Vadasz Number Effects on Convection in a Vertical Rotating Porous Layer, Placed Far from Axis of Rotation, and Subjected to Internal Heat Generation and Centrifugal Jitter

The flow and heat transfer in a rotating vertical porous layer, placed far from the axis of rotation, and subjected to internal heat generation and centrifugal jitter, is considered. The linear stability theory is used to determine the convection threshold, in terms of the critical Rayleigh number. Typical liquids used in engineering applications and heavy liquid metals are used to demonstrate conditions at which the Vadasz number is sufficiently small to warrant the retention of the time derivative in the momentum equation. When considering low amplitude and high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions. In summary, when the Vadasz number is large, centrifugal jitter has no impact on the convection stability criteria. In contrast, when the Vadasz number is small, centrifugal jitter impacts the convection stability criteria.

The Effect of the Vadasz Number on the Onset of Thermal Convection in Rotating Bidispersive Porous Media

The onset of thermal convection in uniformly rotating bidispersive horizontal porous layer, uniformly heated from below, is analyzed. A generalized Darcy equation for the macro-phase is considered to take the Vadasz number into account. It is proved that the presence of the Vadasz number can give rise to oscillatory motion at the loss of stability of thermal conduction solution.

Vadasz Number Effects on Convection in a Horizontal Porous Layer Subjected to Internal Heat Generation and G-Jitter

Flow and heat transfer in a horizontal porous layer subjected to internal heat generation and g-jitter is considered for the Dirichlet thermal boundary condition. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number. For the low amplitude, high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection when the porous layer is heated from below. When the porous layer is cooled from below and heated from above, the vibration has a destabilizing effect in the presence of internal heat generation. It is also demonstrated that when the top and bottoms walls are cooled and rigid/impermeable, the critical Rayleigh number is infinitely large and conduction is the only possible mode of heat transfer. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions.

Effect of Vadasz Number on Magnetoconvection in a Darcy Porous Layer with Concentration Based Internal Heating

In this research article, the effect of Vadasz number on magnetoconvection in a Darcy Porous Layer with concentration based internal heating is studied. The flow is governed by the Oberbeck-Boussineq model for Newtonian fluid. The stability analysis method based on the perturbation of infinitesimal amplitude is carried out using the normal mode analysis. The onset criterion for both the stationary and oscillatory convection on the stability of system is obtained. The analysis examines the effects of pertinent parameters on the stability of the system: magnetic field parameter, solutal Rayleigh number, Lewis number and Vadasz number. The result show that, internal heat parameter, and Lewis number, , hastens the onset of instability in the system, whereas magnetic field, , Vadasz number, and solutal Rayleigh number, delay the onset of instability.

Vadasz Number Influence on Vibration in a Rotating Porous Layer Placed Far Away From the Axis of Rotation

We consider vibration effects on the classical Rayleigh–Be’nard problem and the classical Vadasz (1994, “Stability of Free Convection in a Narrow Porous Layer Subject to Rotation,” Int. Commun. Heat Mass Transfer, 21, pp. 881–890) problem, which includes rotation of a vertical porous layer about the z-axis. In particular, we focus on the influence of the Vadasz number on vibration for small to moderate and large Vadasz numbers. For small to moderate Vadasz numbers, we develop an analogy between the Vadasz problem (Vadasz, 1994, “Stability of Free Convection in a Narrow Porous Layer Subject to Rotation,” Int. Commun. Heat Mass Transfer, 21, pp. 881–890) placed far away from the axis of rotation and classical Rayleigh–Be’nard problem, both of which include the effects of vibration. It is shown here that the stability criteria are identical to the Rayleigh–Be’nard problem with vibration when g∗=ω∗2X0∗. The analysis for the large Vadasz number scaling indicates that a frozen time approximation is appropriate where the effect of vibration is modeled as small variations in the Rayleigh number definition.