Double-Diffusive Convection in Bidispersive Porous Medium with Coriolis Effect
Abstract
:1. Introduction
2. Mathematical Formulation
3. Linear Stability Analysis
3.1. Stationary Convection:
3.2. Oscillatory Convection
4. Discussion
5. Conclusions
- and increase as the Taylor number increases, indicating that has a stabilizing effect on the onset of convection.
- and are increasing functions of and decreasing functions of .
- S does not show any effect on , as is independent of S.
- There exists a threshold for the solute Rayleigh number such that, if , then the convection arises via an oscillatory mode.
- The oscillatory convection sets in and, as soon as the value of S attains a critical value (∈(0.6, 0.7)), the convection ceases to be oscillatory, and stationary convection occurs as the first bifurcation.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Acceleration coefficient | |
Permeability in macro pores | |
Permeability in micro pores | |
Interaction coefficient | |
Fluid viscosity | |
g | Gravity |
Coefficient of thermal expansion | |
Density coefficient for salinity | |
Heat capacity ratio | |
Macro porosity | |
Micro porosity | |
Density | |
Thermal conductivity of the solid | |
Thermal conductivity of the fluid | |
Product of density and specific heat in the solid skeleton | |
Product of density and specific heat in the pores | |
Reference density | |
Thermal conductivity | |
Pressure in macro pores | |
Pressure in micro pores | |
T | Temperature |
C | Salt concentration field |
R | Rayleigh number |
Solutal Rayleigh number | |
Taylor number | |
Lewis number | |
S | Soret number |
d | Length |
Superscripts | |
′ | Perturbated quantity |
c | Critical value |
Subscripts | |
b | Base state |
0 | Reference valve |
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Rc | Stationary R | Stationary a | Oscillatory R | Oscillatory a | Instability |
---|---|---|---|---|---|
0 | 61.6464 | 3.9578 | 62.7612 | 3.9578 | Stationary |
1 | 62.1464 | 3.9578 | 62.7793 | 3.9578 | Stationary |
2 | 62.6464 | 3.9578 | 62.7973 | 3.9578 | Stationary |
3 | 63.1464 | 3.9578 | 62.8154 | 3.9578 | Oscillatory |
4 | 63.6464 | 3.9578 | 62.8335 | 3.9578 | Oscillatory |
5 | 64.1464 | 3.9578 | 62.8516 | 3.9578 | Oscillatory |
S | Stationary R | Stationary a | Oscillatory R | Oscillatory a | Instability |
---|---|---|---|---|---|
0.1 | 1018.7706 | 8.2527 | 992.2842 | 8.2527 | Oscillatory |
0.2 | 1013.7706 | 8.2527 | 992.2842 | 8.2527 | Oscillatory |
0.3 | 1008.7706 | 8.2527 | 992.2842 | 8.2527 | Oscillatory |
0.4 | 1003.7706 | 8.2527 | 992.2842 | 8.2527 | Oscillatory |
0.5 | 998.7706 | 8.2527 | 992.2842 | 8.2527 | Oscillatory |
0.6 | 993.7706 | 8.2527 | 992.2842 | 8.2527 | Oscillatory |
0.7 | 988.7706 | 8.2527 | 992.2842 | 8.2527 | Stationary |
0.8 | 983.7706 | 8.2527 | 992.2842 | 8.2527 | Stationary |
0.9 | 978.7706 | 8.2527 | 992.2842 | 8.2527 | Stationary |
Stationary R | Stationary a | Oscillatory R | Oscillatory a | Instability | |
---|---|---|---|---|---|
1 | 983.7706 | 8.2540 | 992.2842 | 8.2540 | Stationary |
2 | 691.3454 | 6.4421 | 694.5709 | 6.4421 | Stationary |
3 | 588.8136 | 5.5171 | 590.1849 | 5.5171 | Stationary |
4 | 546.4455 | 4.9469 | 547.0506 | 4.9469 | Stationary |
5 | 531.2631 | 4.5668 | 531.5936 | 4.5668 | Stationary |
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Ramchandraiah, C.; Kishan, N.; Reddy, G.S.K.; Paidipati, K.K.; Chesneau, C. Double-Diffusive Convection in Bidispersive Porous Medium with Coriolis Effect. Math. Comput. Appl. 2022, 27, 56. https://doi.org/10.3390/mca27040056
Ramchandraiah C, Kishan N, Reddy GSK, Paidipati KK, Chesneau C. Double-Diffusive Convection in Bidispersive Porous Medium with Coriolis Effect. Mathematical and Computational Applications. 2022; 27(4):56. https://doi.org/10.3390/mca27040056
Chicago/Turabian StyleRamchandraiah, Chirnam, Naikoti Kishan, Gundlapally Shiva Kumar Reddy, Kiran Kumar Paidipati, and Christophe Chesneau. 2022. "Double-Diffusive Convection in Bidispersive Porous Medium with Coriolis Effect" Mathematical and Computational Applications 27, no. 4: 56. https://doi.org/10.3390/mca27040056