# Modeling of Subcooled Flow Boiling with Nanoparticles under the Influence of a Magnetic Field

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## Abstract

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## 1. Introduction

_{2}O

_{3}nanoparticles on the critical heat flux of R-123 and the flow boiling heat transfer. In their experimental work, they measured and compared the critical heat flux (CHF) of each plate with different mass fluxes. Their results showed that in the nanoparticle-coated tube, CHF was increased by up to 17% compared to the uncoated state. Rashidi et al. [32] studied entropy generation in a circular tube heat exchanger using nanofluids. The primary purpose of that paper was to compare the single-phase and two-phase modeling methods for forced displacement of water/TiO2 nanoparticles. The intended geometry was a horizontal tube with boundary conditions of a constant wall heat flux and a turbulent flow regime. In their results, the entropy production values for heat dissipation and turbulence for single-phase and mixed models were very close. However, as the volume fraction of nanoparticles increased, differences between the models appeared. It was found that the entropy production of turbulent nanofluid flow was mainly due to the component of frictional entropy production fluctuations. The importance of this component for higher amounts of nanoparticle volume fractions and Reynolds numbers has increased significantly.

^{2}and a temperature of 50 °C, the first nuclear boiling in the tube appeared, and the contact angles of water with the presence of 300 mg/L and 1200 mg/L of TDS material were 74° and 124°, respectively. The heat transfer was improved due to the presence of TDS materials.

^{2}, the production of hydrogen increased by 20 kg), as the Rankin cycle gave more power to the polymer electrolyte membrane (PEM) electrolyzer. The efficiency of the hybrid system increased by approximately 9% when the ambient temperature was enhanced from 5 to 40 °C. When higher nanofluid volume fractions were used, the power generated by the Rankin cycle and the hydrogen produced by the electrolyzer increased. The overall energy and exergy efficiency of the hybrid system at a solar radiation intensity of 600 W/m

^{2}with a nanoparticle volume fraction of zero were 1.55 and 1.4 times higher, respectively, than the nanoparticle volume fraction of 0.03.

_{3}O

_{4}-ethylene glycol nanoparticles was investigated. The finite element method was used to obtain the effects of the Fe

_{3}O

_{4}volume fraction, Reynolds number, and applied voltage. Nanofluid viscosity was considered to be a function of the electric field, according to the experimental data. Their results showed that the coulomb force helped the convection to increase the temperature gradient with increasing voltage. The greatest improvement in the Nusselt number was due to an electric field at a lower lip velocity.

_{3}O

_{4}) were equally exposed in the test areas. The increase in CHF through the nanoparticle deposition ranged from 0%–40%. CHF was enhanced with increasing mass flux, which resulted in lower output quality. It was also observed that increments of CHF in low mass fluxes in a slug flow were relatively lower than in high mass fluxes in a vapor clot. Bhatti et al. [47] investigated mass and energy transfer by applying a magnetic field on a two-phase peristaltic motion (suspension of particle fluids) across the planar channel. It was perceived that the velocity tended to increase due to the larger electric field and the electro-osmotic parameter, although the magnetic field and the two-phase volume fraction induced an apparent resistance to the current. The effect of an electric field and the electro-osmotic parameter showed inverse behavior on the temperature and the distribution of the two-phase flow concentration. Therefore, the chemical reaction parameter significantly reduced the concentration distribution.

## 2. Materials and Methods

## 3. Governing Equations

#### Nanofluid Properties

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | area cross-section (m^{2}) | z | coordinate system along the electric field (m) |

B | magnetic flux (T) | Greek Symbols | |

${C}_{P}$ | heat capacity (J/(kg K)) | Α | volume fraction (m^{2}/s) |

d | diameter (m) | $\rho $ | density (kg/m^{3}) |

EO | Eötvös number | ${\rm M}$ | viscosity (kg/(m s)) |

f′_{i} | friction coefficient at wall on phase i | σ | electric conductivity (S/m) |

f′_{I,i} | interfacial drag force coefficient on phase i | ${\tau}_{yy}$ | shear stress in boundary layer (Pa) |

F | force (N) | Subscripts | |

Fr | Froude number | base | base |

g | gravitational acceleration (m/s^{2}) | bf | base fluid |

G | mass velocity (kg/m^{2}s), $\dot{m}$/A | conv | convection |

h | heat transfer coefficient (watt/m^{2}K) | crit | critical |

${j}^{*}$ | superficial velocity (m/s) | D | diameter |

L | length (m) | f | fluid |

$\dot{m}$ | mass flow rate (kg/s) | g | gas phase |

m′ | mass flow rate between phases (kg/s) | i | species i |

P | pressure (Pa) | in | Inlet |

q_{r} | radiation heat flux (J/m^{2}s) | mass | mass |

q″ | wall heat transfer (J/m^{2}s) | max | maximum |

q_{i,j}″ | heat transfer between phases (J/m^{2}s) | mix | mixture |

T | temperature (K) | np | nanoparticle |

u | specific internal energy (J/kg) | out | outlet |

v | velocity (m/s) | rad | radiation |

w | external work applied on the volume (J/m^{3}) | RMS | root mean square |

We | Weber number | sat | saturation |

x | coordinate system along the magnetic field (m) | wall | wall |

y | coordinate system along the tube (m) |

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**Figure 1.**Schematic of the geometry investigated: vertical pipe with heat flux applied to the right side of the pipe.

