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1.
The article deals with nonlinear thermal instability problem of double-diffusive convection in a porous medium subjected to
temperature/gravity modulation. Three types of imposed time-periodic boundary temperature (ITBT) are considered. The effect
of imposed time-periodic gravity modulation (ITGM) is also studied in this problem. In the case of ITBT, the temperature gradient
between the walls of the fluid layer consists of a steady part and a time-dependent periodic part. The temperature of both
walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally
imposed time-periodic part. Using power series expansion in terms of the amplitude of modulation, which is assumed to be small,
the problem has been studied using the Ginzburg–Landau amplitude equation. The individual effects of temperature and gravity
modulation on heat and mass transports have been investigated in terms of Nusselt number and Sherwood number, respectively.
Further the effects of various parameters on heat and mass transports have been analyzed and depicted graphically. 相似文献
2.
M. V. Filinov 《Fluid Dynamics》1967,2(3):29-31
We shall consider the problem of injecting a mixture of two incompressible fluids having different viscosities into an infinite nonhomogeneous porous stratum which is initially filled with a third fluid. The filtration rate of each of the phases depends basically on its concentration and viscosity, and therefore in the displacement process in the general case their rates of movement will be different, and as a result of this, zones of three-, two-, and single-phase flow are formed. These zones will be separated from one another by moving interfaces (fronts) at which there are jumps of the corresponding concentration levels.We shall assume for simplicity that in the entire region where there is combined flow of several fluids they are incompressible and insoluble, and outside this region, in the external zone, a homogeneous elastic fluid moves. 相似文献
3.
The stability of a fluid-saturated horizontal rotating porous layer subjected to time-periodic temperature modulation is investigated
when the condition for the principle of exchange of stabilities is valid. The linear stability analysis is used to study the
effect of infinitesimal disturbances. A regular perturbation method based on small amplitude of applied temperature field
is used to compute the critical values of Darcy–Rayleigh number and wavenumber. The shift in critical Darcy–Rayleigh number
is calculated as a function of frequency of modulation, Taylor number, and Darcy–Prandtl number. It is established that the
convection can be advanced by the low frequency in-phase and lower-wall temperature modulation, where as delayed by the out-of-phase
modulation. The effect of Taylor number and Darcy–Prandtl number on the stability of the system is also discussed. We found
that by proper tuning of modulation frequency, Taylor number, and Darcy–Prandtl number it is possible to advance or delay
the onset of convection. 相似文献
4.
The stability of a conducting fluid saturating a porous medium, in the presence of a uniform magnetic field, is investigated using the Brinkman model. In the first part of the paper constant-flux thermal boundary conditions are considered for which the onset of convection is known to correspond to a vanishingly small wave number. The external magnetic field is assumed to be aligned with gravity. Closed form solutions are obtained, based on a parallel flow assumption, for a porous layer with either rigid-rigid, rigid-free or free-free boundaries. In the second part of the paper, the linear stability of a porous layer, heated isothermally from below, is investigated using the normal mode technique. The external magnetic field is applied either vertically or horizontally. Solutions are obtained for the case of a porous layer with free boundaries. Results for a pure viscous fluid and a Darcy (densely packed) porous medium emerge from the present analysis as limiting cases. 相似文献
5.
The coupled streamfuction–temperature equations governing the Darcian flow and convection process in a fluid-saturated porous enclosure with an isothermal sinusoidal bottom sun face, has been numerically analyzed using a finite element method (FEM). No restrictions have been imposed on the geometrical non-linearity arising from the parameters like wave amplitude (a), number of waves per unit length (N), wave phase (Φ), aspect ratio (A) and also on the flow driving parameter Rayleigh number (Ra). The numerical simulations for varying values of Ra bring about interesting flow features, like the transformation of a unicellular flow to a multicellular flow. Both with increasing amplitude and increasing number of waves per unit length, owing to the shift in the separation and reattachment points, a row–column pattern of multicellular flow transforms to a simple row of multicellular flow. A cycle of n celluar and n+1 cellular flows, with the flow in adjacent cells in the opposite direction, periodically manifest with phase varying between 0 and 360°. The global heat transfer into the system has been found to decrease with increasing amplitude and increasing number of waves per unit length. Only marginal changes in the global heat flux are observed, either with increasing Ra or varying Φ. Effectively, sinusoidal bottom surface undulations of the isothermal wall of a porous enclosure reduces the heat transfer into the system. © 1998 John Wiley & Sons, Ltd. 相似文献
6.
