# Study of Two-Phase Newtonian Nanofluid Flow Hybrid with Hafnium Particles under the Effects of Slip

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## Abstract

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## 1. Introduction

## 2. Mathematical Model

#### 2.1. Geometries

#### 2.2. Mathematical Model

#### 2.3. Boundary Conditions

## 3. Results

## 4. Discussion

## 5. Conclusions

- The velocity decreases against Hartmann number $M$ and Helmholtz–Smoluchowski ${U}_{HS}$ in all cases.
- The velocity of particle phase decreases against the slip parameter, ${\beta}_{1}$ in geometry I and geometry II whereas it increases in geometry III.
- The velocity increases against $m$, in the three geometries for both particles and fluid phases.
- Inclined behavior of velocity is observed for both phases in three geometries against $m$.
- In the case of Hartmann number $M$, Helmholtz–Smoluchowski ${U}_{HS}$, and slip parameter ${\beta}_{1}$, the graphs of streamlines are the same for all three geometries. However, the reduction of the streamlines for electro-osmotic parameter $m$, is observed. This behavior is due to the curve-like structure of the channel.

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Ellahi, R.; Hussain, F.; Asad Abbas, S.; Sarafraz, M.M.; Goodarzi, M.; Shadloo, M.S. Study of Two-Phase Newtonian Nanofluid Flow Hybrid with Hafnium Particles under the Effects of Slip. *Inventions* **2020**, *5*, 6.
https://doi.org/10.3390/inventions5010006

**AMA Style**

Ellahi R, Hussain F, Asad Abbas S, Sarafraz MM, Goodarzi M, Shadloo MS. Study of Two-Phase Newtonian Nanofluid Flow Hybrid with Hafnium Particles under the Effects of Slip. *Inventions*. 2020; 5(1):6.
https://doi.org/10.3390/inventions5010006

**Chicago/Turabian Style**

Ellahi, Rahmat, Farooq Hussain, Syed Asad Abbas, Mohammad Mohsen Sarafraz, Marjan Goodarzi, and Mostafa Safdari Shadloo. 2020. "Study of Two-Phase Newtonian Nanofluid Flow Hybrid with Hafnium Particles under the Effects of Slip" *Inventions* 5, no. 1: 6.
https://doi.org/10.3390/inventions5010006