1,721,039 research outputs found
Unstable mixed convection in an inclined porous channel with uniform wall heat flux
No full textThe aim of this paper is to analyse the onset of convective instability in a plane porous channel inclined
to the horizontal. A net upslope or downslope flow is considered, so that mixed convection takes place
as caused by the uniform and symmetric heat fluxes prescribed on the impermeable bounding walls.
The thermoconvective instability of the basic flow is studied versus small-amplitude wavelike per-
turbations. The hybrid analytical-numerical technique adopted in this paper, in order to track and
illustrate the parametric changes of neutral stability curves, is Galerkin’s method of weighted resid-
uals. Numerical values at significant points on the neutral stability curves are obtained by employing
an accurate Runge-Kutta solver combined with the shooting method
Onset of buoyancy driven convection in an inclined porous layer with an isobaric boundary
No full textThe linear stability analysis of a fluid saturated porous layer is carried out. The porous layer is inclined to the horizontal and is infinitely wide. One boundary of the layer is permeable while the other one is impermeable. The two boundaries are subject to different temperatures, so that convective instability may arise when such a temperature difference exceeds a threshold value. The basic state whose stability is studied consists of a single cell with no net mass flow rate. The critical values of the governing parameters are computed numerically and are presented as functions of the inclination angle. The threshold relative to the horizontal layer recovers the results already present in the literature. The inclination angle comes out to be a stabilising parameter such that the vertical layer cannot become unstable
Corrigendum to: The Horton-Rogers-Lapwood problem for an inclined porous layer with permeable boundaries
No full text[This corrects the article DOI: 10.1098/rspa.2018.0021.]
Instability of Combined Forced and Free Flow in an Inclined Porous Channel
No full textThe aim of this paper is to analyze the onset of convective instability in a plane porous channel inclined to the horizontal. A net upslope or downslope flow is considered, so that mixed convection takes place as caused by the uniform and symmetric heat fluxes prescribed on the impermeable bounding walls. The thermoconvective instability of the basic flow is studied versus small-amplitude wavelike perturbations. The hybrid analytical–numerical technique adopted in this paper, in order to track and illustrate the parametric changes of neutral stability curves, is Galerkin's method of weighted residuals. Numerical values at significant points on the neutral stability curves are obtained by employing an accurate Runge–Kutta solver combined with the shooting method
Marangoni convection of a viscous fluid over a vibrating plate
No full textThis research presents a new insight into Marangoni convection through investigating, both numerically and analytically, the surface tension driven instability activated by a coupled effect of a vibrating plate and viscous dissipation. A horizontal, thin fluid layer is bounded from below by an impermeable, adiabatic plate that vibrates in the horizontal direction. The upper boundary is modelled by a free surface subject to a thermal boundary condition of the third kind (Robin). The internal heat generation due to viscous dissipation yields a vertical, potentially unstable temperature gradient. The linear stability analysis of the stationary terms of the basic state is performed. The perturbed flow, in the form of plane waves, is superimposed onto the basic state. The obtained system of ordinary differential equations is solved numerically by means of the Runge-Kutta method coupled with the shooting method. For the two limiting cases, the isothermal upper boundary and adiabatic upper boundary, the analytical solutions of the eigenvalue problem are obtained. The values of the critical parameter, which identifies the threshold for the onset of Marangoni convection, are presented
Onset of convection in a non-Newtonian viscous flow through a horizontal porous channel
No full textAn impermeable horizontal fluid saturated porous layer is studied with respect to the onset of thermal convection. The saturating fluid is a Ostwald-de Waele type of non-Newtonian fluid. The viscous dissipation is the only heat source present inside the layer. A basic throughflow whose direction is arbitrary in the horizontal plane occurs. The basic flow produces, by means of viscous dissipation, a basic non-uniform vertical temperature gradient. The lâinear stability analysis of the basic state is carried out. The critical values are obtained as functions of the magnitude and of the inclination of the basic throughflow and as functions of the power-law index. The identification of the most unstable mode is performed: while for pseudoplastic fluids the most unstable modes are transverse rolls, for dilatant fluids the most unstable modes can be either longitudinal or transverse rolls
