RayleighBard Convection in a Bi-viscous Bingham Fluid with Weak Vertical Harmonic Oscillations: Linear and Non-linear Analyses
- Title
- RayleighBard Convection in a Bi-viscous Bingham Fluid with Weak Vertical Harmonic Oscillations: Linear and Non-linear Analyses
- Creator
- Keerthana S.; Siddheshwar P.G.; Tarannum S.; Idris R.
- Description
- Linear and weakly non-linear stability analyses of RayleighBard convection in a bi-viscous Bingham fluid layer are performed in the presence of vertical harmonic vibrations. In the linear analysis, expression is obtained for the correction Rayleigh-number arising due to the vibrations. The non-linear-analysis based on the GinzburgLandau equation is used to compute the Nusselt-number in terms of the correction Rayleigh-number. The mean-Nusselt-number is then obtained as a function of the scaled-Rayleigh-number, the frequency and the amplitude of modulation, the Prandtl number, and the bi-viscous Bingham fluid parameter. The non-autonomous amplitude-equation is numerically solved using the RungeKuttaFehlberg45 method. It is found that the influence of increasing the amplitude of modulation is to result in a delayed-onset situation and thereby to an enhanced-heat-transport situation. For small and moderate frequencies, the influence of increasing the frequency of oscillations is to decrease the critical Rayleigh-number. However, the mean-Nusselt-number decreases with increase in the frequency of oscillations only in the case of small frequencies. An increase in the value of the bi-viscous Bingham fluid parameter leads to advanced-onset and thereby to an enhanced-heat-transport situation. At very large frequencies, the effect of modulation on onset and heat-transport ceases. 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.
- Source
- International Journal of Applied and Computational Mathematics, Vol-9, No. 3
- Date
- 2023-01-01
- Publisher
- Springer
- Subject
- Bi-viscous Bingham fluid; GinzburgLandau method; RayleighBard convection; Vertical harmonic oscillation and Nusselt-number
- Coverage
- Keerthana S., Department of Mathematics, Centre for Mathematical Needs, CHRIST (Deemed to be University), Bengaluru, 560029, India; Siddheshwar P.G., Department of Mathematics, Centre for Mathematical Needs, CHRIST (Deemed to be University), Bengaluru, 560029, India; Tarannum S., Department of Professional Studies, CHRIST (Deemed to be University), Bengaluru, 560029, India; Idris R., Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Terengganu, Kuala Nerus, 21030, Malaysia
- Rights
- Restricted Access
- Relation
- ISSN: 23495103
- Format
- Online
- Language
- English
- Type
- Article
Collection
Citation
Keerthana S.; Siddheshwar P.G.; Tarannum S.; Idris R., “RayleighBard Convection in a Bi-viscous Bingham Fluid with Weak Vertical Harmonic Oscillations: Linear and Non-linear Analyses,” CHRIST (Deemed To Be University) Institutional Repository, accessed March 1, 2025, https://archives.christuniversity.in/items/show/14246.