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1.
Leiv Storesletten 《Transport in Porous Media》1993,12(1):19-29
The present paper is concerned with free convection in a horizontal porous layer with anisotropic thermal diffusivity. It is assumed that the diffusivity has rotational symmetry, with a symmetry axis making an arbitrary angle against the vertical. The critical Rayleigh number and wave number at marginal stability are calculated and the steady motion occurring at convection onset is examined. It is found that there are two different types of convection cells, depending on whether the longitudinal diffusivity is larger than the transverse diffusivity or not. In the former case, the convection cells are rectangular with vertical lateral walls. In the latter case, however, the lateral cell walls are tilted as well as curved. 相似文献
2.
Xi ChenShaowei Wang Jianjun Tao Wenchang Tan 《International Journal of Heat and Fluid Flow》2011,32(1):78-87
A stability analysis is carried out to investigate the onset of thermosolutal convection in a horizontal porous layer when the solid and fluid phases are not in a local thermal equilibrium, and the solubility of the dissolved component depends on temperature. To study how the reaction and thermal non-equilibrium affect the double-diffusive convection, the effects of scaled inter-phase heat transfer coefficient H and dimensionless reaction rate k on thermosolutal convection are discussed . The critical Rayleigh number and the corresponding wave number for the stability and overstability convections are obtained. Specially, asymptotic analysis for both small and large values of H and k is presented, and the corresponding asymptotic solutions are compared with numerical results. At last, a nonlinear stability analysis is presented to study how H and k affect the Nusselt number. 相似文献
3.
Received October 30, 2000 / Published online January 23, 2001 相似文献
4.
We investigate the stability of a nonuniformly heated fluid in the gravitational field in a plane horizontal porous layer
through which vertical forced motion is effected. A similar system was studied in [1, 2]. In the present paper, the nonuniformity
of the permeability of the porous layer with respect to the depth and the dependence of the viscosity of the saturating fluid
on the temperature are taken into account in addition. As a result of the application of the linear stability theory, an eigenvalue
problem arises, which is solved numerically. A family of curves representing the dependence of the critical modified Rayleigh
number Ra
k
⋆
on the injection parameter (the Péclet number Pe) for different degrees of inhomogeneity of the permeability and the viscosity
is obtained. It is found that although Pe=0 corresponds to Ra
k
⋆
for uniform permeability and viscosity and the stability increases monotonically as Pe increases, the presence of nonuniformity
of the permeability or the viscosity leads to the appearance of a stability minimum in the region Pe≈1, while under the simultaneous
influence of these two factors, the minimum is shifted into the region Pe≈2. The results of the paper can be used, for example,
in the investigation of heat transfer in the case of forced fluid motion in the fissures of a permeable rock mass, when, in
the case of pumping through a horizontal fissure, the fluid penetrates vertically across its permeable walls into the stratum.
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–7, November–December, 1986. 相似文献
5.
Heat and Mass Transfer - The buoyancy-induced flows of non-Newtonian fluids in a horizontal fluid saturated porous layer is studied analytically and numerically using the power-law model to... 相似文献
6.
This article presents a theory of how the melt region advances as an intrusion layer along the top boundary of a solid phase-change material that is heated from the side. The phase-change material fills the pores of a solid matrix. We show that the thickness of the horizontal melt layer increases as x3/5, where x is the horizontal distance measured by from the leading edge of the layer. The total length of the intrusion layer increases as t3/4, and as Tmax5/4. Finite-difference simulations of convection melting in the Darcy-Rayleigh number range of 200–800 agree with the theoretical results. We also show that in a rectangular porous medium heated from the side, the size of the entire melt region is dominated by the melting contributed by the horizontal intrusion layer, if the time is great enough so that the group (Ste Fo)3/4 is greater than 1. 相似文献
7.
