Stability of a Buoyant Oldroyd-B Flow Saturating a Vertical Porous Layer with Open Boundaries

The performance of several engineering applications are strictly connected to the rheology of the working fluids and the Oldroyd-B model is widely employed to describe a linear viscoelastic behaviour. In the present paper, a buoyant Oldroyd-B flow in a vertical porous layer with permeable and isothermal boundaries is investigated. Seepage flow is modelled through an extended version of Darcy’s law which accounts for the Oldroyd-B rheology. The basic stationary flow is parallel to the vertical axis and describes a single-cell pattern where the cell has an infinite height. A linear stability analysis of such a basic flow is carried out to determine the onset conditions for a multicellular pattern. This analysis is performed numerically by employing the shooting method. The neutral stability curves and the values of the critical Rayleigh number are evaluated for different retardation time and relaxation time characteristics of the fluid. The study highlights the extent to which the viscoelasticity has a destabilising effect on the buoyant flow. For the limiting case of a Newtonian fluid, the known results available in the literature are recovered, namely a critical value of the Darcy–Rayleigh number equal to 197.081 and a corresponding critical wavenumber of 1.05950.

Thermal convection for a Darcy-Brinkman rotating anisotropic porous layer in local thermal non-equilibrium

The onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under the hypothesis of local thermal non-equilibrium, is analysed. Since the porosity of the medium is assumed to be high, the more suitable Darcy-Brinkman model is adopted. Linear instability analysis of the conduction solution is carried out. Nonlinear stability with respect to $$L^2$$ L 2 -norm is performed in order to prove the coincidence between the linear instability and the global nonlinear stability thresholds. The effect of both rotation and thermal and mechanical anisotropies on the critical Rayleigh number for the onset of instability is discussed.

The effect of controlled vibrations on Rayleigh-Benard convection

The paper presents the results of a numerical study of convective heat transfer in a long horizontal layer heated from below with and without the vibration effect of the lower wall. The simulation was carried out on the basis of solving the Navier-Stokes 2D equations for an incompressible fluid in the Boussinesq approximation. It is shown that the influence of vibrations of the lower heated wall on the wave number of the convective flow roll structure, on the time and on the critical Rayleigh number of convection. The influence of controlled harmonic vibrations of wall on the structure of convective flow in the Rayleigh-Benard problem has been investigated. It is shown that the wave number of the periodic convective structure, the critical Rayleigh number, and the time of occurrence of Rayleigh-Benard convection under the vertical vibration effect on the horizontal layer from the lower wall are reduced.

Effect of Local Thermal Non-Equilibrium On the Stability of the Flow in a Vertical Channel Filled with Nanofluid Saturated Porous Medium

The stability of nanofluid flow in a vertical channel packed with a porous medium is examined for the local thermal non-equilibrium state of the fluid, particle and solid-matrix phases. The effects of Brownian motion along with thermophoresis are incorporated in the nanofluid model. The Darcy-Brinkman model for the flow in a porous medium and three-field model, each representing the fluid, particle and solid-matrix phases separately, for temperature is used. A normal mode analysis is used to obtain the eigenvalue problem for the perturbed state, which is then solved using the Chebyshev spectral collocation technique. The critical Rayleigh number and corresponding wavenumber are presented graphically for the effect of different local thermal non-equilibrium parameters. It is noticed that the influence of LTNE parameters on the convective instability is significant.

Effect of obstacle height on the nanofluid convection patterns inside a hollow square enclosure

This paper contains natural convection of Ag–MgO/water micropolar hybrid nanofluid in a hollow hot square enclosure equipped by four cold obstacles on the walls. The simulations were performed by the lattice Boltzmann method (LBM). The influences of Rayleigh number and volume fraction of nanoparticle on the fluid flow and heat transfer performance were studied. Moreover, the effects of some geometric parameters, such as cold obstacle height and aspect ratio, were also considered in this study. The results showed that when the aspect ratio is not large ([Formula: see text] or 0.4), at low Rayleigh number (103), the two secondary vortices are established in each main vortex and this kind of secondary vortex does not form at high Rayleigh number (106). However, at [Formula: see text], these secondary vortices occur again in the middle two vortices at [Formula: see text], which is similar to that at [Formula: see text]. At [Formula: see text], the critical Rayleigh number, when the dominated mechanism of heat transfer changes from conduction to convection, is 104. However, the critical Rayleigh number becomes 105 at [Formula: see text] or 0.6. When the cold obstacle height increases, the shape of the vortices inside the enclosure changes due to the different spaces. Besides, at [Formula: see text], for different cold obstacle heights, the location of the thermal plume is different, owing to the different shapes of vortices. Accordingly, the average Nusselt number increases by increment of the Rayleigh number, nanoparticle volume fraction, cold obstacle height and aspect ratio.

