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An investigation of the basic nanoconvective flow to be applied in evaluating the limit of validity of the transient hot wire experimental (THW) method for nanofluids is presented. Analytical solutions for the basic temperature, basic nanoparticles volume fraction, and basic natural convection velocity are being derived and analyzed. These basic solutions are needed in follow-up linear and nonlinear stability analyses aiming to establish the time required for natural convective heat flux to develop and invalidate transient hot wire experimental results. While the first part of the paper presents the current status of knowledge related to the transient hot wire experimental method and the theoretical aspects governing the validity of the method, the second part aims at presenting new results that can provide additional and more accurate conditions for the validity of that experimental method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the basic state, with particular regard to the behaviour of stability thresholds with respect to the relevant physical parameters characterizing the problem. The Chebyshev- τ method and the shooting method are employed and accurately implemented to solve the differential eigenvalue problems arising from linear and nonlinear analyses to determine critical Rayleigh numbers. Via numerical simulations, the stabilizing effect of the upper bounding plane temperature, of the Darcy number and of the interaction coefficient for the heat exchange, is demonstrated. [ABSTRACT FROM AUTHOR]

In the present paper, the effect of the Vadasz inertia term on the onset of convective motions for a Darcy–Brinkman model is investigated. It is proved that this term leads to the possibility for oscillatory convection to occur. Hence, convection can occur via either oscillatory or steady motions. It is proved analytically that the onset of steady convection is not affected by the Vadasz term, while oscillatory convection is favoured by it. Moreover, conditions to rule out the occurrence of oscillatory convection are determined numerically. The influence of rotation, interaction coefficient and mechanical and thermal anisotropies on the onset of instability is investigated, both analytically and numerically. [ABSTRACT FROM AUTHOR]

The present paper investigates penetrative convection in a bi‐disperse porous medium. In particular, penetrative convection is modeled via a quadratic dependence on the temperature for the fluid density. For the problem under examination, convection can occur only through a secondary stationary motion since the validity of the principle of exchange of stabilities is proved. Via linear instability analysis of the conduction solution, the critical Rayleigh number for the onset of penetrative convection is determined. Moreover, the nonlinear stability is investigated via weighted energy method. In order to analyze the behavior of the stability and instability thresholds, numerical simulations are performed through Chebyshev‐ τ$$ \tau $$ method, proving the stabilizing effect of the upper boundary layer temperature on the onset of convective motion. [ABSTRACT FROM AUTHOR]

Thermal convection in a fluid saturating an anisotropic porous medium in local thermal nonequilibrium (LTNE) is investigated, with specific attention to the effect of variable viscosity on the onset of convection. Many fluids show a remarkable dependence of viscosity on temperature that cannot be neglected. For this reason, we take into account a fluid whose viscosity decreases exponentially with depth, according to Straughan (Acta Mech. 61:59–72, 1986), Torrance and Turcotte (J. Fluid Mech. 47(1):113–125, 1971). The novelty of this paper is to highlight how variable viscosity coupled with the LTNE assumption affects the onset of convection. A numerical procedure shows the destabilising effect of depth-dependent viscosity. Moreover, it comes out that the LTNE hypothesis makes the influence of viscosity more intense. Linear instability analysis of the conduction solution is carried out by means of the Chebyshev-tau method coupled to the QZ algorithm, which provides the critical Rayleigh number for the onset of convection in a straightforward way. The energy method is employed in order to study the nonlinear stability. The optimal result of coincidence between the linear instability threshold and the global nonlinear stability threshold is obtained. The influence of anisotropic permeability and conductivity, weighted conductivity ratio, and interaction coefficient on the onset of convection is highlighted. [ABSTRACT FROM AUTHOR]

The periodic solution has period I T i = 2 I i / I i , where HT ht is the angular frequency. [Extracted from the article]

In this paper, the instability of a vertical fluid motion, or throughflow, is investigated in a horizontal bidisperse porous layer that is uniformly heated from below. By means of the order-1 Galerkin approximation method, the critical Darcy–Rayleigh number for the onset of steady instability is determined in closed form. The coincidence between the linear instability threshold and the global nonlinear stability threshold, in the energy norm, is shown. [ABSTRACT FROM AUTHOR]

Thermal convection in a horizontally isotropic bi-disperse porous medium (BDPM) uniformly heated from below is analysed. The combined effects of uniform vertical rotation and Brinkman law on the stability of the steady state of the momentum equations in a BDPM are investigated. Linear and nonlinear stability analysis of the conduction solution is performed, and the coincidence between linear instability and nonlinear stability thresholds in the L 2 -norm is obtained. [ABSTRACT FROM AUTHOR]

