Impact of boundary conditions on Rayleigh-Bard convection: stability, heat transfer and chaos
- Title
- Impact of boundary conditions on Rayleigh-Bard convection: stability, heat transfer and chaos
- Creator
- Arshika N.S.; Siddheshwar P.G.; Tarannum S.; Kanchana C.
- Description
- The paper compares the results of Rayleigh-Bard convection problem for rigid-rigid-isothermal, rigid-free-isothermal and free-free isothermal boundaries. A minimal Fourier-Galerkin expansion yields the generalized-Lorenz-model whose scaled version is reduced to the Stuart-Landau-model using the multiscale-method. Nusselt number is estimated for both steady and unsteady regimes. Regular, chaotic, and periodic natures of the solution are studied using the Hopf-Rayleigh-number and by means of a bifurcation diagram. The linear and weakly-nonlinear-analyses reveal that the onset of regular and chaotic motions in the case of rigid-free-isothermal boundaries happens later than that of free-free isothermal boundaries but earlier than rigid-rigid-isothermal boundaries. It is shown that the scaled-Lorenz-model possesses all the features of the classical-Lorenz-model. Beyond the value of the Hopf-Rayleigh-number, we observe chaotic-motion between two consecutive spells of periodic motion. It is found that one can also have a window of periodicity for all three boundaries. 2024 Informa UK Limited, trading as Taylor & Francis Group.
- Source
- International Journal of Ambient Energy, Vol-45, No. 1
- Date
- 2024-01-01
- Publisher
- Taylor and Francis Ltd.
- Subject
- Chaos; Hopf-bifurcation; Lorenz-model; Rayleigh-Bard; RungeKutta
- Coverage
- Arshika N.S., Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India; Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India; Tarannum S., Department of Professional Studies, CHRIST (Deemed to be University), Bengaluru, India; Kanchana C., Instituto de Alta Investigaci, CEDENNA, Universidad de Tarapac Arica, Chile
- Rights
- Restricted Access
- Relation
- ISSN: 1430750; CODEN: IJAED
- Format
- Online
- Language
- English
- Type
- Article
Collection
Citation
Arshika N.S.; Siddheshwar P.G.; Tarannum S.; Kanchana C., “Impact of boundary conditions on Rayleigh-Bard convection: stability, heat transfer and chaos,” CHRIST (Deemed To Be University) Institutional Repository, accessed February 25, 2025, https://archives.christuniversity.in/items/show/13815.