Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source
In this paper, the influence of gravitational modulation on weakly nonlinear biothermal convection in a porous rotating layer is investigated. We consider a layer of porous medium saturated with Newtonian fluid, containing gyrotactic microorganisms, and subject to gravitational modulation, rotation,...
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| Format: | Article |
| Language: | English |
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V.N. Karazin Kharkiv National University Publishing
2024-03-01
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| Series: | East European Journal of Physics |
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| Online Access: | https://periodicals.karazin.ua/eejp/article/view/22612 |
| _version_ | 1797272711811039232 |
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| author | Michael I. Kopp Volodymyr V. Yanovsky |
| author_facet | Michael I. Kopp Volodymyr V. Yanovsky |
| author_sort | Michael I. Kopp |
| collection | DOAJ |
| description | In this paper, the influence of gravitational modulation on weakly nonlinear biothermal convection in a porous rotating layer is investigated. We consider a layer of porous medium saturated with Newtonian fluid, containing gyrotactic microorganisms, and subject to gravitational modulation, rotation, and internal heating. To analyze linear stability, it is sufficient to represent disturbances in the form of normal modes, while nonlinear analysis includes a truncated Fourier series containing a harmonic of the nonlinear interaction. A six-dimensional nonlinear Lorentz-type model is constructed, exhibiting both reflection symmetry and dissipation. We determined heat and mass transfer using a weakly nonlinear theory based on the representation of a truncated Fourier series. Additionally, the behavior of nonstationary Nusselt and Sherwood numbers was investigated by numerically solving finite amplitude equations. Applying the expansion of regular perturbations in a small parameter to a six-dimensional model of Lorentz equations with periodic coefficients, we obtained the Ginzburg-Landau (GL) equation. This equation describes the evolution of the finite amplitude of the onset of convection. The amplitude of convection in the unmodulated case is determined analytically and serves as a standard for comparison. The study examines the effect of various parameters on the system, including the Vadasz number, modified Rayleigh-Darcy number, Taylor number, cell eccentricity, and modulation parameters such as amplitude and frequency. By varying these parameters, in different cases, we analyzed heat and mass transfer, quantitatively expressed by the Nusselt and Sherwood numbers. It has been established that the modulation amplitude has a significant effect on the enhancement of heat and mass transfer, while the modulation frequency has a decreasing effect. |
| first_indexed | 2024-03-07T14:33:18Z |
| format | Article |
| id | doaj.art-c4ce2a430f59454d8aaaf1fc5a896ffa |
| institution | Directory Open Access Journal |
| issn | 2312-4334 2312-4539 |
| language | English |
| last_indexed | 2024-03-07T14:33:18Z |
| publishDate | 2024-03-01 |
| publisher | V.N. Karazin Kharkiv National University Publishing |
| record_format | Article |
| series | East European Journal of Physics |
| spelling | doaj.art-c4ce2a430f59454d8aaaf1fc5a896ffa2024-03-05T22:41:10ZengV.N. Karazin Kharkiv National University PublishingEast European Journal of Physics2312-43342312-45392024-03-01117519110.26565/2312-4334-2024-1-1522612Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat SourceMichael I. Kopp0Volodymyr V. Yanovsky1Institute for Single Cristals, Nat. Academy of Science Ukraine, Kharkiv, UkraineInstitute for Single Cristals, Nat. Academy of Science Ukraine, Kharkiv, Ukraine; V.N. Karazin Kharkiv National University, Kharkiv, UkraineIn this paper, the influence of gravitational modulation on weakly nonlinear biothermal convection in a porous rotating layer is investigated. We consider a layer of porous medium saturated with Newtonian fluid, containing gyrotactic microorganisms, and subject to gravitational modulation, rotation, and internal heating. To analyze linear stability, it is sufficient to represent disturbances in the form of normal modes, while nonlinear analysis includes a truncated Fourier series containing a harmonic of the nonlinear interaction. A six-dimensional nonlinear Lorentz-type model is constructed, exhibiting both reflection symmetry and dissipation. We determined heat and mass transfer using a weakly nonlinear theory based on the representation of a truncated Fourier series. Additionally, the behavior of nonstationary Nusselt and Sherwood numbers was investigated by numerically solving finite amplitude equations. Applying the expansion of regular perturbations in a small parameter to a six-dimensional model of Lorentz equations with periodic coefficients, we obtained the Ginzburg-Landau (GL) equation. This equation describes the evolution of the finite amplitude of the onset of convection. The amplitude of convection in the unmodulated case is determined analytically and serves as a standard for comparison. The study examines the effect of various parameters on the system, including the Vadasz number, modified Rayleigh-Darcy number, Taylor number, cell eccentricity, and modulation parameters such as amplitude and frequency. By varying these parameters, in different cases, we analyzed heat and mass transfer, quantitatively expressed by the Nusselt and Sherwood numbers. It has been established that the modulation amplitude has a significant effect on the enhancement of heat and mass transfer, while the modulation frequency has a decreasing effect.https://periodicals.karazin.ua/eejp/article/view/22612darcy-brinkman modelbio-thermal convectiongravity modulationporous rotating mediumgyrotactic microorganism |
| spellingShingle | Michael I. Kopp Volodymyr V. Yanovsky Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source East European Journal of Physics darcy-brinkman model bio-thermal convection gravity modulation porous rotating medium gyrotactic microorganism |
| title | Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source |
| title_full | Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source |
| title_fullStr | Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source |
| title_full_unstemmed | Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source |
| title_short | Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source |
| title_sort | weakly nonlinear bio thermal convection in a porous media layer under rotation gravity modulation and heat source |
| topic | darcy-brinkman model bio-thermal convection gravity modulation porous rotating medium gyrotactic microorganism |
| url | https://periodicals.karazin.ua/eejp/article/view/22612 |
| work_keys_str_mv | AT michaelikopp weaklynonlinearbiothermalconvectioninaporousmedialayerunderrotationgravitymodulationandheatsource AT volodymyrvyanovsky weaklynonlinearbiothermalconvectioninaporousmedialayerunderrotationgravitymodulationandheatsource |