The linear stability of a viscoelastic liquid saturated horizontal anisotropic porous layer heated from below and cooled from
above is investigated by considering the Oldroyd type liquid. A generalized Darcy model, which takes into account the viscoelastic
properties, the mechanical and thermal anisotropy is employed as momentum equation. The critical Rayleigh number, wavenumber,
for stationary and oscillatory states and frequency of oscillation are determined analytically. It is shown that oscillatory
instabilities can set in before stationary modes are exhibited. The effect of the viscoelastic parameter, the mechanical and
thermal anisotropy parameters and specific heat ratio on the linear stability of the system is analyzed and presented graphically. 相似文献
7.
The onset of buoyancy-driven convection in an initially quiescent ferrofluid saturated horizontal porous layer in the presence
of a uniform vertical magnetic field is investigated. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different
from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed
to be rigid-paramagnetic, while the upper paramagnetic boundary is considered to be either rigid or stress-free. The thermal
conditions include fixed heat flux at the lower boundary, and a general convective–radiative exchange at the upper boundary,
which encompasses fixed temperature and fixed heat flux as particular cases. The resulting eigenvalue problem is solved numerically
using the Galerkin technique. It is found that increase in the Biot number Bi, porous parameter σ, viscosity ratio Λ, magnetic susceptibility χ, and decrease in the magnetic number M
1 and non-linearity of magnetization M
3 is to delay the onset of ferroconvection in a porous medium. Further, increase in M
1, M
3, and decrease in χ, Λ, σ and Bi is to decrease the size of convection cells. 相似文献
8.
Salvatore Rionero 《Continuum Mechanics and Thermodynamics》2012,24(4-6):629-641
A triply convective-diffusive fluid mixture saturating a porous horizontal layer in the Darcy–Oberbeck–Boussinesq scheme is studied. The nonlinear stability analysis of the conduction solution is performed when the layer is heated from below and salted from above by one salt and below by another salt. Denoting by P i , (i = 1, 2), the salts Prandtl numbers, it is shown that in the cases {P 1 = 1; P 2 = 1; P 1 = P 2} do not exist subcritical instabilities and the thermal Rayleigh critical number of global stability in a simple closed form is given. The methodology used and the results obtained appear to be new in the existing literature and useful for the applications. 相似文献
9.
L. K. Filippov-Tsabek 《Fluid Dynamics》1982,17(6):908-915
The paper contains an analysis, confirmed by computer-calculated numerical examples, of the one-dimensional nonstationary system of equations describing the concentration distributions of sorbable gases or liquids in a porous sorbent and in a flow through it. Solutions in the form of propagating waves are investigated in detail. The wave regimes for model sorption isotherms are classified. A representation for quasitraveling and quasispreading waves is introduced.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 114–123, November–December, 1982. 相似文献
10.
11.
Mahesha Narayana P. Sibanda S. S. Motsa P. A. Lakshmi-Narayana 《Heat and Mass Transfer》2012,48(5):863-874
The stability analysis of the quiescent state in a Maxwell fluid-saturated densely packed porous medium subject to vertical
concentration and temperature gradients is presented. A single phase model with local thermal equilibrium between the porous
matrix and the Maxwell fluid is assumed. The critical Darcy–Rayleigh numbers and the corresponding wave numbers for the onset
of stationary and oscillatory convection are determined. A Lorenz like system is obtained for weakly nonlinear stability analysis. 相似文献
12.
13.
This study examines the stability of a horizontally extended second-grade fluid layer heated from below, when a steady temperature difference between the walls is superimposed on sinusoidal temperature perturbations. A linear stability analysis proposed by Venezian (J. Fluid Mech. 35 (1969) 243) is employed to obtain the critical Rayleigh numbers for different types of temperature modulation. The free–free and isothermal boundary conditions are considered so as to allow analytic solutions. The stability characterized by the shift in critical Rayleigh number R2c is calculated as a function of the modulation frequency ω, the Prandtl number Pr, and the viscoelastic parameter Q. It is found that the onset of convection can be delayed or advanced by these parameters. 相似文献
14.
