1
|
Thermal Instability of a Micropolar Fluid Layer with Temperature-Dependent Viscosity. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES 2020. [DOI: 10.1007/s40010-018-0591-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
2
|
Abstract
A thermal convection model is considered that consists of a layer of viscous incompressible fluid contained between two horizontal planes. Gravity is acting vertically downward, and the fluid has a density maximum in the active temperature range. A heat source/sink that varies with vertical height is imposed. It is shown that in this situation there are three possible (different) sub-layers that may induce convective overturning instability. The possibility of resonance between the motion in these layers is investigated. A region is discovered where a very sharp increase in Rayleigh number is observed. In addition to a linearized instability analysis, two global (unconditional) nonlinear stability thresholds are derived.
Collapse
Affiliation(s)
- B. Straughan
- Department of Mathematical Sciences, University of Durham, DH1 3LE, UK
| |
Collapse
|
3
|
Hill AA, Carr M. Sharp global nonlinear stability for a fluid overlying a highly porous material. Proc Math Phys Eng Sci 2009. [DOI: 10.1098/rspa.2009.0322] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The stability of convection in a two-layer system in which a layer of fluid with a temperature-dependent viscosity overlies and saturates a highly porous material is studied. Owing to the difficulties associated with incorporating the nonlinear advection term in the Navier–Stokes equations into a stability analysis, previous literature on fluid/porous thermal convection has modelled the fluid using the linear Stokes equations. This paper derives global stability for the full nonlinear system, by utilizing a model proposed by Ladyzhenskaya. The nonlinear stability boundaries are shown to be sharp when compared with the linear instability thresholds.
Collapse
Affiliation(s)
- Antony A. Hill
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Magda Carr
- School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK
| |
Collapse
|
4
|
Affiliation(s)
- B. Straughan
- Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, UK
| |
Collapse
|