# Instability of Vertical Throughflows in Porous Media under the Action of a Magnetic Field

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

## 3. Instability Analysis Via Normal Modes

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Stabilizing effect of the vertical constant throughflow when $\{{\tilde{P}}_{m}=1,Le=0.3,\omega =0.5,{\tilde{Q}}^{2}=10,{R}_{C}=10\}$.

**Left**: behaviour of ${R}_{S}$ versus $Pe$;

**Right**: behaviour of ${R}_{O}$ versus $Pe$.

**Table 1.**Onset of steady or oscillatory instability for some particular values of ${\tilde{P}}_{m},Le,\omega ,{\tilde{Q}}^{2},Pe,{R}_{C}$.

${\tilde{\mathit{P}}}_{\mathit{m}}$ | $\mathit{Le}$ | $\mathit{\omega}$ | ${\tilde{\mathit{Q}}}^{2}$ | $\mathit{Pe}$ | ${\mathit{R}}_{\mathit{C}}$ | ${\mathit{R}}_{\mathit{S}}$ | ${\mathit{R}}_{\mathit{O}}$ | Instability |
---|---|---|---|---|---|---|---|---|

0.5 | 1 | 0.2 | 10 | 0.5 | 50 | 235.067 | − | Steady |

1 | 1.5 | 0.2 | 0.3 | 0.2 | 50 | 95.1889 | 17,107.7 | Steady |

2.5 | 2 | 0.5 | 0.001 | 0.4 | 50 | 89.06 | 47.2763 | Oscillatory |

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**MDPI and ACS Style**

Capone, F.; De Luca, R.; Gentile, M.
Instability of Vertical Throughflows in Porous Media under the Action of a Magnetic Field. *Fluids* **2019**, *4*, 191.
https://doi.org/10.3390/fluids4040191

**AMA Style**

Capone F, De Luca R, Gentile M.
Instability of Vertical Throughflows in Porous Media under the Action of a Magnetic Field. *Fluids*. 2019; 4(4):191.
https://doi.org/10.3390/fluids4040191

**Chicago/Turabian Style**

Capone, Florinda, Roberta De Luca, and Maurizio Gentile.
2019. "Instability of Vertical Throughflows in Porous Media under the Action of a Magnetic Field" *Fluids* 4, no. 4: 191.
https://doi.org/10.3390/fluids4040191