Stability of double-diffusive convection induced by selective absorption of radiation in a fluid layer

Wicks, Thomas J.; Hill, Antony A.

Abstract

Linear and nonlinear stability analyses were performed on a fluid layer with a concentration-based internal heat source. Clear bimodal behaviour in the neutral curve (with stationary and oscillatory modes) is observed in the region of the onset of oscillatory convection, which is a previously unobserved phenomenon in radiation-induced convection. The numerical results for the linear instability analysis suggest a critical value γ c of γ, a measure for the strength of the internal heat source, for which oscillatory convection is inhibited when γ > γ c. Linear instability analyses on the effect of varying the ratio of the salt concentrations at the upper and lower boundaries conclude that the ratio has a significant effect on the stability boundary. A nonlinear analysis using an energy approach confirms that the linear theory describes the stability boundary most accurately when γ is such that the linear theory predicts the onset of mostly stationary convection. Nevertheless, the agreement between the linear and nonlinear stability thresholds deteriorates for larger values of the solute Rayleigh number for any value of γ. © 2012 Springer-Verlag.

• Journal Article Type: Article
• Publication Date: May 1, 2012
• Deposit Date: Sep 29, 2014
• Journal: Continuum Mechanics and Thermodynamics
• Print ISSN: 0935-1175
• Electronic ISSN: 1432-0959
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 3
• Pages: 229-237
• DOI: https://doi.org/10.1007/s00161-012-0234-0
• Keywords: double-diffusive convection, internal heat source, subcritical instability
• Public URL: https://uwe-repository.worktribe.com/output/956415
• Publisher URL: http://dx.doi.org/10.1007/s00161-012-0234-0
• Contract Date: Nov 15, 2016