Non-linear stability bounds for a horizontal layer of a porous medium with an exothermic reaction on the lower boundary

被引：3

作者：

Scott, Nicola L. ^{[1
]}

机构：

[1] Univ Durham, Dept Math, Durham DH1 3LE, England

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2013年 / 57卷

关键词：

Porous media; Convection; Non-linear; Energy method; Exothermic reaction; Stability; SUBCRITICAL CONVECTIVE INSTABILITY; SURFACE-REACTION; FLUID; DRIVEN; ENERGY; ONSET;

D O I：

10.1016/j.ijnonlinmec.2013.07.004

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We use the energy method to find regions of stability for a horizontal layer of a Darcy porous medium with an exothermic reaction on the lower layer. The results are compared to the linear instability results for this model found by Scott and Straughan [16]. It is shown that there is a region in which sub-critical instabilities may occur, but for small Lewis numbers, 0 < Le < 10, the non-linear stability boundary is reasonably close to the linear instability boundary. The effect of varying the parameters of the reaction on the stability curve is discussed. (C) 2013 The Author. Published by Elsevier Ltd. All rights reserved.

引用

页码：163 / 167

页数：5

共 19 条

[1] STABILITY OF A MICROPOLAR FLUID LAYER HEATED FROM BELOW
AHMADI, G
[J]. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1976, 14 (01) : 81 - 89
[2] Nonlinear stability of a convective motion in a porous layer driven by a horizontally periodic temperature gradient
Capone, F
Rionero, S
[J]. CONTINUUM MECHANICS AND THERMODYNAMICS, 2003, 15 (06) : 529 - 538
[3] COURANT R, 1953, METHODS MATH PHYS, V1
[4] Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems
Dongarra, JJ
Straughan, B
Walker, DW
[J]. APPLIED NUMERICAL MATHEMATICS, 1996, 22 (04) : 399 - 434
[5] Compositional convection in the presence of a magnetic field. I. A single interface
Eltayeb, IA
Hamza, EA
Jervase, JA
Krishnan, E
Loper, DE
[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2004, 460 (2052): : 3505 - 3528
[6] Global stability for penetrative convection with throughflow in a porous material
Hill, A. A.
Rionero, S.
Straughan, B.
[J]. IMA JOURNAL OF APPLIED MATHEMATICS, 2007, 72 (05) : 635 - 643
[7] Joseph D.D., 1965, Arch. Ration. Mech. Anal., V20, P59, DOI [10.1007/BF00250190, DOI 10.1007/BF00250190]
[8] SUBCRITICAL CONVECTIVE INSTABILITY .I. FLUID LAYERS
JOSEPH, DD
SHIR, CC
[J]. JOURNAL OF FLUID MECHANICS, 1966, 26 : 753 - &
[9] JOSEPH DD, 1966, ARCH RATION MECH AN, V22, P163
[10] SUBCRITICAL CONVECTIVE INSTABILITY .2. SPHERICAL SHELLS
JOSEPH, DD
CARMI, S
[J]. JOURNAL OF FLUID MECHANICS, 1966, 26 : 769 - &

← 1 2 →