The causes of the oscillation of the separation-induced shock formed in supersonic flow over a step are investigated on the basis of measurements of the spatial correlations of the boundary pressure fluctuations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 168–170, July–August, 1990. 相似文献
8.
N. G. Taktarov 《Fluid Dynamics》2016,51(5):703-708
Viscous fluid flow induced by rotational-oscillatorymotion of a porous sphere submerged in the fluid is determined. The Darcy formula for the viscous medium drag is supplementedwith a term that allows for the medium motion. The medium motion is also included in the boundary conditions. Exact analytical solutions are obtained for the time-dependent Brinkman equation in the region inside the sphere and for the Navier–Stokes equations outside the body. The existence of internal transverse waves in the fluid is shown; in these waves the velocity is perpendicular to the wave propagation direction. The waves are standing inside the sphere and traveling outside of it. The particular cases of low and high oscillation frequencies are considered. 相似文献
9.
The structures of the convective motions and the nature of the heat transfer in a horizontal cylindrical layer are studied numerically for the Forchheimer model of a porous medium in the Boussinesq approximation. New asymmetric solutions of the equations of convection flow through a porous medium are found. Their development, domains of existence, and stability are investigated. One consists of a multivortex structure with asymmetric vortices in the near-polar region. Another asymmetric solution is realized at large Grashof numbers in the form of a convective plume deflected from the vertical. The threshold Grashof number of formation of the asymmetric motions depends on the Prandtl number and the cylindrical layer thickness. 相似文献
10.
The linear and weakly nonlinear thermal convection in a rotating porous layer is investigated by constructing a simplified
model involving a system of fifth-order nonlinear ordinary differential equations. The flow in the porous medium is described
by Lap wood-Brinkman-extended Darcy model with fluid viscosity different from effective viscosity. Conditions for the occurrence
of possible bifurcations are obtained. It is established that Hopf bifurcation is possible only at a lower value of the Rayleigh
number than that of simple bifurcation. In contrast to the non-rotating case, it is found that the ratio of viscosities as
well as the Darcy number plays a dual role on the steady onset and some important observations are made on the stability characteristics
of the system. The results obtained from weakly nonlinear theory reveal that, the steady bifurcating solution may be either
sub-critical or supercritical depending on the choice of physical parameters. Heat transfer is calculated in terms of Nusselt
number. 相似文献
11.
12.
The nonlinear global exponential pointwise stability of a vertical steady flow driven by a horizontal periodic temperature gradient in a porous layer is performed. It is shown that the stability threshold depends on the supremum of a quadratic functional, having non constant coefficients, and new in the literature on the convection problem. In solving the variational problem, a suitable functional transformation is used.Received: 27 January 2003, Accepted: 10 March 2003, Published online: 12 September 2003
Correspondence toF. Capone 相似文献
13.
The two-dimensional problem of the stability of the flow of an incompressible fluid over a rigid surface perturbed by a wave travelling in the propagation direction of the flow is discussed in the linear approximation. The problem is solved in the coordinate system at rest with respect to the travelling wave. The parameters of this wave are not eigenvalues of the corresponding linear problem of the stability. The solution is sought in the form of a series in powers of the wave amplitude with an accuracy out to the quadratic term inclusively. Calculations are made of the dependence of the neutral stability curve on the amplitude, wavelength, and phase velocity.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, No. 5, pp. 49–52, September–October, 1979. 相似文献
14.
We apply a velocity-field approach to investigate the interaction between spiral waves and the travelling wave modulation
of system excitability which leads to a prediction: the direction of the straight-line drift of spiral waves is linearly adjusted
by the propagation direction of the travelling waves. Direct numerical computations of the Oregonator model and the formulas
of drift-velocity field confirm the validity and robustness of our theoretical prediction. 相似文献
15.
Princewill Baysa Olali 《Meccanica》2013,48(1):201-210
A linear instability analysis for the inception of double-diffusive convection with a concentration based internal heat source is presented. The system encompasses a layer of fluid which lies above a porous layer saturated with the same fluid. Detailed stability characteristics results are presented for key physical parameters including the solute Rayleigh number, depth ratio of the fluid to porous layer and strength of radiative heating. 相似文献
16.
