanced Phase Change Material for Cooling of Surface Acoustic Wave Sensor. *Fluids*. 2021; 6(1):31.
https://doi.org/10.3390/fluids6010031

**Chicago/Turabian Style**

Abdollahzadeh Jamalabadi, Mohammad Yaghoub.
2021. "Use of Nanoparticle Enhanced Phase Change Material for Cooling of Surface Acoustic Wave Sensor" *Fluids* 6, no. 1: 31.
https://doi.org/10.3390/fluids6010031