Stability and convection in compressible partially ionized plasma layers: nonlinear and linear analysis
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Vishal Chandel
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Sunil
und
Reeta Devi
Abstract
The thermal convection of compressible, partially ionized plasma has been investigated using nonlinear and linear analyses across three boundary configurations. Nonlinear analysis was carried out via the energy method, while linear analysis was assessed using the normal mode method. For free-free boundaries, exact solutions were obtained, whereas, for rigid-rigid and rigid-free boundaries, the higher-order Galerkin-weighted residual method was employed for numerical results. The critical Rayleigh numbers for both analyses coincide, indicating global stability and confirming the absence of subcritical regions. The impact of collisional frequency on energy decay was quantified, revealing a significant effect on the decay rate, although it does not affect the Rayleigh number. The principle of exchange of stabilities was confirmed in the linear analysis. Compressibility delays the onset of convection. The critical Rayleigh numbers were computed as 986.267, 2,561.64, and 1,650.97 for the free–free, rigid–rigid, and rigid–free cases, respectively, demonstrating that plasma confined between rigid–rigid surfaces exhibits the highest thermal stability.
Acknowledgments
The authors wish to express their sincere gratitude to the esteemed editorial board and reviewers for their invaluable feedback and insightful recommendations. Their contributions have greatly enhanced the quality and depth of our work.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: None declared.
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Data availability: Not applicable.
References
[1] R. C. Sharma and Sunil, “Thermal instability of a compressible finite Larmor radius, Hall plasma in porous medium,” Phys. Plasmas, vol. 2, no. 6, pp. 1886–1892, 1995. https://doi.org/10.1063/1.871275.Suche in Google Scholar
[2] B. Straughan, The Energy Method, Stability, and Nonlinear Convection, New York, Springer-Verlag, 2004.10.1007/978-0-387-21740-6Suche in Google Scholar
[3] Sunil and A. Mahajan, “A nonlinear stability analysis for magnetized ferrofluid heated from below,” Proc. R. Soc. A, vol. 464, no. 2089, pp. 83–98, 2008. https://doi.org/10.1098/rspa.2007.1906.Suche in Google Scholar
[4] D. Yadav, R. Bhargava, and G. S. Agrawal, “Thermal instability in a nanofluid layer with a vertical magnetic field,” J. Eng. Math., vol. 80, no. 1, pp. 147–164, 2013. https://doi.org/10.1007/s10665-012-9598-1.Suche in Google Scholar
[5] A. Thakur, S. Kumar, and R. Devi, “A nonlinear stability analysis for magnetized ferrofluid heated from below in the presence of couple stresses for combination of different bounding surfaces,” Numer. Heat Transfer, Part B, pp. 1–17, 2023. https://doi.org/10.1080/10407790.2023.2275728.Suche in Google Scholar
[6] A. Thakur, Sunil, and R. Devi, “The effect of couple stresses on stability analysis of magnetized ferrofluid saturating a porous medium heated from below,” J. Porous Media, vol. 27, no. 5, pp. 85–106, 2024. https://doi.org/10.1615/jpormedia.2023050054.Suche in Google Scholar
[7] A. Thakur, S. Kumar, and R. Devi, “The effect of rotation on ferroconvection in the presence of couple stress forces in porous medium: a nonlinear analysis,” Eur. Phys. J. Plus, vol. 139, no. 3, p. 236, 2024. https://doi.org/10.1140/epjp/s13360-024-05048-8.Suche in Google Scholar
[8] Sunil and P. Sharma, “Stability analysis of thermosolutal convection in a rotating Navier–Stokes–Voigt fluid,” Z. Naturforsch. A, vol. 79, no. 7, pp. 689–702, 2024. https://doi.org/10.1515/zna-2023-0284.Suche in Google Scholar
[9] V. Tripathi, B. M. Shankar, A. Mahajan, and I. S. Shivakumara, “Global nonlinear stability of bidispersive porous convection with throughflow and depth-dependent viscosity,” Phys. Fluids, vol. 36, no. 1, 2024, Art. no. 014110. https://doi.org/10.1063/5.0174734.Suche in Google Scholar