Nonlinear study cellular convection in a sparsely packed fluid saturated porous medium is investigated, considering the Brinkman model, using the technique of spectral analysis. It is established how the Brinkman model with free-free boundaries generalizes the study of convection in a porous medium in the sense that it yields the results tending to those of viscous and Darcy flows respectively for very small and very large values of the permeability parameter σ2. It also provides results for the transition zone (i.e. 102<σ2<103). The cross-interaction of the linear modes caused by non-linear effects are considered through the modal Rayleigh number Rγ. The possibility of the existence of steady solution with two self-excited modes in certain regions is predicted. The similarities of present analysis with and advantages over that of the power integral technique are brought out. A detailed discussion of the heat transport, with the effect of permeability thereon, is made. The theoretical values of the Nusselt number are found to be in good agreement with experimental results. 相似文献
15.
A theoretical analysis of buoyancy-driven instability under transient basic fields is conducted in an initially quiescent,
fluid-saturated, horizontal porous layer. Darcy’s law is used to explain characteristics of fluid motion and the anisotropy
of permeability is considered. Under the Boussinesq approximation and the principle of exchange of stabilities, the stability
equations are derived by using the linear stability theory and the energy method. The linear stability equations are analyzed
numerically by using the frozen-time model and the linear amplification theory and the global stability limits are obtained
numerically from the energy method. For the various anisotropic ratios, the critical times are predicted as a function of
the Darcy–Rayleigh number and the critical Darcy–Rayleigh number is also obtained. The present predictions are compared each
another and with existing theoretical ones. 相似文献
16.
The problem of plane convective flow through a porous medium in a rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. The onset of unsteady regimes is investigated numerically. It is shown that their onset scenarios depend on the vessel dimensions and the seepage Rayleigh number and may be as follows: the generation of stable and unstable periodic regimes as a result of a one-sided bifurcation, the generation of a stable periodic regime as a result of an Andronov-Hopf cosymmetric bifurcation, the formation of a chaotic attractor, the branching-out of a stable quasi-periodic regime from a point of a single-parameter family of steady-state regimes, and the generation of unstable periodic regimes as a result of disintegration of homoclinic trajectories. The specifics of most of the bifurcations mentioned above are attributable to the cosymmetry of the problem considered. 相似文献
17.
18.
Nonlinear Dynamics - In this paper, we investigate a three-component AB model, which characterizes the baroclinic instability processes in the geophysical flows. Via the Darboux transformation, the... 相似文献
19.
B. S. Bhadauria 《Transport in Porous Media》2007,67(2):297-315
The linear stability of thermal convection in a rotating horizontal layer of fluid-saturated porous medium, confined between
two rigid boundaries, is studied for temperature modulation, using Brinkman’s model. In addition to a steady temperature difference
between the walls of the porous layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal
disturbances are considered. The combined effect of rotation, permeability and modulation of walls’ temperature on the stability
of flow through porous medium has been investigated using Galerkin method and Floquet theory. The critical Rayleigh number
is calculated as function of amplitude and frequency of modulation, Taylor number, porous parameter and Prandtl number. It
is found that both, rotation and permeability are having stabilizing influence on the onset of thermal instability. Further
it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation
of the walls’ temperature. 相似文献
20.
J. L. Lage
A. Bejan
J. G. Georgiadis 《International Journal of Heat and Fluid Flow》1992,13(4):408-411This note focuses on Kladias and Prasad's claim that the critical Rayleigh number for the onset of Bénard convection in an infinite horizontal porous layer increases as the Prandtl number decreases, and argues that the critical Rayleigh number (Rac) depends only on the Darcy number (Da), as linear stability analysis indicates. The two-dimensional steady-convection problem is then solved numerically to document the convection heat transfer effect of the Rayleigh number, Darcy number, Prandtl number, and porosity. The note concludes with an empirical correlation for the overall Nusselt number, which shows the effect of Prandtl number at above-critical Rayleigh numbers. The correlation is consistent with the corresponding correlation known for Bénard convection in a pure fluid. 相似文献