# Numerical Investigations on Magnetohydrodynamic Pump Based Microchannel Cooling System for Heat Dissipating Element

^{1}

^{2}

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## Abstract

**:**

_{2}-water and Al

_{2}O

_{3}-water nanofluids on heat transfer performance of MHD pump-based microchannel is evaluated. As the applied voltage increased from 0.05 V to 0.35 V at Hartmann number 1.41, the heat removal rate increased by 39.5%. The results reveal that for low Hartmann number, average Nusselt number is increasing function of applied voltage and Hartmann number. At the Hartmann number value of 3.74 and applied voltage value of 0.35 V, average Nusselt numbers were 12.3% and 15.1% higher for Cu-water nanofluid compared to TiO

_{2}-water and Al

_{2}O

_{3}-water nanofluids, respectively. The proposed magnetohydrodynamic microcooling system is effective without any moving part.

## 1. Introduction

_{2}-water and Al

_{2}O

_{3}-water, are considered, and their influence on heat transfer performance is compared. The comparative heat transfer performance and potentials of various nanofluids in MHD pump application for microchannel cooling have not been realized. This study provides a comprehensive understanding of MHD pump performance, heat transfer performance of MHD pump-based microchannel cooling systems, and the influence of various nanofluids on heat transfer performance.

## 2. Method

#### 2.1. Numerical Modeling

#### 2.2. Governing Equations and Boundary Conditions

_{2}-water, and Al

_{2}O

_{3}-water nanofluids. The base fluid for all the nanofluids is water. The boundary condition of opening at atmospheric pressure is applied at the coolant inlet and coolant outlet. The density of water is considered as 997.0 kg/m

^{3}at 25 °C and assumed as an incompressible fluid. The thermal conductivity of water is considered as 0.6069 W/m-K at 25 °C. The specific heat of water is considered as 4181.7 J/kg-K. The details about the boundary conditions and thermophysical properties of water and nanoparticles are presented in Table 2.

#### 2.3. Nanofluid Relations

_{2}-water nanofluid and compared the predictions using the Equation (6) within 0.54%. Therefore, in the current study, the density of various nanofluids with different volume fraction is calculated using Equation (6), where $\rho $ denotes density and$\varphi $ denotes volume fraction.

#### 2.4. Mesh Independency

^{4}elements, which is a coarse mesh, whereas mesh type 5 contains 1.45 × 10

^{6}elements, which is a finer mesh. As the mesh elements increased from 9.65 × 10

^{5}to 1.45 × 10

^{6}, the Lorentz force and average velocity varied only 0.008% and 0.166%, respectively. Considering the computational cost and accuracy of the numerical simulations, mesh type 4 with 9.65 × 10

^{5}elements, is selected for carrying out numerical simulations as shown in Table 3.

#### 2.5. Data Reduction

_{avg}). The heat transfer rate is evaluated as shown in Equation (15) [43].

_{h}represents the hydraulic diameter and k

_{f}represents the thermal conductivity of the fluid.

## 3. Results and Discussion

_{2}-water nanofluid and Al

_{2}O

_{3}-water nanofluid. The study provided an in-depth understanding of the MHD pump functioning and its application in micro-cooling systems.

#### 3.1. Validation

#### 3.2. Magnetohydrodynamic Pump (MHD) Performance

#### 3.3. MHD-Based Microchannel Cooling System

#### 3.4. Influence of Various Nanofluids

_{2}-water and Al

_{2}O

_{3}-water are considered with a volume fraction of 0.1%. For performance comparison, the volume fraction of nanoparticles in nanofluids is kept constant. To evaluate the thermal performance of MHD pumps with various nanofluids, the heat transfer rate, efficiency and Nusselt number variation are considered.

_{2}-water and Al

_{2}O

_{3}-water nanofluids. As previously noted, for a lower Hartmann number, the rate of change heat removal rate is large, whereas for higher Hartmann number, the rate of change of heat removal rate is small. The Cu-based nanofluid showed a better heat transfer rate owing to the high thermal conductivity of copper nanoparticles.

_{2}-water and Al

_{2}O

_{3}-water nanofluids. For lower Hartmann number, the rate of change efficiency is large, whereas for higher Hartmann number, the rate of change of efficiency is small. This is because the dominance of magnetic force increased as the Hartmann number increased. The Cu-based nanofluid shows better efficiency owing to high thermal conductivity of copper nanoparticles.

_{2}-water and Al

_{2}O

_{3}-water nanofluids. Interestingly, the Nusselt number for the TiO

_{2}based nanofluid and Al

_{2}O

_{3}based nanofluid are found to be close. The Cu-based nanofluid showed a better average Nusselt number owing to the high thermal conductivity of copper nanoparticles.

