共查询到20条相似文献,搜索用时 15 毫秒
1.
The effect of vertical heterogeneity of permeability, on the onset of convection in a horizontal layer of a saturated porous medium, uniformly heated from below but with a non-uniform basic temperature gradient resulting from vertical throughflow, is studied analytically using linear stability theory. It is found that, to first order, a linear variation of the reciprocal of permeability with depth has no effect on the critical value of the Rayleigh number Ra c based on the harmonic mean of the permeability, but a quadratic variation increasing in the upwards direction leads to a reduction in Ra c. 相似文献
2.
The problem for determining the critical Rayleigh number for the onset of convection in a horizontal porous layer with vertical
throughflow is re-examined with the aim of obtaining analytical formulas applicable in the cases of weak and strong throughflow.
For the case of strong throughflow an asymptotic analysis is performed. 相似文献
3.
We present an analytical investigation of the effect of vertical throughflow on the onset of convection, induced by internal heating, in a composite porous medium consisting of two horizontal layers. If convection is induced by internal heating, the bulk of the convection occurs in the upper half of the layer where the buoyancy force is destabilizing. For the case of heterogeneous porous medium, if the permeability increases in the upward direction, or if the thermal conductivity decreases in the upward direction, instability is increased. It is also found that upward throughflow is stabilizing but a modest amount of downward throughflow is destabilizing. 相似文献
4.
This paper investigates the onset of convection in a vertical cylinder occupied by a saturated porous medium of vertically heterogeneous permeability. The flow is induced by an applied vertical temperature gradient and an imposed solute concentration gradient. The main interest of this paper is studying the effect of vertical throughflow on the onset of instability in this system. The study is performed using linear stability theory. The problem is of considerable interest for hydrological and geophysical situations. 相似文献
5.
The effects of hydrodynamic and thermal heterogeneity, for the case of variation in both the horizontal and vertical directions,
on the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below, with weak vertical
throughflow, are studied analytically for the case of weak heterogeneity. It is found that when the boundary conditions at
the upper and lower boundaries are symmetric, the throughflow magnitude and the permeability and conductivity gradients enter
the expression for the critical Rayleigh number at second order. The throughflow on its own is stabilizing but the combination
of throughflow and heterogeneity may be either stabilizing or destabilizing. 相似文献
6.
The effect of vertical throughflow on the onset of convection in a rectangular box occupied by a saturated porous medium uniformly
heated from below, is studied using linear stability theory. It is found that, for small values of the throughflow, the stabilizing
effect of the throughflow and the stabilizing effect of the confining lateral walls of the box are approximately independent
of each other. 相似文献
7.
The Brinkman extended Darcy model including Lapwood and Forchheimer inertia terms with fluid viscosity being different from effective viscosity is employed to investigate the effect of vertical throughflow on thermal convective instabilities in a porous layer. Three different types of boundary conditions (free–free, rigid–rigid and rigid–free) are considered which are either conducting or insulating to temperature perturbations. The Galerkin method is used to calculate the critical Rayleigh numbers for conducting boundaries, while closed form solutions are achieved for insulating boundaries. The relative importance of inertial resistance on convective instabilities is investigated in detail. In the case of rigid–free boundaries, it is found that throughflow is destabilizing depending on the choice of physical parameters and the model used. Further, it is noted that an increase in viscosity ratio delays the onset of convection. Standard results are also obtained as particular cases from the general model presented here. 相似文献
8.
9.
10.
The purpose of this paper is to investigate the effect of vertical throughflow on the onset of bioconvection in a suspension
of gyrotactic microorganisms. A dilute suspension of gyrotactic microorganisms in a shallow system that consists of superimposed
fluid and porous layers is considered. A linear instability analysis of this problem is performed and the Galerkin method
is utilized to solve the eigenvalue problem. The analysis leads to an equation for the critical Rayleigh number. It is shown
that the vertical throughflow stabilizes the system. 相似文献
11.
The effect of vertical heterogeneity of permeability, on the onset of convection in a horizontal layer of a saturated porous
medium, uniformly heated from below but with a non-uniform basic temperature gradient resulting from transient heating or
otherwise, is studied analytically using linear stability theory. Two particular situations, corresponding to instantaneous
bottom heating and constant-rate bottom heating, are studied. Estimates of the timescale for the development of convection
instability are obtained. 相似文献
12.
The effect of strong throughflow and strong heterogeneity on the onset of convection induced by a vertical density gradient
in a saturated porous medium governed by Darcy’s law is investigated. The general case, where there is heterogeneity in both
the vertical and horizontal directions, and where there is heterogeneity in permeability, thermal conductivity, and applied
temperature gradient, is considered. A computer package has been extended to deal with the case of vertical throughflow. 相似文献
13.
