INSTABILITY OF THE BENARD-MARANGONI CONVECTION IN A POROUS LAYER AFFECTED BY A NON-VERTICAL MAGNETIC FIELD

被引:0
作者
Abdullah, A. Ah. [1 ]
Rashed, Z. Z. [2 ]
机构
[1] Umm Al Qura Univ, Dept Math Sci, Mecca 21955, Saudi Arabia
[2] Al Jouf Univ, Dept Math, Al Jouf, Saudi Arabia
关键词
Benard-Marangoni; porous layer; Brinkman model; non-vertical magnetic field; FLUID; STABILITY; CURRENTS;
D O I
10.1134/S0021894418050188
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The onset of the Benard-Marangoni convection in a horizontal porous layer permeated by a magnetohydrodynamic fluid with a nonlinear magnetic permeability is examined. The porous layer is assumed to be governed by the Brinkman model; it is bounded by a rigid surface from below and by a non-deformable free surface from above and subjected to a non-vertical magnetic field. The critical effective Marangoni number and the critical Rayleigh number are obtained for different values of the effective Darcy number, Biot number, Chandrasekhar number, nonlinear magnetic parameter, and angle from the vertical axis for the cases of stationary convection and overstability. The related eigenvalue problem is solved by using the first-order Chebyshev polynomial method.
引用
收藏
页码:903 / 911
页数:9
相关论文
共 15 条
  • [1] BENARD CONVECTION IN A NONLINEAR MAGNETIC FLUID
    ABDULLAH, AA
    LINDSAY, KA
    [J]. ACTA MECHANICA, 1990, 85 (1-2) : 27 - 42
  • [2] THERMAL INSTABILITY IN SUPERPOSED POROUS AND FLUID LAYERS IN THE PRESENCE OF A MAGNETIC FIELD USING THE BRINKMAN MODEL
    Banjer, Hanadi
    Abdullah, Abdullah
    [J]. JOURNAL OF POROUS MEDIA, 2012, 15 (01) : 1 - 10
  • [3] Benard M., 1900, Rev. Gen. Sci. Pure Appl, V11, P1309, DOI DOI 10.1051/JPHYSTAP:019000090051300
  • [4] Gangadharaiah YH, 2016, J APPL FLUID MECH, V9, P1551
  • [5] Porous media and the Benard-Marangoni problem
    Hennenberg, M
    Saghir, MZ
    Rednikov, A
    Legros, JC
    [J]. TRANSPORT IN POROUS MEDIA, 1997, 27 (03) : 327 - 355
  • [6] CONVECTION CURRENTS IN A POROUS MEDIUM
    HORTON, CW
    ROGERS, FT
    [J]. JOURNAL OF APPLIED PHYSICS, 1945, 16 (06) : 367 - 370
  • [7] SURFACE TENSION AND BUOYANCY EFFECTS IN CELLULAR CONVECTION
    NIELD, DA
    [J]. JOURNAL OF FLUID MECHANICS, 1964, 19 (03) : 341 - 352
  • [8] Nield DA, 2006, CONVECTION POROUS ME, V3
  • [9] ON CONVECTION CELLS INDUCED BY SURFACE TENSION
    PEARSON, JRA
    [J]. JOURNAL OF FLUID MECHANICS, 1958, 4 (05) : 489 - 500
  • [10] Stability analysis of Rayleigh-Benard convection in a porous medium
    Rajagopal, K. R.
    Saccomandi, G.
    Vergori, L.
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2011, 62 (01): : 149 - 160