UNCONDITIONAL NONLINEAR STABILITY FOR TEMPERATURE-DEPENDENT DENSITY FLOW IN A POROUS MEDIUM

2003 ◽  
Vol 13 (02) ◽  
pp. 207-220 ◽  
Author(s):  
MAGDA CARR
Keyword(s):  
Porous Medium ◽  
Nonlinear Stability ◽  
Saturated Porous Medium ◽  
Unconditional Stability ◽  
Nonlinear Stability Analysis ◽  
Temperature Dependent ◽  
Density Flow ◽  
Unconditional Nonlinear Stability ◽  
Dependent Density ◽  
Drag Term

A nonlinear stability analysis of thermal convection in a saturated porous medium is presented. Density is assumed to have a cubic temperature dependence and the equations of flow in the porous medium are described via Darcy's law with a Forchheimer drag term. Unconditional stability is established using L3 and L4 norms and it is shown that L2 theory is insufficient to obtain similar results. Previous authors have established conditional nonlinear stability but we believe this is the first analysis that addresses the important problem of unconditional stability for the system in hand.

A nonlinear stability analysis in a double-diffusive magnetized ferrofluid with magnetic-field-dependent viscosity saturating a porous medium

2009 ◽  
Vol 87 (6) ◽  
pp. 659-673 ◽  
Author(s):  
Sunil ◽  
Amit Mahajan
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nonlinear Stability ◽  
Stability Result ◽  
Darcy Number ◽  
Linear Instability ◽  
Nonlinear Stability Analysis ◽  
Field Dependent ◽  
Magnetized Ferrofluid ◽  
Mfd Viscosity

A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic-field-dependent (MFD) viscosity saturating a porous medium, in the stress-free boundary case. The mathematical emphasis is on how to control the nonlinear terms caused by the magnetic-body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that, in case of a non-ferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of the magnetic parameter, M3; solute gradient, Sf; Darcy number, Da; and MFD viscosity parameter, δ; on the subcritical instability region has also been analyzed.

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