0000000000002015
AUTHOR
L. Storesletten
Viscous dissipation and thermoconvective instabilities in a horizontal porous channel heated from below
Accepted version of av article from the journal: International Journal of Thermal Sciences. Published version available on Science Direct: http://dx.doi.org/10.1016/j.ijthermalsci.2009.10.010 A linear stability analysis of the basic uniform flow in a horizontal porous channel with a rectangular cross section is carried out. The thermal boundary conditions at the impermeable channel walls are: uniform incoming heat flux at the bottom wall, uniform temperature at the top wall, adiabatic lateral walls. Thermoconvective instabilities are caused by the incoming heat flux at the bottom wall and by the internal viscous heating. Linear stability against transverse or longitudinal roll disturbances …
Linear instability of mixed convection of cold water in a porous layer induced by viscous dissipation
Accepted version of an article published in the journal: International Journal of Thermal Sciences, Elsevier Published version available on Science Direct: http://dx.doi.org/10.1016/j.ijthermalsci.2008.06.012 An analysis of linear stability of the stationary laminar Darcy flow in a horizontal porous layer is performed. The porous layer is saturated with cold water. The upper plane boundary is assumed to be subject to heat transfer with finite conductance to an environment at the temperature of maximum density of cold water. The lower plane boundary is adiabatic. Convective instabilities are caused by flow viscous dissipation, inducing a basic temperature distribution that decreases in the u…
Onset of convection in a porous rectangular channel with external heat transfer to upper and lower fluid environments
Published version of an article in the journal: Transport in Porous Media. Also available from the publisher at: http://dx.doi.org/10.1007/s11242-012-0018-9 The conditions for the onset of convection in a horizontal rectangular channel filled with a fluid saturated porous medium are studied. The vertical sidewalls are assumed to be impermeable and adiabatic. The horizontal upper and lower boundary walls are considered as impermeable and subject to external heat transfer, modelled through a third-kind boundary condition on the temperature field. The external fluid environments above and below the channel, kept at different temperatures, provide the heating-from-below mechanism which may lead…
Convective Instability in a Horizontal Porous Channel with Permeable and Conducting Side Boundaries
Published version of an article in the journal: Transport in Porous Media. Also available on Science Direct: http://dx.doi.org/10.1007/s11242-013-0198-y The stability analysis of the motionless state of a horizontal porous channel with rectangular cross-section and saturated by a fluid is developed. The heating from below is modelled by a uniform flux, while the top wall is assumed to be isothermal. The side boundaries are considered as permeable and perfectly conducting. The linear stability of the basic state is studied for the normal mode perturbations. The principle of exchange of stabilities is proved, so that only stationary normalmodes need to be considered in the stability analysis.…
Adiabatic eigenflows in a vertical porous channel
AbstractThe existence of an infinite class of buoyant flows in a vertical porous channel with adiabatic and impermeable boundary walls, called adiabatic eigenflows, is discussed. A uniform heat source within the saturated medium is assumed, so that a stationary state is possible with a net vertical through-flow convecting away the excess heat. The simple isothermal flow with uniform velocity profile is a special adiabatic eigenflow if the power supplied by the heat source is zero. The linear stability analysis of the adiabatic eigenflows is carried out analytically. It is shown that these basic flows are unstable. The only exception, when the power supplied by the heat source is zero, is th…
On the thermal instability in a horizontal rectangular porous channel heated from below by a constant flux
Published version of an article in the journal: Journal of Physics: Conference Series. Also available from the publisher at: http://dx.doi.org/10.1088/1742-6596/501/1/012003 Open Access The onset of thermoconvective instability in a rectangular horizontal channel filled with a fluid-saturated porous medium is studied. The channel is heated from below with a constant flux. The top wall is maintained at a uniform constant temperature, while the lateral boundaries are permeable and perfectly conducting. The stability of the basic motionless state is analysed with respect to small-amplitude disturbances. The eigenvalue problem for the neutral stability condition is solved analytically for the n…
Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation
The onset of convection in an inclined porous layer which is heated internally by a uniform distribution of heat sources is considered. We investigate the combined effects of inclination, anisotropy and internal heat generation on the linear instability of the basic parallel flow. When the Rayleigh number is sufficiently large, instability occurs and a convective motion is set up. It turns out that the preferred motion at convection onset depends quite strongly on the anisotropy ratio, &xi
