Parametric Study of Extended Brinkman’s-Darcy Model for Triple Diffusive Convection System under the Effect of Rotational Modulation: Bifurcation Analysis

Pervinder Singh, Shruti Tomar, Vinod Kumar Gupta, Naresh M Chadha

Article ID: 9733
Vol 8, Issue 3, 2025

VIEWS - 3 (Abstract)

Abstract


In this study, we consider the extended Brinkman’s-Darcy model for a triple diffusive convection system which consists of some parameters such as Taylor number (Ta), Solutal Rayleigh numbers (RC1 , RC2 ), and Prandtl number (Pr). To investigate the range of these parameters, a dynamical system of the Ginzburg-Landau equation is developed. The parametric analysis and comparative study of the model for the three Rayleigh numbers which leads to the clear fluid layer, sparsely packed porous layer, and densely packed porous layer is done with the help of bifurcation maps and the Lyapunov exponents. It is found that for a certain range of parameters, the system exhibits a chaotic behaviour.

Keywords


Eextended Brinkman ’s-Darcy model, Dynamical system, Bifurcation Maps, the Lyapunov Exponents, Chaotic behaviour.



References

  1. BM Boubnov and Georgi S Golitsyn. Convection in rotating fluids, volume 29.
  2. Springer Science & Business Media, 2012.
  3. RJ Tayler. Convection in rotating stars. Monthly Notices of the Royal Astronomical Society, 165(1):39–52, 1973.
  4. Suresh Chand. Effect of rotation on triple-diffusive convection in a magnetized
  5. ferrofluid with internal angular momentum saturating a porous medium. Applied
  6. Mathematical Sciences, 6(65):3245–3258, 2012.
  7. Suresh Chand. Effect of rotation on triple-diffusive convection in walters’(model
  8. b´) fluid in porous medium. Research Journal of Science and Technology,
  9. (1):184–188, 2013.
  10. Sameena Tarannum and S Pranesh. Heat and mass transfer of triple diffusive
  11. convection in a rotating couple stress liquid using ginzburg-landau model. International Journal of Mechanical and Mechatronics Engineering, 11(3):583–588,
  13. M Rudziva, P Sibanda, OAI Noreldin, and S Goqo. On trigonometric cosine,
  14. square, sawtooth, and triangular wave-type rotational modulations on triplediffusive convection in salted water. Heat Transfer, 50(7):6886–6914, 2021.
  15. PG Siddheshwar, BS Bhadauria, and Alok Srivastava. An analytical study of nonlinear double-diffusive convection in a porous medium under temperature/gravity
  16. modulation. Transport in porous media, 91:585–604, 2012.
  17. Vinod K Gupta. Study of mass transport in rotating couple stress liquid under
  18. concentration modulation. Chinese journal of physics, 56(3):911–921, 2018.
  19. Pervinder Singh and Vinod K Gupta. Simultaneous action of modulated temperature and third diffusing component on natural convection. In International
  20. workshop of Mathematical Modelling, Applied Analysis and Computation, pages
  21. –231. Springer, 2022.
  22. Pervinder Singh, Vinod K Gupta, Isaac Lare Animasaun, Taseer Muhammad,
  23. and Qasem M Al-Mdallal. Dynamics of newtonian liquids with distinct concentrations due to time-varying gravitational acceleration and triple diffusive convection: Weakly non-linear stability of heat and mass transfer. Mathematics,
  24. (13):2907, 2023.
  25. Pervinder Singh, Jogendra Kumar, and BS Bhadauria. Weakly non-linear stability
  26. analysis of g-jitter induced rayleigh–b´enard convection under inclined surfaces.
  27. Chinese Journal of Physics, 91:525–537, 2024.
  28. Pervinder Singh, Vinod K Gupta, and Naresh M Chadha. Study of heat and mass transports due to modulated rotational flow in a triply diffusive newtonian
  29. liquid saturated porous medium/fluid layer: A comparative study. International
  30. Journal of Heat and Fluid Flow, 108:109449, 2024.
  31. Uttam Ghosh, Swadesh Pal, and Malay Banerjee. Memory effect on bazykin’s
  32. prey-predator model: Stability and bifurcation analysis. Chaos, Solitons Fractals,
  33. :110531, 2021.
  34. Kamyar Hosseini, Evren Hin¸cal, and Mousa Ilie. Bifurcation analysis, chaotic
  35. behaviors, sensitivity analysis, and soliton solutions of a generalized schr¨odinger
  36. equation. Nonlinear Dynamics, 111(18):17455–17462, 2023.
  37. Qianqian Zhang, Biao Tang, Tianyu Cheng, and Sanyi Tang. Bifurcation analysis
  38. of a generalized impulsive kolmogorov model with applications to pest and disease
  39. control. SIAM Journal on Applied Mathematics, 80(4):1796–1819, 2020.
  40. Jinying Guo, Huailong Shi, Ren Luo, and Jing Zeng. Bifurcation analysis of a railway wheelset with nonlinear wheel–rail contact. Nonlinear Dynamics, 104(2):989–
  41. , 2021.
  42. Pankaj Kumar and S Narayanan. Chaos and bifurcation analysis of stochastically
  43. excited discontinuous nonlinear oscillators. Nonlinear Dynamics, 102:927–950,
  45. Asit Saha, Khalid K Ali, Hadi Rezazadeh, and Yogen Ghatani. Analytical optical
  46. pulses and bifurcation analysis for the traveling optical pulses of the hyperbolic
  47. nonlinear schr¨odinger equation. Optical and Quantum Electronics, 53:1–19, 2021.
  48. Shruti Tomar and Naresh M Chadha. Study of fixed points and chaos in wave
  49. propagation for the generalized damped forced korteweg-de vries equation using
  50. bifurcation analysis. Chaos Theory and Applications, 5(4):286–292, 2023.
  51. Shruti Tomar, Naresh M Chadha, and Ankita Khanna. A mathematical model to
  52. study regulatory properties and dynamical behaviour of glycolytic pathway using
  53. bifurcation analysis. In Computational Methods for Biological Models, pages 81–
  54. Springer, 2023.
  55. Shruti Tomar, Naresh M Chadha, and Santanu Raut. Bifurcation analysis of
  56. generalized damped forced kdv equation and its analytical solitary wave solutions.
  57. In AIP Conference Proceedings, volume 2852. AIP Publishing, 2023.
  58. Ndolane Sene. Qualitative analysis of class of fractional-order chaotic system via
  59. bifurcation and lyapunov exponents notions. Journal of Mathematics, 2021:1–18,
  61. Steven H Strogatz. Nonlinear dynamics and chaos with student solutions manual:
  62. With applications to physics, biology, chemistry, and engineering. CRC press,
  64. Jonathan B Dingwell. Lyapunov exponents. Wiley encyclopedia of biomedical
  65. engineering, 2006.
  66. Lu´ıs Barreira. Lyapunov exponents. Springer, 2017.
  67. Naresh M Chadha, Shruti Tomar, and Santanu Raut. Parametric analysis of
  68. dust ion acoustic waves in superthermal plasmas through non-autonomous kdv
  69. framework. Communications in Nonlinear Science and Numerical Simulation,
  70. :107269, 2023.


DOI: https://doi.org/10.24294/tse9733

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