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Fluid-filled porous medium heated from the bottom and subjected to periodic gravity: analysis and microcontroller implementation

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Abstract

The analysis and microcontroller implementation of a Newtonian fluid-filled porous medium heated from the bottom and subjected to sinusoidal or non-sinusoidal periodic gravity is investigated in this paper. The Newtonian fluid-filled porous medium with a bottom source of heat and subjected to periodic gravity modulation is described by the equation of conservation of energy and hydrodynamic equations modified following the Boussinesq–Darcy approximation. Galerkin-truncated approximation is applied in reducing the resulting set of partial differential equations into a Lorenz-like system of ordinary differential equations of order 1. The Lorenz-like system obtained in this case is found to have three equilibrium points whose stability depends on the system parameters. Without gravity modulation and by varying the scaled Rayleigh number, it is demonstrated that the obtained Lorenz-like system displays steady convection, periodic convection, chaotic convection, reverse period doubling to chaotic convection and coexistence between steady and chaotic convections. In the presence of sinusoidal or non-sinusoidal periodic gravity modulation and by varying the scaled Rayleigh number, the obtained Lorenz-like system exhibits periodic convections, bistable periodic convections and period doubling to chaotic convections. Finally, the existence of periodic convections, bistable periodic convections and chaotic convections is confirmed by microcontroller results obtained from the microcontroller implementation of the obtained Lorenz-like system.

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Acknowledgements

This work is partially funded by the Centre for Nonlinear Systems, Chennai Institute of Technology, India via funding number CIT/CNS/2023/Rp-007.

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, University of Bamenda, P.O. Box 39, Bamenda, Cameroon

    Noel Nyang Kibanya

  2. Center for Artificial Intelligence, Chennai Institute of Technology, Chennai, Tamilnadu, 600 069, India

    Gayathri Vivekanandan

  3. Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon

    Alhadji Abba Oumate

  4. Department of Physics, Higher Teacher Training College, University of Bamenda, P.O. Box, 39, Bamenda, Cameroon

    Gaetan Fautso Kuiate

  5. Department of Mechanical, Petroleum and Gas Engineering, National Advanced School of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon

    Sifeu Takougang Kingni

  6. Department of Mechanical and Industrial Engineering, National Higher Polytechnic Institute, University of Bamenda, P.O. Box 39, Bamenda, Cameroon

    Gaetan Fautso Kuiate

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  1. Noel Nyang Kibanya
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  2. Gayathri Vivekanandan
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  3. Alhadji Abba Oumate
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  4. Gaetan Fautso Kuiate
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  5. Sifeu Takougang Kingni
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Correspondence to Noel Nyang Kibanya.

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Kibanya, N.N., Vivekanandan, G., Oumate, A.A. et al. Fluid-filled porous medium heated from the bottom and subjected to periodic gravity: analysis and microcontroller implementation. Pramana - J Phys 97, 175 (2023). https://doi.org/10.1007/s12043-023-02651-9

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  • DOI: https://doi.org/10.1007/s12043-023-02651-9

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