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Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries

  • Palle Kiran ORCID logo EMAIL logo
Published/Copyright: November 30, 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 3

Abstract

This paper investigates the effect of gravity modulation on Rayleigh–Bénard convection using the rigid isothermal boundary conditions. We calculate heat transfer results using the Nusselt and mean Nusselt numbers through the finite-amplitude of convection, which we got from the Ginzburg–Landau equation (GLE). The Ginzburg–Landau equation is derived analytically from the Fredholm solvability condition at third order. The finite amplitude equation (GLE) is a function of system parameters and solved numerically. The gravity modulation considered in terms of steady and sinusoidal parts. The sinusoidal part defines gravity modulation in terms of amplitude and frequency. Our study shows that gravity modulation controls the heat transfer results. The amplitude of modulation enhances heat transfer for low frequencies and diminishes for high frequencies. Further, we found that rigid isothermal boundary conditions are diminishing heat transfer than free and isothermal boundaries. Finally, we concluded that rigid isothermal boundary conditions and gravity modulation controls heat transfer results.

Keywords: Ginzburg–Landau equation; gravity modulation; heat transport; rigid boundary; weakly nonlinear theory
Corresponding author: Palle Kiran, Department of Mathematics, Chaitanya Bharathi Institute of Technology, Hyderabad, Telangana 500075, India, E-mail:

Acknowledgment

The author Dr. Palle Kiran acknowledges Chaitanya Bharathi Institute of Technology, Hyderabad, India for providing research specialities in the Department. This work is done during the period of Research coordinator of the Dept. of Mathematics CBIT. I thank Prof. BS. Bhadauria (Dean, BBAU) for basic inputs and ideas of the work.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-02-09
Revised: 2021-08-14
Accepted: 2021-11-04
Published Online: 2021-11-30

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2021-0054
Keywords for this article
Ginzburg–Landau equation; gravity modulation; heat transport; rigid boundary; weakly nonlinear theory

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation
  4. Hopf bifurcations in a network of FitzHugh–Nagumo biological neurons
  5. Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries
  6. A new numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ equation
  7. Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems
  8. Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces
  9. Elastic trend filtering
  10. A new approach to representations of homothetic motions in Lorentz space
  11. Numerical simulation of variable-order fractional differential equation of nonlinear Lane–Emden type appearing in astrophysics
  12. Stability analysis and numerical simulations of the fractional COVID-19 pandemic model
  13. Numerical solutions of the Bagley–Torvik equation by using generalized functions with fractional powers of Laguerre polynomials
  14. N-fold Darboux transformation and exact solutions for the nonlocal Fokas–Lenells equation on the vanishing and plane wave backgrounds
  15. Closed form soliton solutions to the space-time fractional foam drainage equation and coupled mKdV evolution equations
  16. Master-slave synchronization in the Duffing-van der Pol and Φ6 Duffing oscillators
  17. Singularity analysis and analytic solutions for the Benney–Gjevik equations
  18. Trajectory controllability of nonlinear fractional Langevin systems
  19. Similarity transformations for modified shallow water equations with density dependence on the average temperature
  20. Non-equidistant partition predictor–corrector method for fractional differential equations with exponential memory
  21. Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction
  22. Dynamic response of Mathieu–Duffing oscillator with Caputo derivative
  23. Non-Newtonian fluid flow having fluid–particle interaction through a porous zone in a channel with permeable walls
  24. A class of computationally efficient Newton-like methods with frozen inverse operator for nonlinear systems
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