# Thermal Convection in a Rotating Anisotropic Fluid Saturated Darcy Porous Medium

## Abstract

**:**

## 1. Introduction

## 2. Governing Equations

## 3. The Principle of Exchange of Stabilities Ignoring Inertia Term

## 4. Linear Instability Analysis

## 5. Nonlinear Stability Analysis

## 6. Numerical Results

## 7. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Critical Rayleigh number ${R}_{c}$ as function of $\xi $, for ${\tilde{T}}^{2}=5$ increasing to ${\tilde{T}}^{2}=25$.

**Figure 2.**Critical wave number ${a}_{c}$ as function of $\xi $, for ${\tilde{T}}^{2}=5$ increasing to ${\tilde{T}}^{2}=25$.

**Table 1.**Critical values of Rayleigh number ${R}_{c}$, vs. $\xi $, for ${\tilde{T}}^{2}=5,10,15,20,25$.

${R}_{c}$ | |||||||
---|---|---|---|---|---|---|---|

$\mathit{\xi}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{0}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{5}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{10}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{15}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{20}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{25}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{100}$ |

1 | 39.478 | 117.438 | 183.903 | 246.740 | 307.588 | 367.130 | 1205.076 |

2 | 57.524 | 147.335 | 220.890 | 289.315 | 354.926 | 418.690 | 1297.116 |

3 | 73.668 | 172.573 | 251.568 | 324.280 | 393.546 | 460.550 | 1370.037 |

4 | 88.826 | 195.398 | 278.979 | 355.306 | 427.653 | 497.389 | 1433.062 |

5 | 103.356 | 216.682 | 304.304 | 383.815 | 458.876 | 531.019 | 1489.762 |

6 | 117.438 | 236.871 | 328.145 | 410.535 | 488.051 | 562.370 | 1541.969 |

7 | 131.182 | 256.230 | 350.864 | 435.901 | 515.674 | 591.993 | 1590.772 |

8 | 144.657 | 274.932 | 372.693 | 460.194 | 542.068 | 620.249 | 1636.881 |

9 | 157.914 | 293.097 | 393.795 | 483.611 | 567.457 | 647.388 | 1680.786 |

10 | 170.987 | 310.813 | 414.288 | 506.293 | 592.006 | 673.591 | 1722.848 |

**Table 2.**Critical values of wave number ${a}_{c}$, vs. $\xi $, for ${\tilde{T}}^{2}=0,5,10,15,20,25,100$.

${a}_{c}$ | |||||||
---|---|---|---|---|---|---|---|

$\mathit{\xi}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{0}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{5}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{10}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{15}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{20}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{25}$ | ${\tilde{\mathit{T}}}^{\mathbf{2}}=\mathbf{100}$ |

1 | 3.142 | 4.917 | 5.721 | 6.283 | 6.725 | 7.094 | 9.959 |

2 | 2.642 | 4.135 | 4.811 | 5.284 | 5.655 | 5.965 | 8.375 |

3 | 2.387 | 3.736 | 4.347 | 4.774 | 5.110 | 5.390 | 7.567 |

4 | 2.221 | 3.477 | 4.046 | 4.443 | 4.755 | 5.016 | 7.042 |

5 | 2.101 | 3.288 | 3.826 | 4.202 | 4.497 | 4.744 | 6.660 |

6 | 2.007 | 3.142 | 3.656 | 4.015 | 4.297 | 4.533 | 6.363 |

7 | 1.931 | 3.023 | 3.517 | 3.863 | 4.135 | 4.361 | 6.123 |

8 | 1.868 | 2.924 | 3.402 | 3.736 | 3.999 | 4.218 | 5.922 |

9 | 1.814 | 2.839 | 3.303 | 3.628 | 3.883 | 4.096 | 5.750 |

10 | 1.767 | 2.765 | 3.217 | 3.533 | 3.782 | 3.989 | 5.601 |

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Haddad, S.
Thermal Convection in a Rotating Anisotropic Fluid Saturated Darcy Porous Medium. *Fluids* **2017**, *2*, 44.
https://doi.org/10.3390/fluids2030044

**AMA Style**

Haddad S.
Thermal Convection in a Rotating Anisotropic Fluid Saturated Darcy Porous Medium. *Fluids*. 2017; 2(3):44.
https://doi.org/10.3390/fluids2030044

**Chicago/Turabian Style**

Haddad, Shatha.
2017. "Thermal Convection in a Rotating Anisotropic Fluid Saturated Darcy Porous Medium" *Fluids* 2, no. 3: 44.
https://doi.org/10.3390/fluids2030044