1,721,209 research outputs found
Modal and absolute thermal instability in a vertical porous layer
Full text linkThe conduction regime in a vertical porous layer subject to a horizontal temperature gradient is studied. The boundaries are considered as isothermal, with different temperatures, and permeable to the external environment. The linear stability of this basic flow state is analysed by testing the dynamics of the normal modes of perturbation. The numerical solution of the stability eigenvalue problem leads to the determination of the neutral stability condition. Then, the evolution in time of localised wavepacket perturbations is investigated leading to the determination of the threshold to absolute instability
The Horton–Rogers–Lapwood problem for an inclined porous layer with permeable boundaries
No full textA formulation of the Horton–Rogers–Lapwood problem for a porous layer inclined with respect to the horizontal and characterized by permeable (isobaric) boundary conditions is presented. This formulation allows one to recover the results reported in the literature for the limiting cases of horizontal and vertical layer. It is shown that a threshold inclination angle exists which yields an upper bound to a parametric domain where the critical wavenumber is zero. Within this domain, the critical Darcy–Rayleigh number can be determined analytically. The stability analysis is performed for linear perturbations. The solution is found numerically, for the inclination angles above the threshold, by employing a Runge–Kutta method coupled with the shooting method
Anisotropy and the Onset of the Thermoconvective Instability in a Vertical Porous Layer
Full text linkThe thermoconvective instability of the parallel vertical flow in a fluid saturated porous layer bounded by parallel open boundaries is studied. The open boundaries are assumed to be kept at constant uniform pressure while their temperatures are uniform and different, thus forcing a horizontal temperature gradient across the layer. The anisotropic permeability of the porous layer is accounted for by assuming the principal axes to be oriented along the directions perpendicular and parallel to the layer boundaries. A linear stability analysis based on the Fourier normal modes of perturbation is carried out by testing the effect of the inclination of the normal mode wavevector to the vertical. The neutral stability curves and the critical Rayleigh number for the onset of the instability are evaluated by solving numerically the stability eigenvalue problem
Corrigendum to Onset of buoyancy driven convection in an inclined porous layer with an isobaric boundary [International Journal of Heat and Mass Transfer, Vol. 132 (2019) 782–788] (International Journal of Heat and Mass Transfer (2019) 132 (782–788), (S001793101834465X), (10.1016/j.ijheatmasstransfer.2018.11.077))
No full textCorrigendum to Onset of buoyancy driven convection in an inclined porous layer with an isobaric boundary [International Journal of Heat and Mass Transfer, Vol. 132 (2019) 782–788
Convective and absolute instability of horizontal flow in porous media
No full textThe onset of instability in flow systems has a dual nature depending on the dynamics of the growing normal modes. When the time evolution of a wave packet perturbation is tested, the growth of individual Fourier normal modes can be concealed to an observer in the laboratory reference frame. The reason is that the growing mode can be convected away by the basic flow, so that no effective growth is detected for the wave packet. The convective instability just focusses on the dynamics of each Fourier mode of perturbation, disregarding the actual amplitude growth of a wave packet, measured at a given position. When not only the Fourier modes, but all localised wave packets grow in time at a given position, then the instability becomes absolute. The two types of instability are generally distinct. This paper illustrates the transition from convective to absolute instability starting from a simple one-dimensional case. Then, this concept is employed for the stability analysis of a porous medium flow with heating from below. While the one-dimensional flow system is studied analytically, the porous medium flow stability is investigated numerically
Unstable wave-packet perturbations in an advective Cahn-Hilliard process
No full textA study of the perturbation dynamics in a one-dimensional advective Cahn-Hilliard system, characterized by a nonvanishing driving force, is carried out to test the stability of a uniform basic solution. The linear stability of small-amplitude perturbations is analyzed both in the case of normal Fourier modes, with a given wave number, and in the case of wave packets localized in space. The dual nature of the instability, either of convective or absolute type, is studied, revealing that the driving force creates a gap between the parametric threshold to instability of normal modes and that to instability of wave packets. When the driving force is zero, also the gap between such thresholds disappears
Onset of convective instability within an inclined porous layer with a permeable boundary
No full textThe investigation of the thresholds that identify the onset of convective instability in a fluid saturated porous layer is performed. The layer is inclined with respect to the horizontal and the boundaries are held at different uniform temperatures. The layer is also semi-permeable: one boundary is impermeable and the other one is permeable. This configuration yields a basic state characterised by a single convective cell, with zero mass flow rate, that fades for small inclination becoming completely motionless for the horizontal case. Since the central part of this cell is considered, the basic flow is parallel and the basic temperature profile is dominated by conduction. This basic state is perturbed employing small-amplitude disturbances such that the linear stability analysis can be performed. A Squire-type transformation is applied to reduce the complexity of the problem. A numerical procedure is employed to obtain the critical values of the governing parameters
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