The onset of convection in a two-layered porous medium with anisotropic permeability
We consider convection in a horizontal porous layer of uniform thickness which is heated from below and which is composed of two anisotropic sublayers with principal axes lying in the three coordinate directions. The aim is to determine criteria for the onset of convection by finding the critical Rayleigh number, wavenumber and roll orientation relative to the coordinate axes. The full set of nondimensional parameters has at least six members even when the sublayers are considered to be thermally isotropic, and therefore, we select some special cases in order to illuminate the type of qualitative behaviour which may be expected. One such case is where the anisotropic sublayers are identical…
Onset of convective rolls in a circular porous duct with external heat transfer to a thermally stratified environment
A horizontal circular duct filled with a fluid saturated porous medium is studied. The external wall is assumed to exchange heat with an external environment thermally stratified in the vertical direction. The external heat transfer is modeled through a third kind boundary condition, and a Biot number associated with the external heat transfer coefficient is defined. The linear stability of the basic state where the velocity field is zero is studied numerically. The condition of neutral stability is determined, by solving the system of elliptic governing equations for the disturbances through a Galerkin finite-element method. The neutral stability curves, together with the critical values o…
Linear instability of the vertical throughflow in a horizontal porous layer saturated by a power-law fluid
Abstract The effects of the vertical throughflow of a non-Newtonian power-law fluid on the onset of convective instability in a horizontal porous layer are investigated. The extended Darcy’s model of momentum diffusion is employed together with the Oberbeck–Boussinesq approximation. A stationary basic solution for the vertical throughflow is determined analytically. The basic velocity and temperature fields turn out to be independent of the non-Newtonian rheology. A linear stability analysis is carried out, leading to a fourth-order eigenvalue problem. A numerical solution of the eigenvalue problem is employed to obtain the neutral stability curves and the critical Rayleigh number for the o…
Stability of Flow with Viscous Dissipation in a Horizontal Porous Layer with an Open Boundary Having a Prescribed Temperature Gradient
Published version of an article in the journal: Transport in Porous Media. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s11242-010-9588-6 A buoyancy-induced stationary flow with viscous dissipation in a horizontal porous layer is investigated. The lower boundary surface is impermeable and subject to a uniform heat flux. The upper open boundary has a prescribed, linearly varying, temperature distribution. The buoyancy-induced basic velocity profile is parallel and non-uniform. The linear stability of this basic solution is analysed numerically by solving the disturbance equations for oblique rolls arbitrarily oriented with respect to the basic velo…
Thermoconvective instability and local thermal non-equilibrium in a porous layer with isoflux-isothermal boundary conditions
The effects of lack of local thermal equilibrium between the solid phase and the fluid phase are taken into account for the convective stability analysis of a horizontal porous layer. The layer is bounded by a pair of plane parallel walls which are impermeable and such that the lower wall is subject to a uniform flux heating, while the upper wall is isothermal. The local thermal non-equilibrium is modelled through a two-temperature formulation of the energy exchange between the phases, resulting in a pair of local energy balance equations: one for each phase. Small-amplitude disturbances of the basic rest state are envisaged to test the stability. Then, the standard normal mode procedure is…
A Non-normal-Mode Marginal State of Convection in a Porous Rectangle
Author's accepted manuscript (postprint). This is a post-peer-review, pre-copyedit version of an article published in Transport in Porous Media. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11242-019-01263-5. The fourth-order Darcy–Bénard eigenvalue problem for onset of thermal convection in a 2D rectangular porous box is investigated. The conventional type of solution has normal-mode dependency in at least one of the two spatial directions. The present eigenfunctions are of non-normal-mode type in both the horizontal and the vertical direction. A numerical solution is found by the finite element method, since no analytical method is known for this non-…
Thermally unstable throughflow of a power–law fluid in a vertical porous cylinder with arbitrary cross–section