The Effect of Open Boundaries on the Buoyant Viscoelastic Flow in a Vertical Porous Layer

The Oldroyd–B model for a linear viscoelastic fluid is employed to investigate the buoyant flow in a vertical porous layer with permeable boundaries kept at different uniform temperatures. Seepage flow in the viscoelastic fluid saturated porous layer is modelled through an extended version of Darcy’s law taking into account the Oldroyd–B rheology. The basic stationary flow is parallel to the vertical axis and describes a single–cell vertical pattern where the cell has an infinite vertical height. A linear stability analysis of such a basic flow is carried out to determine the onset conditions for a multicellular pattern. The neutral stability curves and the values of the critical Rayleigh number are evaluated numerically for different retardation time and relaxation time characteristics of the fluid.

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 rotation on double diffusive convection: perspectives from linear stability analysis

Diffusive convection can occur when two constituents of a stratified fluid have opposing effects on its stratification and different molecular diffusivities. This form of convection arises for the particular temperature and salinity stratification in the Arctic Ocean and is relevant to heat fluxes. Previous studies have suggested that planetary rotation may influence diffusive-convective heat fluxes, although the precise physical mechanisms and regime of rotational influence are not well understood. A linear stability analysis of a temperature and salinity interface bounded by two mixed layers is performed here to understand the stability properties of a diffusive-convective system, and in particular the transition from non-rotating to rotationally-controlled heat transfer. Rotation is shown to stabilize diffusive convection by increasing the critical Rayleigh number to initiate instability. In the rotationally-controlled regime, a −4/3 power law is found between the critical Rayleigh number and the Ekman number, similar to the scaling for rotating thermal convection. The transition from non-rotating to rotationally-controlled convection, and associated drop in heat fluxes, is predicted to occur when the thermal interfacial thickness exceeds about 4 times the Ekman layer thickness. A vorticity budget analysis indicates how baroclinic vorticity production is counteracted by the tilting of planetary vorticity by vertical shear, which accounts for the stabilization effect of rotation. Finally, direct numerical simulations yield generally good agreement with the linear stability analysis. This study, therefore, provides a theoretical framework for classifying regimes of rotationally-controlled diffusive-convective heat fluxes, such as may arise in some regions of the Arctic Ocean.

Linear analysis on the onset of thermal convection of highly compressible fluids with variable viscosity and thermal conductivity in spherical geometry: implications for the mantle convection of super-Earths

In this paper, we carried out a series of linear analyses on the onset of thermal convection of highly compressible fluids whose physical properties strongly vary in space in convecting vessels either of a three-dimensional spherical shell or a two-dimensional spherical annulus geometry. The variations in thermodynamic properties (thermal expansivity and reference density) with depth are taken to be relevant for the super-Earths with ten times the Earth’s mass, while the thermal conductivity and viscosity are assumed to exponentially depend on depth and temperature, respectively. Our analysis showed that, for the cases with strong temperature dependence in viscosity and strong depth dependence in thermal conductivity, the critical Rayleigh number is on the order of 108–109, implying that the mantle convection of massive super-Earths is most likely to fall in the stagnant-lid regime very close to the critical condition, if the properties of their mantle materials are quite similar to the Earth’s. Our analysis also demonstrated that the structures of incipient flows of stagnant-lid convection in the presence of strong adiabatic compression are significantly affected by the depth dependence in thermal conductivity and the geometries of convecting vessels, through the changes in the static stability of thermal stratification of the reference state. When the increase in thermal conductivity with depth is sufficiently large, the thermal stratification can be greatly stabilized at depth, further inducing regions of insignificant fluid motions above the bottom hot boundaries in addition to the stagnant lids along the top cold surfaces. We can therefore speculate that the stagnant-lid convection in the mantles of massive super-Earths is accompanied by another motionless regions at the base of the mantles if the thermal conductivity strongly increases with depth (or pressure), even though their occurrence is hindered by the effects the spherical geometries of convecting vessels.

Visualisation and measurement of a laminar boundary layer on the surface of an isothermal section-triangular roof

Natural convection in air over a heated section-triangular roof with a fixed aspect ratio of 0.1 is experimentally investigated. The development of the flow over the roof subject to a range of temperatures is measured by digital interferometry and thermocouples. The experiments present distinct images of the thermal boundary layer, which changes from a quasi-steady to an unsteady state as the surface temperature of the triangular roof increases. Contrary to numerical simulations previously published, the observed flow becomes unsteady, which is very likely influenced by uncontrolled perturbations at the critical Rayleigh number where a pitchfork bifurcation of a steady flow is theoretically expected.