Global stability for thermal convection in a fluid overlying a highly porous material

Hill, Antony A.; Straughan, Brian

Abstract

This paper investigates the instability thresholds and global nonlinear stability bounds for thermal convection in a fluid overlying a highly porous material. A two-layer approach is adopted, where the Darcy-Brinkman equation is employed to describe the fluid flow in the porous medium. An excellent agreement is found between the linear instability and unconditional nonlinear stability thresholds, demonstrating that the linear theory accurately emulates the physics of the onset of convection. © 2008 The Royal Society.

• Journal Article Type: Article
• Publication Date: Jan 8, 2009
• Deposit Date: Oct 24, 2012
• 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: 465
• Issue: 2101
• Pages: 207-217
• DOI: https://doi.org/10.1098/rspa.2008.0303
• Keywords: superposed porous-fluid convection, energy method, Darcy–Brinkman
• Public URL: https://uwe-repository.worktribe.com/output/1003082
• Publisher URL: http://dx.doi.org/10.1098/rspa.2008.0303
• Contract Date: Nov 15, 2016