[10] M. Gentile and B. Straughan, “Thermal convection with a Cattaneo heat flux model,” Proc. R. Soc. A, vol. 480, no. 2282, 2024, Art. no. 20230771. https://doi.org/10.1098/rspa.2023.0771.Suche in Google Scholar
[11] M. Iqbal, N. S. Khan, W. Khan, S. B. H. Hassine, S. A. Alhabeeb, and H. A. E. W. Khalifa, “Partially ionized bioconvection Eyring–Powell nanofluid flow with gyrotactic microorganisms in thermal system,” Therm. Sci. Eng. Prog., vol. 47, 2024, Art. no. 102283. https://doi.org/10.1016/j.tsep.2023.102283.Suche in Google Scholar
[12] A. Bansal and O. P. Suthar, “Temperature modulation effects on chaos and heat transfer in Darcy–Bénard convection using a local thermal non-equilibrium model,” Nonlinear Dyn., vol. 112, no. 18, pp. 16475–16493, 2024. https://doi.org/10.1007/s11071-024-09869-1.Suche in Google Scholar
[13] A. Mahajan and M. Raj, “The impact of internal heating on natural convection in a rectangular porous container,” Chin. J. Phys., vol. 90, pp. 651–663, 2024. https://doi.org/10.1016/j.cjph.2024.05.049.Suche in Google Scholar
[14] R. Soler and J. L. Ballester, “Theory of fluid instabilities in partially ionized plasmas: an overview,” Front. Astron. Space Sci., vol. 9, 2022, Art. no. 789083. https://doi.org/10.3389/fspas.2022.789083.Suche in Google Scholar
[15] H. Alfvén, On the Origin of the Solar System, Oxford, Clarendon Press, 1954.Suche in Google Scholar
[16] H. K. Hans, “Larmor radius and collisional effects on the combined Taylor and Kelvin instabilities in a composite medium,” Nucl. Fusion, vol. 8, no. 2, pp. 89–92, 1968. https://doi.org/10.1088/0029-5515/8/2/002.Suche in Google Scholar
[17] R. C. Sharma, “Finite larmor radius and Hall effects on thermal instability of a rotating plasma,” Phys. Fluids, vol. 15, no. 10, pp. 1822–1826, 1972. https://doi.org/10.1063/1.1693781.Suche in Google Scholar
[18] R. Sharma, “Thermal hydromagnetic instability of a partially ionized medium,” Physica B+C, vol. 81, no. 1, pp. 199–204, 1976. https://doi.org/10.1016/0378-4363(76)90259-x.Suche in Google Scholar
[19] N. Ogbonna and P. K. Bhatia, “Effect of magnetic resistivity on the stability of a partially ionized compressible Hall plasma,” Astrophys. Space Sci., vol. 103, no. 1, pp. 9–19, 1984. https://doi.org/10.1007/bf00650038.Suche in Google Scholar
[20] R. C. Sharma and Sunil, “Thermal instability of a compressible finite-Larmor-radius Hall plasma in a porous medium,” J. Plasma Phys., vol. 55, no. 1, pp. 35–45, 1996. https://doi.org/10.1017/s002237780001864x.Suche in Google Scholar
[21] S. Kaothekar, “Thermal instability of partially ionized viscous plasma with Hall effect FLR corrections flowing through porous medium,” J. Porous Media, vol. 21, no. 8, pp. 679–699, 2018. https://doi.org/10.1615/jpormedia.2018017559.Suche in Google Scholar
[22] S. Kaothekar, S. Mishra, and S. Phadke, “Transverse thermal instability of partially ionized radiative plasma with impact of neutral collisions and finite electron inertia effect in ISM,” Mater. Today: Proc., vol. 89, pp. 24–33, 2023. https://doi.org/10.1016/j.matpr.2023.05.596.Suche in Google Scholar
[23] T. V. Zaqarashvili, M. L. Khodachenko, and H. O. Rucker, “Magnetohydrodynamic waves in solar partially ionized plasmas: two-fluid approach,” Astron. Astrophys., vol. 529, p. A82, 2011. https://doi.org/10.1051/0004-6361/201016326.Suche in Google Scholar
[24] J. E. Leake, V. S. Lukin, M. G. Linton, and E. T. Meier, “Multi-fluid simulations of chromospheric magnetic reconnection in a weakly ionized reacting plasma,” Astrophys. J., vol. 760, no. 2, p. 109, 2012. https://doi.org/10.1088/0004-637x/760/2/109.Suche in Google Scholar
[25] R. C. Sharma and Sunil, “Rayleigh-Taylor instability of a partially ionized plasma in a porous medium in presence of a variable magnetic field,” Z. Naturforsch. A, vol. 47, no. 12, pp. 1227–1231, 1992. https://doi.org/10.1515/zna-1992-1208.Suche in Google Scholar
[26] A. K. Patidar, H. Joshi, S. Patidar, R. K. Pensia, and S. Mansuri, “The effect of magnetized quantum plasma on Jeans instability,” Z. Naturforsch. A, vol. 78, no. 9, pp. 833–840, 2023. https://doi.org/10.1515/zna-2023-0084.Suche in Google Scholar
