# Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag

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## Abstract

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## 1. Introduction

## 2. Governing Equations

## 3. Weakly Nonlinear Analysis

## 4. Analysis of the Amplitude Equations

## 5. The Stability of Rolls

## 6. The Effect of Forchheimer Terms on Hexagonal Cells

## 7. Effect of the Forchheimer Terms on Stability

## 8. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic showing the difference between the solution curves for hexagons (continuous lines) and rolls (dashed lines). $A=0$ is a solution in both cases.

**Figure 2.**Schematics showing the solution curves for hexagonal cells for different values of the scaled Forchheimer parameter, $\gamma $.

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**MDPI and ACS Style**

Rees, D.A.S.; Magyari, E.
Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag. *Fluids* **2017**, *2*, 27.
https://doi.org/10.3390/fluids2020027

**AMA Style**

Rees DAS, Magyari E.
Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag. *Fluids*. 2017; 2(2):27.
https://doi.org/10.3390/fluids2020027

**Chicago/Turabian Style**

Rees, D. Andrew S., and Eugen Magyari.
2017. "Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag" *Fluids* 2, no. 2: 27.
https://doi.org/10.3390/fluids2020027