Horizontally isotropic bidispersive thermal convection

Straughan, B.

Abstract

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores due to cracks or fissures in the solid skeleton. We present general equations for thermal convection in a bidispersive porous medium when the permeabilities, interaction coefficient and thermal conductivity are anisotropic but symmetric tensors. In this case, we show exchange of stabilities holds and fluid movement will commence via stationary convection, and additionally we show the global nonlinear stability threshold is the same as the linear instability one. Attention is then focused on the case where the interaction coefficient and thermal conductivity are isotropic, and the permeability is isotropic in the horizontal directions, although the permeability in the vertical direction is different. The nonlinear stability threshold is calculated in this case and numerical results are presented and discussed in detail.

Citation

Straughan, B. (2018). Horizontally isotropic bidispersive thermal convection. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2213), Article 20180018. https://doi.org/10.1098/rspa.2018.0018

• Journal Article Type: Article
• Acceptance Date: Apr 13, 2018
• Online Publication Date: May 16, 2018
• Publication Date: May 16, 2018
• Deposit Date: Jun 5, 2018
• Publicly Available Date: Jun 5, 2018
• Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-5021
• Electronic ISSN: 1471-2946
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 474
• Issue: 2213
• Article Number: 20180018
• DOI: https://doi.org/10.1098/rspa.2018.0018
• Public URL: https://durham-repository.worktribe.com/output/1329510