Gravity-modulated RayleighBard convection in a Newtonian liquid bounded by rigidfree boundaries: a comparative study with other boundary conditions
- Title
- Gravity-modulated RayleighBard convection in a Newtonian liquid bounded by rigidfree boundaries: a comparative study with other boundary conditions
- Creator
- Francis R.; Narayana M.; Siddheshwar P.G.
- Description
- Effect of different boundaries on the gravity-modulated RayleighBard convection has been investigated with an emphasis on rigidfree boundaries. Small-amplitude and large-amplitude modulations are studied using the linear stability analysis. The modified Venezian approach is used to study small-amplitude modulations using different modes of perturbations and the superposition principle. The existence of subharmonic motions for the case of large-amplitude modulations was explored using the Mathieu equation arising from the linear stability analysis. Floquet theory was used together with Hills infinite determinant method to compute the critical Rayleigh number for the case of large-amplitude modulations. Weakly non-linear analysis is performed leading to the cubic StuartLandau equation from the Lorenz system. Heat transport was quantified using the Nusselt number and the mean Nusselt numbers for different amplitudes and frequencies. It was found that gravity modulation has, in general, a stabilizing effect on the convection process in all three boundary types, and the heat transport was found to be an increasing function of amplitude. Another important outcome of the study is that the critical Rayleigh number for the onset of convection for rigidfree boundaries lies between those of the corresponding values of the freefree and rigidrigid boundaries in the case of both harmonic and subharmonic motions which could be exploited in controlling convection. 2023, The Author(s), under exclusive licence to Springer Nature B.V.
- Source
- Journal of Engineering Mathematics, Vol-139, No. 1
- Date
- 2023-01-01
- Publisher
- Springer Science and Business Media B.V.
- Subject
- Gravity modulation; Heat transport; RayleighBard convection; Rigidfree; StuartLaundau equation
- Coverage
- Francis R., Department of Mathematics, The University of the West Indies, Mona Campus, Kingston 7, St. Andrew, State, Kingston, Jamaica; Narayana M., Department of Mathematics, The University of the West Indies, Mona Campus, Kingston 7, St. Andrew, State, Kingston, Jamaica; Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, CHRIST(Deemed to be University), Hosur Road, Karnataka, Bengaluru, 560029, India
- Rights
- Restricted Access
- Relation
- ISSN: 220833
- Format
- Online
- Language
- English
- Type
- Article
Collection
Citation
Francis R.; Narayana M.; Siddheshwar P.G., “Gravity-modulated RayleighBard convection in a Newtonian liquid bounded by rigidfree boundaries: a comparative study with other boundary conditions,” CHRIST (Deemed To Be University) Institutional Repository, accessed February 24, 2025, https://archives.christuniversity.in/items/show/14322.