The effect of local thermal non-equilibrium on the onset of convection in a porous medium consisting of two horizontal layers is studied analytically. Linear stability theory is applied. Variations of permeability, fluid conductivity, solid conductivity, interphase heat transfer coefficient and porosity are considered. It is found that heterogeneity of permeability and fluid conductivity have a major effect, heterogeneity of interphase heat transfer coefficient and porosity have a lesser effect, while heterogeneity of solid conductivity is relatively unimportant. 相似文献
14.
15.
In this second part of our analysis of the destabilization of transverse modes in an extended horizontal layer of a saturated
porous medium with inclined temperature gradient and vertical throughflow, we apply the mathematical formalism of absolute
and convective instabilities to studying the nature of the transition to instability of such modes by assuming on physical
grounds that the transition is triggered by growing localized wavepackets. It is revealed that in most of the parameter cases
treated in the first part of the analysis (Brevdo and Ruderman 2009), at the transition point the evolving instability is
convective. Only in the cases of zero horizontal thermal gradient, and in the cases of zero vertical throughflow and the horizontal
Rayleigh number R
h < 49, the instability is absolute implying that, as the vertical Rayleigh number, R
v, increases passing through its critical value, R
vc, the destabilization tends to affect the base state throughout and eventually destroys it at every point in space. For the
parameter values considered, for which the destabilization has the nature of convective instability, we found that, as R
v, increases beyond the critical value, while the horizontal Rayleigh number, R
h, and the Péclet number, Q
v, are kept fixed, the flow experiences a transition from convective to absolute instability. The values of the vertical Rayleigh
number, R
v, at the transition from convective to absolute instability are computed. For convectively unstable, but absolutely stable
cases, the spatially amplifying responses to localized oscillatory perturbations, i.e., signaling, are treated and it is found
that the amplification is always in the direction of the applied horizontal thermal gradient. 相似文献
16.
The effect of strong throughflow and strong heterogeneity on the onset of convection induced by a vertical density gradient
in a saturated porous medium governed by Darcy’s law is investigated with the aid of a computer package. The general case,
where there is heterogeneity in both the vertical and horizontal directions, and where there is heterogeneity in permeability,
thermal conductivity, and applied temperature gradient, is considered. Previous work on the case of non-periodic global variation
is now extended to the case of either periodic variation or localized variation. 相似文献
17.
Linear stability analysis is applied to the onset of convection due to internal heating in a porous medium with weak vertical and horizontal heterogeneity. It is found that the effect of horizontal heterogeneity of each of permeability and thermal conductivity is slightly destabilizing. Increase of permeability in the upward direction is destabilizing and increase in the downward direction is stabilizing, and the reverse is true for increase of conductivity. 相似文献
18.
The Onset of Convection in a Strongly Heterogeneous Porous Medium with Transient Temperature Profile
The effect of heterogeneity of permeability, on the onset of convection in a horizontal layer of a saturated porous medium,
uniformly heated from below but with a nonuniform basic temperature gradient resulting from transient heating, is studied
analytically using linear stability theory for the case of strong heterogeneity. Two particular situations, corresponding
to instantaneous bottom heating and constant-rate bottom heating, are studied. Estimates of the timescale for the development
of convection instability are obtained. The case of a strongly nonlinear temperature gradient is studied with the help of
a computer package. 相似文献
19.
The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model
used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium, the Brinkman
model is employed. Three cases of free–free, rigid–rigid, and rigid–free boundaries are considered. The analysis reveals that
for a typical nanofluid (with large Lewis number), the prime effect of the nanofluids is via a buoyancy effect coupled with
the conservation of nanoparticles, whereas the contribution of nanoparticles to the thermal energy equation is a second-order
effect. It is found that the critical thermal Rayleigh number can be reduced or increased by a substantial amount, depending
on whether the basic nanoparticle distribution is top-heavy or bottom-heavy, by the presence of the nanoparticles. Oscillatory
instability is possible in the case of a bottom-heavy nanoparticle distribution. 相似文献
20.
Linear stability analysis was applied to the onset of convection due to internal heating in a porous medium saturated by a nanofluid. A model in which the effects of thermophoresis and Brownian motion are taken into account is employed. We utilized more realistic boundary conditions than in the previous work on this subject; now the nanofluid particle fraction is allowed to adapt to the temperature profile induced by the internal heating, subject to the requirement that there is zero perturbation flux across a boundary. The results show that the presence of the nanofluid particles leads to increased instability of the system. We identified two combinations of dimensionless parameters that are the major controllers of convection instability in the layer. 相似文献