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
17.
C. Y. Wang 《Applied Scientific Research》1994,52(2):147-160
Convective stability is studied for an infinite horizontal porous layer containing a vertical porous segment of different properties. The critical Rayleigh number depends on the aspect ratio of the nonhomogeneous region and the ratios of permeability, thermal conductivity, and thermal diffusivity of the matrix. Incipient streamlines may be either symmetric or antisymmetric. 相似文献
18.
Yu. V. Sanochkin 《Fluid Dynamics》1984,19(6):986-992
The article considers stationary thermocapillary convection in a thin horizontal layer of fluid with Prandtl number Pr < 1 when it is being locally heated from above in conditions in which the curvature of the free surface is small. It is shown that the motion has a cellular structure. The size of the convective cell is determined from the solution to the spectral problem to which the integration of the free convection system of equations reduces. If the Maragoni (Péclet) number is sufficiently high, the length of the convective cell turns out to be large in comparison with the thickness of the layer. The convection picture is considered and an expression obtained for the velocity of the developing flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 146–152, November–December, 1984. 相似文献
19.
Anuar Ishak 《Heat and Mass Transfer》2009,46(2):147-151
The effects of thermal radiation and thermal buoyancy on the steady, laminar boundary layer flow over a horizontal plate is
investigated. The plate temperature is assumed to be inversely proportional to the square root of the distance from the leading
edge. The set of similarity equations is solved numerically, and the solutions are given for some values of the radiation
and buoyancy parameters for Prandtl number unity. It is found that dual solutions exist for negative values of the buoyancy
parameter, up to certain critical values. Beyond these values, the solution does no longer exist. Moreover, it is found that
there is no local heat transfer at the surface except in the singular point at the leading edge. The radiation parameter is
found to increase the local Stanton number. 相似文献
20.
The seepage velocity arising from pressure and buoyancy driving forces in a slender vertical layer of fluid-saturated porous media is considered. Quadratic drag (Forcheimer effects) and Brinkman viscous forces are included in the analysis. Parameters are identified which characterize the influence of matrix permeability, quadratic drag and buoyancy. An explicit solution is obtained for pressure-driven flow which illustrates the influence of quadratic drag and the strong boundary layer behavior expected for low permeability media. The experimental data of Givler and Altobelli [2] for water seepage through a high porosity foam is found to yield good agreement with the present analysis. For the case of buoyancy-driven flow, a uniformly valid approximate solution is found for low permeability media. Comparison with the pressure-driven case shows strong similarities in the near-wall region.Nomenclature
B
function of
-
d
layer thickness
-
D
discriminant defined by Equation (9)
-
modified Darcy number
- F
Forcheimer constant
-
g
gravitational acceleration
-
k
porous matrix permeability
-
m
parameter defined by Equation (11)
-
p
pressure
-
p
modified pressure
-
pressure gradient
-
R
buoyancy parameter
-
T
0
nominal layer temperature
-
u
seepage velocity
-
dimensionless seepage velocity
-
c
composite approximation
-
i
boundary layer velocity
-
o
outer or core flow approximation
-
m
midplane velocity
-
U
matching velocity
-
V
cross-sectional average velocity
-
w
variable defined by Equation (12)
-
x, z
Cartesian coordinates
-
,
dimensionless Cartesian coordinates
-
inertia parameter
- T
layer temperature difference
-
larger root of cubic given by Equation (8)
-
fluid dynamic viscosity
-
e
effective viscosity of fluid saturated medium
-
variable defined by Equation (18)
-
0
fluid density
-
smaller root of cubic given by Equation (8)
-
variable defined by Equation (18)
-
stretched inner coordinate
-
porosity
-
function of 相似文献