Throughflow and Gravity Modulation Effects on Double Diffusive Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium

Weakly nonlinear stability analysis has been performed using the finite amplitude Ginzburg-Landau model. The layer is oscillating vertically in sinusoidal manner. Using the finite amplitude analysis heat mass/transfer is quantified in the system. The disturbances of the flow are expanded in power series of small parameter. In addition to the modulation, the effect of throughflow is discussed on heat/mass transfer in the system. The values of viscoelastic parameters are considered in this paper are λ1 > λ2 and Γ < 1 to validate the problem. The time relaxation parameter λ1 has destabilizing effect, while the time retardation parameter λ2 has stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat/mass transports have been analyzed and depicted graphically. The studies establish that the heat/mass transports can be controlled effectively by g-jitter and throughflow. Further, it is found that better results may obtain for an oscillatory mode of convection.

Chaotic Convection of Viscoelastic Fluid in Porous Medium Under G-Jitter

The present article aims at investigating the effect of gravity modulation on chaotic convection of a viscoelastic fluid in porous media. For this, the problem is reduced into Lorenz system (non-autonomous) by employing the truncated Galerkin expansion method. The system shows transitions from periodic to chaotic behavior on increasing the scaled Rayleigh number R. The amplitude of modulation advances the chaotic nature in the system while the frequency of modulation has a tendency to delay the chaotic behavior which is in good agreement with the results due to [1]. The behavior of the scaled relaxation and retardation parameter on the system is also studied. The phase portrait and time domain diagrams of the Lorenz system for suitable parameter values have been used to analyze the system.

MAGNETO-CONVECTIVE INSTABILITY IN A HORIZONTAL VISCOELASTIC NANOFLUID SATURATED POROUS LAYER

Nanofluids have been shown experimentally to have high thermal conductivity. In this study, the convective instabilities in a horizontal viscoelastic nanofluid saturated by porous layer under the influences of gravity and magnetic field are investigated. The linear stability theory is used for the transformation of the partial differential equations to system of ordinary differential equations through infinitesimal perturbations, scaling, linearization and method of normal modes with two-dimensional periodic waves. The system is solved analytically for the closed form solution of the thermal Darcy-Rayleigh number by using the Galerkin-type weighted residuals method to investigate the onset of both stationary and oscillatory convection. The effects of the scaled stress relaxation parameter, scaled strain retardation parameter and Chandrasekhar number on the stability of the system are investigated. The scaled strain retardation parameter stabilizes while the scaled stress relaxation parameter destabilizes the nanofluid system. The system in the presence of magnetic field is more stable than the system in the absence of magnetic field.

Research on the Migration of Naphthalene in the Typical Aquifer Medium in a Petroleum Contaminated Field

Through the column simulation experiments, this paper researched on the naphthalene migration in the typical aquifer media-gravel sand and coarse sand in a petroleum contaminated field. The research also quantified the retardation of the two medium to the important petroleum component-naphthalene, by giving the retardation parameter after the chlorine breakthrough experiment. The results showed that the migration of naphthalene in the medium is not only influenced by the convection and the dispersion, but also the adsorption and the biodegradation, which is much stronger in the coarse sand than it is in the gravel sand.

Elastic Effects on Rayleigh-Be´nard-Marangoni Convection in Liquids With Temperature-Dependent Viscosity

A linear stability analysis of convection in viscoelastic liquids with temperature-dependent viscosity is studied using normal modes and Galerkin method. Stationary convection is shown to be the preferred mode of instability when the ratio of strain retardation parameter to stress relaxation parameter (elasticity ratio) is greater than unity. When the ratio is less than unity the possibility of oscillatory convection is shown to arise. Oscillatory convection is studied numerically for Rivlin-Ericksen, Walters B′, Maxwell and Jeffreys liquids by considering free-free and rigid-free isothermal/adiabatic boundaries. It is found that there is a tight coupling between the Rayleigh and Marangoni numbers, with an increase in one resulting in a decrease in the other. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to Jeffreys description whereas the Rivlin-Ericksen and Walters B′ liquids are comparatively more stable. Rigid-free adiabatic boundary combination is found to give rise to a most stable system, whereas the free isothermal free adiabatic combination gives rise to a most unstable system. The problem has applications in non-isothermal systems having viscoelastic liquids as working media.

Re-entrant corner flows of Oldroyd-B fluids

The method of matched asymptotic expansions is used to construct solutions for the planar steady flow of Oldroyd-B fluids around re-entrant corners of angles π / α (1/2≤ α <1). Two types of similarity solutions are described for the core flow away from the walls. These correspond to the two main dominant balances of the constitutive equation, where the upper convected derivative of stress either dominates or is balanced by the upper convected derivative of the rate of strain. The former balance gives the incompressible Euler or inviscid flow equations and the latter balance the incompressible Navier–Stokes equations. The inviscid flow similarity solution for the core is that first derived by Hinch (Hinch 1993 J. Non-Newtonian Fluid Mech. 50 , 161–171) with a core stress singularity that depends upon the corner angle and radial distance as O ( r −2(1− α ) ) and a velocity behaviour that vanishes as O ( r α (3− α )−1 ). Extending the analysis of Renardy (Renardy 1995 J. Non-Newtonian Fluid Mech. 58 , 83–39), this outer solution is matched to viscometric wall behaviour for both upstream and downstream boundary layers. This structure is shown to hold for the majority of the retardation parameter range. In contrast, the similarity solution associated with the Navier–Stokes equations has a velocity behaviour O ( r λ ) where λ ∈(0,1) satisfies a nonlinear eigenvalue problem, dependent upon the corner angle and an associated Reynolds number defined in terms of the ratio of the retardation and relaxation times. This similarity solution is shown to hold as an outer solution and is matched into stress boundary layers at the walls which recover viscometric behaviour. However, the matching is restricted to values of the retardation parameter close to the relaxation parameter. In this case the leading order core stress is Newtonian with behaviour O ( r −(1− λ ) ).

OSCILLATORY CONVECTION IN VISCOELASTIC, FERROMAGNETIC/DIELECTRIC LIQUIDS

Oscillatory convection in viscoelastic ferromagnetic and dielectric liquids of the Rivlin-Ericksen, Maxwell and Oldroyd types is studied analytically by considering free-free, isothermal boundaries with idealized conditions on the magnetic / electric potential. The linear theory reveals the stabilizing nature of the strain retardation parameter and the destabilizing nature of the stress relaxation and magnetization / dielectric parameters. The Maxwell liquids are found to be more unstable than the one subscribing to the Oldroyd description whereas the Rivlin-Ericksen liquid is comparatively more stable. The results have implications in many non-isothermal applications of ferromagnetic and dielectric liquids especially in energy conversion devices.