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The hydrodynamic stability against small disturbances of plane Couette flow through an incompressible fluid-saturated fixed porous medium between two parallel rigid plates is investigated. The fluid flow occurs because of moving upper and lower plates with a constant speed in the opposite directions, and it is described by using the Brinkman-extended Darcy model with fluid viscosity different from the Brinkman viscosity. The resulting stability eigenvalue problem is solved numerically using the Chebyshev collocation method. The instigation of instability has been determined accurately by computing the critical Brinkman–Reynolds number as a function of the Darcy–Reynolds number. A comparative study between the plane porous-Poiseuille flow and the plane porous-Couette flow has been carried out, and the similarities and the differences are highlighted. For the Darcy and the inviscid fluid cases, the stability of fluid flow is analyzed analytically and found that the flow is always stable. [ABSTRACT FROM AUTHOR]

The electrohydrodynamic instability of a vertical dielectric fluid saturated Brinkman porous layer whose vertical walls are maintained at different temperatures is considered. An external AC electric field is applied across the vertical porous layer to induce an unstably stratified electrical body force. The stability eigenvalue equation is solved numerically using the Chebyshev collocation method. The presence of inertia is found to instill instability on the system and the value of modified Darcy–Prandtl number Pr D at which the transition from stationary to travelling-wave mode takes place is independent of the AC electric field but increases considerably with an increase in the value of Darcy number Da . The presence of AC electric field promotes instability but its effect is found to be only marginal. Although the flow is stabilizing against stationary disturbances with increasing Da , its effect is noted to be dual in nature if the instability is via travelling-wave mode. The streamlines and isotherms for various values of physical parameters at their critical state are presented and analyzed. Besides, energy norm at the critical state is also computed and found that the disturbance kinetic energy due to surface drag, viscous force and dielectrophoretic force have no significant effect on the stability of fluid flow. [ABSTRACT FROM AUTHOR]

The stability of natural convection in a fluid-saturated vertical anisotropic porous layer is investigated. The vertical rigid walls of the porous layer are maintained at different constant temperatures, and anisotropy in both permeability and thermal diffusivity is considered. The flow in the porous medium is described by the Lapwood-Brinkman model, and the stability of the basic flow is analysed numerically using Chebyshev collocation method. The presence of inertia is to inflict instability on the system and in the absence of which the system is always found to be stable. The mechanical and thermal anisotropies exhibit opposing contributions on the stability characteristics of the system. The mode of instability is interdependent on the values of Prandtl number and thermal anisotropy parameter, while it remains unaltered with the mechanical anisotropy parameter. The effect of increasing Prandtl and Darcy numbers shows a destabilizing effect on the system. Besides, simulations of secondary flow and energy spectrum have been analysed for various values of physical parameters at the critical state. [ABSTRACT FROM AUTHOR]

A classical linear stability theory is applied to emphasize the effect of inertia on the stability of buoyancy-driven parallel shear flow in a vertical layer of porous medium. The Lapwood-Brinkman model with fluid viscosity different from effective viscosity is used to describe the flow in a porous medium. The resulting eigenvalue problem is solved numerically using the Chebyshev collocation method. The critical Darcy-Rayleigh number $$R_\mathrm{Dc} $$ , the critical wave number $$a_\mathrm{c}$$ and the critical wave speed $$c_\mathrm{c}$$ are computed over a wide range of values of the Darcy-Prandtl number $$Pr_\mathrm{D}$$ and the Darcy number $${\tilde{D}}a$$ . Depending on the choice of physical parameters, instability occurs due to the presence of inertia. The value of $$Pr_\mathrm{D}$$ at which the transition from stationary to traveling-wave mode instability takes place increases with decreasing $${\tilde{D}}a$$ . Besides, the effect of decreasing $${\tilde{D}}a$$ shows destabilizing effect if the instability is via stationary mode, and on the contrary, it exhibits a dual behavior if the instability is through traveling-wave mode. The streamlines and isotherms presented herein demonstrate the development of complex dynamics at the critical state. In the energy spectrum, transition of instability from one type to another is found to take place as a function of $$Pr_\mathrm{D}$$ . The disturbance kinetic energy due to surface drag and viscous force plays no significant role in the stability of flow throughout the domain of $$Pr_\mathrm{D}$$ considered. [ABSTRACT FROM AUTHOR]

The stability of the conduction regime of natural convection in an electrically conducting fluid saturated porous vertical slab is investigated in the presence of a uniform external transverse magnetic field. The flow in the porous medium is described by modified Brinkman-extended Darcy equation with fluid viscosity different from effective viscosity. The boundaries of the vertical porous slab are assumed to be rigid-isothermal and electrically non-conducting. The resulting stability equations are solved numerically using Galerkin method. The critical Grashof number G c , the critical wave number α c and the critical wave speed c c are computed for a wide range of porous parameter σ p , the ratio of effective viscosity to the fluid viscosity Λ , the Prandtl number P r and the Hartmann number M . Based on these parameters, the stability characteristics of the system are discussed in detail. The presence of advective inertia is to instill instability on the flow in a porous medium and found that the magnetic field, porous parameter and ratio of viscosities have a stabilizing effect on both stationary and oscillatory wave instabilities. Besides, the value of P r at which transition occurs from stationary to oscillatory mode of instability decreases with increasing M , σ p and Λ . [ABSTRACT FROM AUTHOR]

The stability of natural convection in a dielectric fluid-saturated vertical porous layer in the presence of a uniform horizontal AC electric field is investigated. The flow in the porous medium is governed by Brinkman-Wooding-extended-Darcy equation with fluid viscosity different from effective viscosity. The resulting generalized eigenvalue problem is solved numerically using the Chehyshev collocation method. The critical Grashof number Gc the critical wave number ac and the critical wave speed Cc are computed for a wide range of Prandtl number Pr. Darcy number Da, the ratio of effective viscosity to the fluid viscosity A, and AC electric Rayleigh number Rea. Interestingly, the value of Prandtl number at which the transition from stationary to traveling-wave mode takes place is found to he independent of Rea. The interconnectedness of the Darcy number and the Prandtl number on the nature of modes of instability is clearly delineated and found that increasing in Da and Rea is to destabilize the system. The ratio of viscosities A shows stabilizing effect on the system at the stationary mode, but to the contrary, it exhibits a dual behavior once the instability is via traveling-wave mode. Besides, the value of Pr at which transition occurs from stationary to traveling-wave mode instability increases with decreasing A. The behavior of secondary flows is discussed in detail for values of physical parameters at which transition from stationary to traveling-wave mode takes place. [ABSTRACT FROM AUTHOR]