# Magnetohydrodynamic and Nanoparticle Effects in Vertical Annular Subcooled Flow Boiling

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. Geometry and Physical Condition

_{in}(beneath the immersion saturation) and constant inlet normal speed (283.1 kg/m

^{2}s) and there is an overlap of 3.64 cm

^{2}despite the fact that its weight at the exit pressure is fixed as given in Table 1. The annular entry of liquid stream (inward cylinder breadth 12.7 mm, external cylinder width, 25.4 mm, and 114.6 cm length is somewhat homogeneously warmed between the height of 34 cm and 64.6 cm. The magnetic conditions presented in Table 2 are utilized to calculate the force liquid stream in opposition to the vertical motion. To simplify the calculations the issue is broken up in the current examination by the 1D perspective and the pressure-driven measurement (0.123 cm) is not exactly longitudinal size (1.146 cm). No channel surfaces have warmth scattering properties (adiabatic). In CFD, the usual delta speed is recommended and the exit pressure is zero. To force the fluid in a vertical direction, the liquids are guided either through a weight slope (Pin and Pout required) or through a gulf speed with a surge circumstance, or, intermittently, in an elective region. This is common standard where weight angles are concerned.

## 3. Governing Equations

## 4. Result and Discussion

## 5. Conclusions and Recommendation

## Funding

## Conflicts of Interest

## Nomenclature

A | area cross-section (m^{2}) |

B | magnetic flux (T) |

C_{p} | heat capacity, J/(kg_K) |

f′_{i} | friction coefficient at wall on phase i |

f′_{I,i} | interfacial drag force coefficient on phase i |

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

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

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

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

P | pressure (Pa) |

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

q″ | wall heat transfer (J/m^{2}s) |

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

T | temperature (K) |

u | specific internal energy (J/kg) |

v | velocity (m/s) |

W | external work applied on the volume (J/m^{3}) |

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

y | coordinate system along the tube (m) |

z | coordinate system along the electric field (m) |

Greek symbols | |

α | void fraction (m^{2}/s) |

ρ | density (kg/m^{3}) |

μ | viscosity (kg/(m s)) |

σ | electric conductivity (S/m) |

${\tau}_{yy}$ | shear stress in boundary layer (Pa), |

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**Table 1.**Subcooling and physical condition of the experimental rig presented in [6].

Parameter | Value | Unit |
---|---|---|

T_{sat} − T_{in} | 19.7 | (°C) |

q | 478.5 | (kW/m^{2}) |

V_{in} | 0.292 | (m/s) |

p_{outlet} | 1.23 | (bar) |

G | 283.1 | (kg/m^{2}s) |

Case | B (T) |
---|---|

A | 3.16 |

B | 3 |

C | 2.83 |

D | 2.65 |

E | 2.45 |

F | 2 |

G | 1.73 |

H | 1.41 |

I | 1 |

Conservation of | Equation |
---|---|

mass | $\frac{\partial}{\partial t}({\alpha}_{i}{\rho}_{i})+\frac{\partial}{\partial y}({\alpha}_{i}{\rho}_{i}{\upsilon}_{i})={\mathsf{\Gamma}}_{i}=\frac{{m}_{i}^{\prime}}{A},$ |

momentum | $\begin{array}{l}\frac{\partial}{\partial t}({\alpha}_{i}{\rho}_{i}{\upsilon}_{i})+\frac{\partial}{\partial y}({\alpha}_{i}{\rho}_{i}{\upsilon}_{i}^{2})=\frac{{m}_{i}^{\prime}}{A}{\upsilon}_{I}-{\alpha}_{i}{\rho}_{i}g-\frac{\partial}{\partial y}({\alpha}_{i}P)\\ +\frac{\partial}{\partial y}({\alpha}_{i}{\tau}_{i.yy})-{f}_{I,i}^{\prime}({\upsilon}_{i}-{\upsilon}_{j})-{f}_{i}^{\prime}{\upsilon}_{i}-{\sigma}_{i}{\upsilon}_{i}{B}^{2},\end{array}$ |

energy | $\begin{array}{l}\frac{\partial}{\partial t}\left({\alpha}_{i}{\rho}_{i}\left({u}_{i}+\frac{{\upsilon}_{i}^{2}}{2}\right)\right)+\frac{\partial}{\partial y}\left({\alpha}_{i}{\rho}_{i}\left({u}_{i}+\frac{{\upsilon}_{i}^{2}}{2}\right){\upsilon}_{i}\right)=\\ \frac{{m}_{i}^{\prime}}{A}\left({u}_{I}+\frac{{\upsilon}_{I}^{2}}{2}\right)-{\alpha}_{i}{\rho}_{i}{\upsilon}_{i}g-\frac{\partial}{\partial y}({\alpha}_{i}P{\upsilon}_{i})+\\ \frac{\partial}{\partial y}({\alpha}_{i}{\tau}_{i,yy}{\upsilon}_{i})-{q}_{i,j}^{\u2034}+{W}_{i}+{q}_{i}^{\u2033}+{q}_{r},\end{array}$ |

Material Property | Nanofluid | Nanoparticle |
---|---|---|

density | ${\rho}_{nf}=(1-\phi ){\rho}_{bf}+\phi {\rho}_{np}$ | ${\rho}_{np}=3965\text{}\mathrm{kg}\text{}{\mathrm{m}}^{-3}$ |

viscosity | ${\mu}_{nf}={\mu}_{bf}(1+2.5\phi )$ | - |

specific heat capacity | ${C}_{p,nf}=(1-\phi ){C}_{p,bf}+\phi .{C}_{p,np}$ | ${C}_{p,np}=0.795\text{}\mathrm{kJ}\text{}{\mathrm{kg}}^{-1}\text{}{\mathrm{K}}^{-1}$ |

ΔX | Δr | % |
---|---|---|

0.1 | 0.001 | 23.68 |

0.05 | 0.001 | 14.09 |

0.02 | 0.001 | 5.47 |

0.01 | 0.0005 | 0.46 |

0.005 | 0.0005 | 0.0 |

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**MDPI and ACS Style**

Abdollahzadeh Jamalabadi, M.Y.
Magnetohydrodynamic and Nanoparticle Effects in Vertical Annular Subcooled Flow Boiling. *Symmetry* **2019**, *11*, 810.
https://doi.org/10.3390/sym11060810

**AMA Style**

Abdollahzadeh Jamalabadi MY.
Magnetohydrodynamic and Nanoparticle Effects in Vertical Annular Subcooled Flow Boiling. *Symmetry*. 2019; 11(6):810.
https://doi.org/10.3390/sym11060810

**Chicago/Turabian Style**

Abdollahzadeh Jamalabadi, Mohammad Yaghoub.
2019. "Magnetohydrodynamic and Nanoparticle Effects in Vertical Annular Subcooled Flow Boiling" *Symmetry* 11, no. 6: 810.
https://doi.org/10.3390/sym11060810