[27] V. Chandel and Sunil, “Influence of magnetic fields and bounding surface configurations on thermal convection in partially ionised plasmas: nonlinear and linear stability analyses,” Pramana J. Phys., vol. 98, no. 3, p. 107, 2024. https://doi.org/10.1007/s12043-024-02805-3.Suche in Google Scholar
[28] V. Chandel, Sunil, and P. Sharma, “Study of global stability of rotating partially-ionized plasma saturating a porous medium,” Spec. Top. Rev. Porous Media, vol. 15, no. 6, pp. 27–46, 2024.10.1615/SpecialTopicsRevPorousMedia.2024050815Suche in Google Scholar
[29] T. V. Galstyan, D. A. Koshkina, D. A. Klimachkov, and A. S. Petrosyan, “A theory of large-scale flows of rotating partially ionized space and astrophysical plasma in the approximation of Hall magnetohydrodynamics,” Plasma Phys. Rep., vol. 50, no. 9, pp. 1165–1179, 2024. https://doi.org/10.1134/s1063780x24601159.Suche in Google Scholar
[30] E. A. Spiegel and G. Veronis, “On the Boussinesq approximation for a compressible fluid,” Astrophys. J., vol. 131, pp. 442–447, 1960. https://doi.org/10.1086/146849.Suche in Google Scholar
[31] M. F. El-Sayed and R. A. Mohamed, “Gravitational instability of rotating viscoelastic partially ionized plasma in the presence of an oblique magnetic field and Hall current,” Int. Scholarly Res. Not., vol. 2011, 2011, Art. no. 597172. https://doi.org/10.5402/2011/597172.Suche in Google Scholar
[32] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, New York, Dover, 1981.Suche in Google Scholar
[33] R. C. Sharma and J. N. Misra, “Thermal instability of a compressible and partially ionized plasma,” Z. Naturforsch. A, vol. 41, no. 5, pp. 729–732, 1986. https://doi.org/10.1515/zna-1986-0506.Suche in Google Scholar
[34] R. C. Sharma and Sunil, “Compressibility and collisional effects on thermal instability of a partially-ionized Hall plasma in porous medium,” Indian J. Phys., vol. 68B, no. 3, pp. 255–266, 1994.Suche in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Atomic, Molecular & Optical Physics
- Quantum chemical concept of oxidation states
- Dynamical Systems & Nonlinear Phenomena
- Comparative study of novel solitary wave solutions with unveiling bifurcation and chaotic structure modelled by stochastic dynamical system
- Fundamental Concepts of Physical Science
- Fermi motion in nucleons and the generalized Heisenberg uncertainty relation
- Hydrodynamics & Plasma Physics
- Stability and convection in compressible partially ionized plasma layers: nonlinear and linear analysis
- Solid State Physics & Materials Science
- Effective medium theory of a concentric metamaterial bifunctional cloak
- Morphological impact on energy storage properties of 2D-MoS2 and its nanocomposites: a comprehensive review
- Exploring the implications of CoCrFeNiCu high entropy alloy coatings on tribomechanical, wetting behavior, and interfacial microstructural characterizations in microwave-clad AISI 304 stainless steels
Artikel in diesem Heft
- Frontmatter
- Atomic, Molecular & Optical Physics
- Quantum chemical concept of oxidation states
- Dynamical Systems & Nonlinear Phenomena
- Comparative study of novel solitary wave solutions with unveiling bifurcation and chaotic structure modelled by stochastic dynamical system
- Fundamental Concepts of Physical Science
- Fermi motion in nucleons and the generalized Heisenberg uncertainty relation
- Hydrodynamics & Plasma Physics
- Stability and convection in compressible partially ionized plasma layers: nonlinear and linear analysis
- Solid State Physics & Materials Science
- Effective medium theory of a concentric metamaterial bifunctional cloak
- Morphological impact on energy storage properties of 2D-MoS2 and its nanocomposites: a comprehensive review
- Exploring the implications of CoCrFeNiCu high entropy alloy coatings on tribomechanical, wetting behavior, and interfacial microstructural characterizations in microwave-clad AISI 304 stainless steels