Convective to Absolute Instability Transition in a Horizontal Porous Channel with Open Upper Boundary
No full textA linear stability analysis of the parallel uniform flow in a horizontal channel with open upper boundary is carried out. The lower boundary is considered as an impermeable isothermal wall, while the open upper boundary is subject to a uniform heat flux and it is exposed to an external horizontal fluid stream driving the flow. An eigenvalue problem is obtained for the two-dimensional transverse modes of perturbation. The study of the analytical dispersion relation leads to the conditions for the onset of convective instability as well as to the determination of the parametric threshold for the transition to absolute instability. The results are generalised to the case of three-dimensional perturbations
A new hydrodynamic boundary condition simulating the effect of rough boundaries on the onset of Rayleigh-Bénard convection
No full textThis paper introduces a new hydrodynamic boundary condition which enables the simulation of the effects caused by rough boundaries. The classical Rayleigh-Bénard stability analysis is performed here to investigate the onset of thermal convection in a parallel-plate channel with rough boundaries. The hydrodynamic boundary conditions are modified, from the classical treatment, in order to consider channel boundaries characterised by non-negligible roughness. This roughness is simulated as a shallow fluid saturated porous medium and the Saffman interface condition is thus employed to model the hydrodynamic boundary conditions. The normal mode method is employed and the obtained eigenvalue problem is solved numerically. The Principle of Exchange of Stabilities is proved and the critical values of the Rayleigh number and of the wave number are obtained
A new mechanism for buoyancy driven convection in pulsating viscous flows: A theoretical study
No full textA new mechanism for the onset of thermal convection is proposed. This mechanism is the result of the interaction between a pulsating flow, viscous dissipation, and buoyancy within a channel. The study considers a Newtonian fluid moving inside an infinitely wide horizontal channel bounded by impermeable, rigid plates. The basic flow is characterized by a pulsating pressure gradient. Viscous dissipation acts as an internal heat source which produces a potentially unstable basic temperature gradient. The heat source has a vertical non uniform distribution inside the channel. This configuration is investigated with respect to the onset of buoyancy driven convection. The basic state fields are solved analytically by expanding them in series as functions of the pulsating frequency. In order to perform the linear stability analysis, an arbitrarily small perturbation is superimposed upon the basic state order zero solution. The normal mode method is employed and an ordinary differential eigenvalue problem is obtained. The perturbations were found to have zero angular frequency and thus the resonance phenomena between the basic flow and the perturbations can be neglected. The critical values of the governing parameter are obtained by solving the eigenvalue problem numerically. A growth rate analysis of the possibly unstable configurations relative to the most unstable mode is performed. The present study proves, theoretically, that a pulsating flow can undergo thermal convection. A future experimental study is suggested to validate the proposed instability mechanism
Marangoni instability of a liquid film flow with viscous dissipation
No full textA linear stability analysis of a thin liquid film flowing over a plate is performed. The plate is considered as
impermeable and adiabatic. The upper surface of the film is assumed to be a free boundary with a non-negligible
surface tension, characterized by a Robin thermal boundary condition. The thermoconvective instability is
generated by the interplay between the heating due to viscous dissipation and the temperature-dependent surface
tension at the free boundary. A basic parallel flow, arbitrarily oriented, is assumed and the basic temperature
profile is determined analytically. In order to investigate the linear stability of the system, the normal mode method
is employed. A system of ordinary differential equations defining an eigenvalue problem is thus obtained. The
case of longitudinal rolls, where the base flow velocity is parallel to the axis rolls, is solved both analytically
and numerically. Other possible inclinations of the base flow are investigated by means of a numerical procedure
based on combining the Runge-Kutta and the shooting methods
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