Abstract The present paper investigates how the cross–sectional shape of a vertical porous cylinder affects the onset of thermoconvective instability of the Rayleigh–Benard type. The fluid saturating the porous medium is assumed to be a non–Newtonian power–law fluid. A linear stability analysis of the vertical thorughflow is carried out. Three special shapes of the cylinder cross–section are analysed: square, circular and elliptical. The effect of changing the power–law index is investigated. The stability of a steady base state with vertical throughflow is analysed. The resulting stability problem is a differential eigenvalue problem that is solved numerically through the shooting method. …
Local thermal non-equilibrium effects in the Darcy–Bénard instability of a porous layer heated from below by a uniform flux
Abstract The influence of the lack of thermal equilibrium between the solid phase and the fluid phase on the convective instability in a porous medium is studied. A horizontal layer with parallel and impermeable bounding walls is considered. The lower wall is assumed to be isoflux, and the upper wall isothermal. The basic motionless state is perturbed with small-amplitude disturbances, so that a linear analysis of the instability is carried out with a streamfunction-temperature formulation of the local balance equations. Then, the governing equations are solved for the normal modes, leading to an eigenvalue problem for the neutral stability. This eigenvalue problem is solved analytically, t…
Thermoconvective instabilities in an inclined porous channel heated from below
Abstract The thermoconvective instability in an inclined rectangular channel filled with a fluid saturated porous medium and heated from below with a uniform flux is investigated. A stationary parallel buoyant flow with a linear temperature change in the transverse direction is considered. The linear stability to transverse and longitudinal roll disturbances of this basic state is examined. The thermoconvective instability onset of transverse rolls occurs when the Darcy–Rayleigh number exceeds a critical value, that increases with the inclination angle. The critical Darcy–Rayleigh number is discontinuous at the inclination angle 23.4749° above the horizontal. It is shown that, when the incl…
Effect of a finite external heat transfer coefficient on the Darcy-Bénard instability in a vertical porous cylinder
Publised version of an article from the journal: Physics of Fluids. Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. Article appears in Volume 25 issue 4 of the journal: http://dx.doi.org/10.1063/1.4799253 The onset of thermal convection in a vertical porous cylinder is studied by considering the heating from below and the cooling from above as caused by external forced convection processes. These processes are parametrised through a finite Biot number, and hence through third-kind, or Robin, temperature conditions imposed on the lower and upper b…
A three-dimensional study of the onset of convection in a horizontal, rectangular porous channel heated from below
Author's version of an article published in the journal: International Journal of Thermal Sciences. Also available from the publisher at: http://dx.doi.org/10.1016/j.ijthermalsci.2011.12.012 The onset of convection is studied in a rectangular channel filled with a fluid saturated porous medium, bounded above and below by impermeable isothermal walls at unequal temperatures and laterally by partially conducting walls. A three-dimensional linear stability analysis is carried out under the assumption of an infinite longitudinal channel length. Then, this assumption is relaxed in order to determine the threshold length for the three-dimensional convection to be the preferred mode at onset. Sens…
Onset of convection in a vertical porous cylinder with a permeable and conducting side boundary
Abstract The onset of natural convection in a vertical porous cylinder saturated by a fluid is studied. The lateral confinement of the porous cylinder is due to an external porous medium having a permeability much smaller than that of the cylinder. Thus, the vertical side boundary of the cylinder is permeable and constrained by given pressure and temperature distributions. The lower and upper plane boundaries of the cylinder are impermeable walls. The lower wall is subject to a uniform heat flux, while the upper wall has a uniform temperature. The basic motionless state displays a uniform and vertical temperature gradient oriented downward. The linear stability analysis is carried out by us…
Convective Roll Instabilities of Vertical Throughflow with Viscous Dissipation in a Horizontal Porous Layer
Published version of an article from the journal: Transport in Porous Media. The original publication is available at Spingerlink. http://dx.doi.org/10.1007/s11242-009-9417-y The vertical throughflow with viscous dissipation in a horizontal porous layer is studied. The horizontal plane boundaries are assumed to be isothermal with unequal temperatures and bottom heating. A basic stationary solution of the governing equations with a uniform vertical velocity field (throughflow) is determined. The temperature field in the basic solution depends only on the vertical coordinate. Departures from the linear heat conduction profile are displayed by the temperature distribution due to the forced con…