The Effect of the Vadasz Number on the Onset of Thermal Convection in Rotating Bidispersive Porous Media
Abstract
:1. Introduction
2. Preliminaries
3. Linear Instability
3.1. Steady Convection
3.2. Oscillatory Convection
4. Numerical Results
- (1)
- analyze the asymptotic behaviour of with respect to and J; and,
- (2)
- compare and to establish whether the convection arises through a steady state (stationary convection) or via an oscillatory state (oscillatory convection).
- (i)
- if or if , then convection can only arise via a steady state;
- (ii)
- if , convection can only arise via an oscillatory state.
5. Conclusions
- does not depend on the acceleration coefficient, i.e., inertial effects do not affect ;
- increases with the Taylor number, i.e., has—as one is expected—a stabilizing effect on the onset of steady convection; and,
- is a decreasing function of J and there exists a threshold for the inertia coefficient, such that exists and convection arises via an oscillatory state; and,
- is an increasing functions of and there exists a threshold for the Taylor number, such that, for , the convection arises via an oscillatory state.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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J | ||
---|---|---|
0 | ∄ | ∄ |
0.25 | ∄ | ∄ |
0.31 | ∄ | ∄ |
0.32 | 15.3410 | 51.9150 |
0.35 | 14.7812 | 59.7010 |
0.4 | 14.0459 | 49.0951 |
0.7 | 11.9923 | 44.4657 |
1 | 11.2881 | 42.7649 |
5 | 10.3196 | 40.0417 |
10 | 10.2433 | 39.7591 |
7 | 15.3031 | ∄ | 45.5293 | ∄ |
7.07 | 15.3234 | 12.5623 | 45.6906 | 46.0730 |
7.1 | 15.3320 | 12.5674 | 45.7596 | 46.0815 |
7.2 | 15.3603 | 12.5844 | 45.9885 | 46.1098 |
7.26 | 15.3769 | 12.5946 | 46.1253 | 46.1268 |
7.27 | 15.2796 | 12.5963 | 46.1480 | 46.1296 |
7.3 | 15.3878 | 12.6014 | 46.2162 | 46.1381 |
7.5 | 15.4410 | 12.6353 | 46.6677 | 46.1945 |
10 | 15.919 | 13.0503 | 51.9256 | 46.8876 |
20 | 16.1538 | 14.5717 | 67.9956 | 49.4695 |
50 | 15.2776 | 18.2109 | 95.5668 | 55.9909 |
J | CONVECTION | ||||||||
---|---|---|---|---|---|---|---|---|---|
10 | 7 | 2 | 30 | 1.3 | 22.74 | 15.78 | 198.64 | 202.89 | STEADY |
10 | 7 | 2 | 100 | 1.3 | 37.07 | 21.08 | 437.66 | 289.54 | OSCILLATORY |
0.8 | 1.5 | 0.2 | 300 | 10 | 19.25 | 13.92 | 193.25 | 63.84 | OSCILLATORY |
0.8 | 0.5 | 0.2 | 100 | 1 | 21.27 | ∄ | 120.07 | ∄ | STEADY |
0.8 | 0.5 | 0.2 | 100 | 1.5 | 21.27 | 17.10 | 120.07 | 44.72 | OSCILLATORY |
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Capone, F.; De Luca, R. The Effect of the Vadasz Number on the Onset of Thermal Convection in Rotating Bidispersive Porous Media. Fluids 2020, 5, 173. https://doi.org/10.3390/fluids5040173
Capone F, De Luca R. The Effect of the Vadasz Number on the Onset of Thermal Convection in Rotating Bidispersive Porous Media. Fluids. 2020; 5(4):173. https://doi.org/10.3390/fluids5040173
Chicago/Turabian StyleCapone, Florinda, and Roberta De Luca. 2020. "The Effect of the Vadasz Number on the Onset of Thermal Convection in Rotating Bidispersive Porous Media" Fluids 5, no. 4: 173. https://doi.org/10.3390/fluids5040173