## 4. Conclusions

_{2}-water and Al

_{2}O

_{3}-water nanofluids on heat transfer performance of MHD pump-based microchannels is evaluated. At the Hartmann number value of 3.74 and applied voltage value of 0.35 V, average Nusselt numbers are 12.3% and 15.1% higher for Cu-water nanofluid compared to TiO

_{2}-water and Al

_{2}O

_{3}-water nanofluids, respectively. The MHD pump is more useful in cases where space and noise constraint are of particular interest. Especially in the microelectronics device cooling, the removal of heat is important and due to miniaturization, the MHD pump for cooling provides a promising option. The investigations provide an opportunity to further explore the application of MHD pumps in electronics cooling.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

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

$\overrightarrow{B}$ | magnetic field vector (T) |

B | magnitude of the magnetic field (T) |

C_{p} | specific heat at constant pressure (J/kg-K) |

D_{h} | hydraulic diameter (m) |

$\overrightarrow{E}$ | electric field vector (V/m) |

$\overrightarrow{F}$ | electromagnetic force (N) |

h_{avg} | average heat transfer coefficient (W/m^{2}-K) |

Ha | Hartmann number |

$\overrightarrow{J}$ | current density (A/m^{2}) |

L | characteristic length (mm) |

MHD | magnetohydrodynamic |

${\mathit{Nu}}_{\mathit{avg}}$ | average Nusselt number |

P | pressure (Pa) |

Q | heat transfer rate (W) |

T | temperature (°C/K) |

t | time (s) |

$\overrightarrow{V}$ | velocity (m/s) |

Greek symbols | |

$\nabla $ | gradient operator |

α | thermal diffusivity (m^{2}/s) |

σ | electrical conductivity (S/m) |

ρ | density (kg/m^{3}) |

ν | kinematic fluid viscosity (m^{2}/s) |

μ | dynamic viscosity (Pa-s) |

k | thermal conductivity (W/m-K) |

$\varphi $ | volume fraction (%) |

Subscripts | |

avg | average |

bulk | bulk property |

conv | convective heat transfer |

f | fluid |

in | inlet |

LMTD | logarithmic mean temperature difference |

n | nanoparticle |

nf | nanofluid |

out | outlet |

wall | wall |

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**Figure 1.**Schematic view of the magnetohydrodynamic (MHD) pump microchannel cooling system for a heat dissipating element.

**Figure 3.**Mesh details (

**a**) Mesh independency test (

**b**) Meshing of magnetohydrodynamic (MHD) pump microchannel cooling system for heat dissipating element.

**Figure 5.**Current density and velocity (

**a**) Normal current density variation for different applied voltage and different Hartmann number (

**b**) Induced current density distribution (

**c**) Variation of average velocity with current density.

**Figure 6.**Magnetic flux density and magnetic field (

**a**) Magnetic flux density variation with dimensionless width for different applied voltages and different Hartmann number (

**b**) Magnetic field distribution at the center of the MHD pump in the XY-plane.

**Figure 7.**Volumetric Lorentz force variation for different applied voltages and different Hartmann number.

**Figure 8.**Shear stress and Pressure (

**a**) Shear stress variation with dimensionless width for different applied voltages and different Hartmann numbers (

**b**) Pressure contours for the flow cross-sectional area at the center of the pump in the YZ-plane

**Figure 18.**Variation of average Nusselt number with various nanofluids at different Hartmann numbers.

Item | Parameter | Values |
---|---|---|

MHD pump | Length × Height (mm) | 80 × 10 |

Microchannel | Length × Width × Height (mm) | 30 × 30 × 10 |

Number of channel slots (ea) | 4 | |

Single channel | Width × Height (mm) | 4 × 7 |

Magnet radius | Radius × Height (mm) | 15 × 7.5 |

Heat dissipating element | Length × Width × Height (mm) | 10 × 10 × 1 |

Specifications | Values | |||
---|---|---|---|---|

Boundary conditions | ||||

Inlet coolant temperature (°C) | 25 | |||

Applied Voltage (V) | 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35 | |||

Volumetric heat generation rate (W/m^{3}) | 1.0 × 10^{8} | |||

Coolant inlet | Opening at atmospheric pressure | |||

Coolant outlet | Opening at atmospheric pressure | |||

Thermophysical properties | ||||

Water | Cu | TiO_{2} [32] | Al_{2}O_{3} [33] | |

Density (kg/m^{3}) | 997 | 8954 | 4260 | 3970 |

Thermal conductivity (W/m-K) | 0.6069 | 400 | 8.9 | 25 |

Specific heat (J/kg-K) | 4181.7 | 383 | 686.2 | 765 |

Mesh Type | Number of Elements |
---|---|

Type 1 | 5.43 × 10^{4} |

Type 2 | 1.56 × 10^{5} |

Type 3 | 6.09 × 10^{5} |

Type 4 | 9.65 × 10^{5} |

Type 5 | 1.45 × 10^{6} |

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**MDPI and ACS Style**

Seo, J.-H.; Patil, M.S.; Panchal, S.; Lee, M.-Y.
Numerical Investigations on Magnetohydrodynamic Pump Based Microchannel Cooling System for Heat Dissipating Element. *Symmetry* **2020**, *12*, 1713.
https://doi.org/10.3390/sym12101713

**AMA Style**

Seo J-H, Patil MS, Panchal S, Lee M-Y.
Numerical Investigations on Magnetohydrodynamic Pump Based Microchannel Cooling System for Heat Dissipating Element. *Symmetry*. 2020; 12(10):1713.
https://doi.org/10.3390/sym12101713

**Chicago/Turabian Style**

Seo, Jae-Hyeong, Mahesh Suresh Patil, Satyam Panchal, and Moo-Yeon Lee.
2020. "Numerical Investigations on Magnetohydrodynamic Pump Based Microchannel Cooling System for Heat Dissipating Element" *Symmetry* 12, no. 10: 1713.
https://doi.org/10.3390/sym12101713