A reaction–diffusion ecoepidemic model of predator–prey type with a transmissible disease spreading among the predator species only is considered. The longtime behavior of solutions is analyzed and, in particular, absorbing sets in the phase space are determined. Conditions guaranteeing the non existence of non-constant equilibria have been found. Linear and non-linear stability conditions for biologically meaningful equilibria are determined. [ABSTRACT FROM AUTHOR]

A reaction-diffusion system modeling cholera epidemic in a non-homogeneously mixed population is introduced. The interaction between population and toxigenic Vibrio cholerae concentration in contaminated water has been taken into account. The existence of biologically meaningful equilibria is investigated together with their linear and nonlinear stability. Using the data collected during the Haiti cholera epidemic, a numerical simulation is performed. [ABSTRACT FROM AUTHOR]

A reaction-diffusion system modeling the predation between two species is analyzed in the case in which the predators have to search, share and compete for food. The boundedness and uniqueness of the solutions is proved and conditions guaranteeing the global nonlinear asymptotic stability of the positive equilibrium point have been found. These conditions improve those ones present in the existing literature. [ABSTRACT FROM AUTHOR]

Abstract: Non-linear stability of vertical throughflows in porous layers, uniformly heated and salted from below, is analyzed. The definitively boundedness of the solutions (existence of absorbing sets in the phase space) is proved. Conditions guaranteeing global non-linear asymptotic stability have been found. In closed form, the critical Rayleigh number has been found. [Copyright &y& Elsevier]

Abstract: The long-time behavior of triply fluid mixtures saturating horizontal porous layers uniformly rotating around the vertical axis, according to the Brinkman law (holding for large pores), is investigated. The most destabilizing case of layers heated from below and salted from above by two salts, is considered. The ultimately boundedness of the solutions (existence of absorbing sets) is shown. A necessary and sufficient condition guaranteeing the global non-linear asymptotic -stability of the conduction solution is obtained. [Copyright &y& Elsevier]

The linear and nonlinear stability analysis of the motionless state (conduction solution) and of a vertical throughflow in an anisotropic porous medium is performed. In particular, the effect of a nonhomogeneous porosity and a constant anisotropic thermal diffusivity have been taken into account. [ABSTRACT FROM AUTHOR]

The onset of convection in anisotropic porous medium in local thermal non-equilibrium regime is studied. The Cattaneo's law to describe heat propagation in solid phase is allowed, while the Fourier's law in fluid phase is employed. Linear and nonlinear stability of the conduction solution are performed and the critical Rayleigh numbers in a closed form are obtained. The influence of second sound effect, inter-phase heat transfer and anisotropy of the medium on the onset of instability have been analysed via numerical simulations, too. • The influence of Cattaneo's law on the onset of convection is highlighted. • Conditions for the onset of steady and oscillatory convection have been determined. • The influence of inter-phase heat transfer and Darcy number on convection is analysed • Nonlinear stability analysis with respect to L 2-norm has been performed. [ABSTRACT FROM AUTHOR]

A correction to the article "Influence of diffusion on the stability of equilibria in a reaction-diffusion system modeling cholera dynamic," that was published in a previous issue of the journal is presented.

In the present article, a model for penetrative convection in a fluid-saturated inclined porous medium is analyzed. Penetrative convection occurs when an unstably stratified fluid moves into a stably stratified region. In this study, it will be shown that the inclination of the layer plays a relevant role for the penetrative thermal convection of a fluid-saturated porous medium. The results reported in the literature for the limiting case of horizontal layer are recovered and the numerical results for the linear instability, obtained via the Chebyshev- τ method, show that the most destabilizing perturbations are the longitudinal and, as expected, the transverse ones destabilize only up to a certain critical inclination angle of the layer. Moreover, in the numerical analysis of the three-dimensional perturbations, we show that the longitudinal perturbations are the most destabilizing not only with respect to the transverse but also with respect to any general perturbation. We also give nonlinear stability results for the longitudinal perturbations via the weighted energy method. • Influence of upper layer temperature on penetrative convection is highlighted. • Most destabilizing effect of the longitudinal perturbations is found. • Critical inclination angle for transverse perturbations is determined. • Conditions for the onset of steady convection are provided. • Global nonlinear stability analysis of conduction solution has been performed. [ABSTRACT FROM AUTHOR]