**Figure 2.**Validation of numerical results with experimental data for the four modes stated in Table 1: (

**a**) case 1, (

**b**) case 2, (

**c**) case 3, and (

**d**) case 4.

**Figure 3.**Changes in the vapor volume fraction along the pipe length for the four modes stated in Table 1: (

**a**) case 1, (

**b**) case 2, (

**c**) case 3, and (

**d**) case 4.

**Figure 4.**Dimensional number changes of (

**a**) Froude and (

**b**) Eötvös along the channel length for the four different states shown in Table 1 under the influence of the magnetic field.

**Figure 5.**Variations in (

**a**) fluid cross-sectional area forces, (

**b**) fluid wall forces, and (

**c**) root mean squares of the force applied to the fluid cross-section along the channel length under the influence of different magnetic fields.

**Figure 6.**Variations in the (

**a**) mixture velocity, (

**b**) fluid velocity, (

**c**) speed of sound, and (

**d**) fluid superficial velocity along the tube length under the influence of different values of the magnetic field.

**Figure 7.**Variations in the (

**a**) Sauter mean diameter of the bubble, (

**b**) the bubble departure diameter, and (

**c**) the critical diameter of the tube along the channel length under the influence of different magnetic fields.

**Figure 8.**Variations in the (

**a**) liquid Reynolds number and (

**b**) the vapor Reynolds number along the tube under the influence of different values of the magnetic field.

**Figure 9.**Variations in the (

**a**) Weber number, (

**b**) bubble departure frequency, and (

**c**) square root of the ratio of the Froude number to the Weber number along the pipe under the influence of different values of the magnetic field (presented in Table 2).

**Figure 10.**(

**a**) Radiation heat flux variations and (

**b**) changes in the convection heat transfer coefficient along the tube length under the influence of different values of magnetic fields.

**Figure 11.**Variations in the (

**a**) volume fraction, (

**b**) base volume fraction, (

**c**) maximum volume fraction, and (

**d**) critical volume fraction along the tube length under the influence of different values of the magnetic field.

**Figure 12.**Changes in the density of the active nucleation site along the tube length under the influence of different values of the magnetic field.

Case | T_{sat} − T_{in} (°C) | V_{in} (m/s) | p_{out} (bar) | G (kg/m^{2} s) | q (kW/m^{2}) |
---|---|---|---|---|---|

1 | 14.9 | 0.164 | 1.37 | 156.15 | 286.68 |

2 | 22.5 | 0.433 | 1.5 | 411.70 | 705.50 |

3 | 19.7 | 0.292 | 1.23 | 283.1 | 478.5 |

4 | 23.5 | 0.303 | 1.25 | 288.7 | 598.3 |

Case | A | B | C | D | E | F | G | H | I |
---|---|---|---|---|---|---|---|---|---|

B(T) | 7 | 5 | 4 | 3.25 | 2.75 | 2.5 | 1.75 | 1 | 0.5 |

Properties | Density | Specific Heat Capacity |
---|---|---|

Nanoparticle | ${\rho}_{np}=3965\mathrm{kg}{\mathrm{m}}^{-3}$ | ${C}_{p,np}=0.795\mathrm{kJ}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ |

$\Delta \mathit{X}$ | Relative Error (%) |
---|---|

0.1 | 23.68 |

0.05 | 14.09 |

0.02 | 5.47 |

0.01 | 0.46 |

0.005 | 0.0 |

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## Share and Cite

**MDPI and ACS Style**

Abdollahzadeh Jamalabadi, M.Y.; Ghasemi, M.; Alamian, R.; Wongwises, S.; Afrand, M.; Shadloo, M.S.
Modeling of Subcooled Flow Boiling with Nanoparticles under the Influence of a Magnetic Field. *Symmetry* **2019**, *11*, 1275.
https://doi.org/10.3390/sym11101275

**AMA Style**

Abdollahzadeh Jamalabadi MY, Ghasemi M, Alamian R, Wongwises S, Afrand M, Shadloo MS.
Modeling of Subcooled Flow Boiling with Nanoparticles under the Influence of a Magnetic Field. *Symmetry*. 2019; 11(10):1275.
https://doi.org/10.3390/sym11101275

**Chicago/Turabian Style**

Abdollahzadeh Jamalabadi, Mohammad Yaghoub, Milad Ghasemi, Rezvan Alamian, Somchai Wongwises, Masoud Afrand, and Mostafa Safdari Shadloo.
2019. "Modeling of Subcooled Flow Boiling with Nanoparticles under the Influence of a Magnetic Field" *Symmetry* 11, no. 10: 1275.
https://doi.org/10.3390/sym11101275