Double-diffusive convection in a porous medium with a concentration based internal heat source

Hill, Antony A.

Abstract

Linear and nonlinear stability analyses of double-diffusive convection in a fluid-saturated porous layer with a concentration based internal heat source are studied. Darcy's law and the Boussinesq approximation are employed, with the equation of state taken to be linear with respect to temperature and concentration. Both the numerical and analytical analysis for the linear theory strongly suggest the presence of a critical value γc, where γ is essentially a measure of the internal heat source, for which no oscillatory convection occurs when γc ≤ γ. This, in the present literature, appears to be an unobserved phenomenon. A nonlinear energy stability analysis demonstrates more comparable linear and nonlinear thresholds when the linear theory predicts the onset of fully stationary convection. However, irrespective of the γ value, the agreement of the thresholds does deteriorate as the solute Rayleigh number Rc increases. © 2004 The Royal Society.

• Journal Article Type: Article
• Publication Date: Feb 8, 2005
• Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-5021
• Electronic ISSN: 1471-2946
• Publisher: Royal Society, The
• Peer Reviewed: Peer Reviewed
• Volume: 461
• Issue: 2054
• Pages: 561-574
• DOI: https://doi.org/10.1098/rspa.2004.1328
• Keywords: double–diffusive convection, nonlinear heat source, subcritical instabilities
• Public URL: https://uwe-repository.worktribe.com/output/1055168
• Publisher URL: http://dx.doi.org/10.1098/rspa.2004.1328