Effect of Local Thermal Nonequilibrium on the Stability of Natural Convection in an Oldroyd-B Fluid Saturated Vertical Porous Layer

The effect of local thermal nonequilibrium (LTNE) on the stability of natural convection in a vertical porous slab saturated by an Oldroyd-B fluid is investigated. The vertical walls of the slab are impermeable and maintained at constant but different temperatures. A two-field model that represents the fluid and solid phase temperature fields separately is used for heat transport equation. The resulting stability eigenvalue problem is solved numerically using Chebyshev collocation method as the energy stability analysis becomes ineffective in deciding the stability of the system. Despite the basic state remains the same for Newtonian and viscoelastic fluids, it is observed that the base flow is unstable for viscoelastic fluids and this result is qualitatively different from Newtonian fluids. The results for Maxwell fluid are delineated as a particular case from the present study. It is found that the viscoelasticity has both stabilizing and destabilizing influence on the flow. Increase in the value of interphase heat transfer coefficient Ht, strain retardation parameter �v and diffusivity ratio α portray stabilizing influence on the system while increasing stress relaxation parameter �1 and porosity-modified conductivity ratio γ 3 exhibit an opposite trend. Copyright © 2017 by ASME

On the stability of natural convection in a porous vertical slab saturated with an Oldroyd-B fluid

The stability of the conduction regime of natural convection in a porous vertical slab saturated with an Oldroyd-B fluid has been studied. A modified Darcy�s law is utilized to describe the flow in a porous medium. The eigenvalue problem is solved using Chebyshev collocation method and the critical Darcy�Rayleigh number with respect to the wave number is extracted for different values of physical parameters. Despite the basic state being the same for Newtonian and Oldroyd-B fluids, it is observed that the basic flow is unstable for viscoelastic fluids�a result of contrast compared to Newtonian as well as for power-law fluids. It is found that the viscoelasticity parameters exhibit both stabilizing and destabilizing influence on the system. Increase in the value of strain retardation parameter � 2 portrays stabilizing influence on the system while increasing stress relaxation parameter � 1 displays an opposite trend. Also, the effect of increasing ratio of heat capacities is to delay the onset of instability. The results for Maxwell fluid obtained as a particular case from the present study indicate that the system is more unstable compared to Oldroyd-B fluid. © 2016, Springer-Verlag Berlin Heidelberg

Numerical investigation of electrohydrodynamic instability in a vertical porous layer

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 PrD 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. © 2017 Elsevier Inc

Boundary and inertia effects on the stability of natural convection in a vertical layer of an anisotropic Lapwood�Brinkman porous medium

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. © 2017, Springer-Verlag Wien

Effect of Horizontal Alternating Current Electric Field on the Stability of Natural Convection in a Dielectric Fluid Saturated Vertical Porous Layer

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 Chebyshev collocation method. The critical Grashof number G(c), the critical wave number a(c), and the critical wave speed c(c) are computed for a wide range of Prandtl number Pr, Darcy number Da, the ratio of effective viscosity to the fluid viscosity K, and AC electric Rayleigh number R-ea. Interestingly, the value of Prandtl number at which the transition from stationary to traveling-wave mode takes place is found to be independent of R-ea. 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 R-ea is to destabilize the system. The ratio of viscosities K 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 K. 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

Stability of natural convection in a vertical couple stress fluid layer

The stability of buoyancy-driven parallel shear flow of a couple stress fluid confined between vertical plates is investigated by performing a classical linear stability analysis. The plates are maintained at constant but different temperatures. A modified Orr-Sommerfeld equation is derived and solved numerically using the Galerkin method with wave speed as the eigenvalue. The critical Grashof number Gc, critical wave number ac and critical wave speed cc are computed for wide ranges of couple stress parameter Îc and the Prandtl number Pr. Based on these parameters, the stability characteristics of the system are discussed in detail. The value of Prandtl number, at which the transition from stationary to travelling-wave mode takes place, increases with increasing Î c. The couple stress parameter shows destabilising effect on the convective flow against stationary mode, while it exhibits a dual behaviour if the instability is via travelling-wave mode. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state. © 2014 Elsevier Ltd. All rights reserved

Stability of fluid flow in a Brinkman porous medium-A numerical study

The stability of fluid flow in a horizontal layer of Brinkman porous medium with fluid viscosity different from effective viscosity is investigated. A modified Orr-Sommerfeld equation is derived and solved numerically using the Chebyshev collocation method. The critical Reynolds number Re-c, the critical wave number alpha(c) and the critical wave speed c(c) are computed for various values of porous parameter and ratio of viscosities. Based on these parameters, the stability characteristics of the system are discussed in detail. Streamlines are presented for selected values of parameters at their critical state

Effect of Horizontal AC Electric Field on the Stability of Natural Convection in a Vertical Dielectric Fluid Layer

The stability of buoyancy-driven parallel shear flow of a dielectric fluid confined between differentially heated vertical plates is investigated under the influence of a uniform horizontal AC electric field. The resulting generalized eigenvalue problem is solved numerically using Chebyshev collocation method with wave speed as the eigenvalue. The critical Grashof number Gc, the critical wave number αc and the critical wave speed cc are computed for wide ranges of AC electric Rayleigh number Rea and the Prandtl number Pr. Based on these parameters, the stability characteristics of the system are discussed in detail. It is found that the AC electric Rayleigh number is to instill instability on convective flow against both stationary and travelling-wave mode disturbances. Nonetheless, the value of Prandtl number at which the transition from stationary to travelling-wave mode takes place is found to be independent of AC electric Rayleigh number. The streamlines and isotherms presented demonstrate the development of complex dynamics at the critical state

Weakly Nonlinear Stability Analysis of Triple Diffusive Convection in a Maxwell Fluid Saturated Porous Layer

The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves are found to exist, indicating that three critical thermal Darcy-Rayleigh numbers are required to specify the linear instability criteria. However, another distinguishing feature predicted from that of Newtonian fluids is the impossibility of quasi-periodic bifurcation from the rest state. Besides, the co-dimensional two bifurcation points are located in the Darcy-Prandtl number and the stress relaxation parameter plane. It is observed that the value of the stress relaxation parameter defining the crossover between stationary and oscillatory bifurcations decreases when the Darcy-Prandtl number increases. A cubic Landau equation is derived based on the weakly nonlinear stability analysis. It is found that the bifurcating oscillatory solution is either supercritical or subcritical, depending on the choice of the physical parameters. Heat and mass transfers are estimated in terms of time and area-averaged Nusselt number

The effect of rare regions on a disordered itinerant quantum antiferromagnet with cubic anisotropy

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one loop renormalization group analysis of the effective action shows that for order parameter dimensions $p<4$ the rare regions destroy the conventional critical behavior. For order parameter dimensions $p>4$ the critical behavior is not influenced by the rare regions, it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition in this system.Comment: 6 pages RevTe