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1.
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 velocity field. The onset conditions of thermal instability are governed by the Rayleigh number associated with
the prescribed wall heat flux at the lower boundary, by the horizontal Rayleigh number associated with the imposed temperature
gradient on the upper open boundary, and by the Gebhart number associated with the effect of viscous dissipation. The critical
value of the Rayleigh number for the onset of the thermal instability is evaluated as a function of the horizontal Rayleigh
number and of the Gebhart number. It is shown that the longitudinal rolls, having axis parallel to the basic velocity, are
the most unstable in all the cases examined. Moreover, the imposed horizontal temperature gradient tends to stabilise the
basic flow, while the viscous dissipation turns out to have a destabilising effect. 相似文献
2.
Nonlinear Dynamics - We present a detailed study of Rayleigh–Bénard magnetoconvection with periodic gravity modulation and uniform vertical magnetic field. Linear stability analysis is... 相似文献
3.
Antonio Barletta Eugenia Rossi di Schio Leiv Storesletten 《Transport in Porous Media》2010,81(3):461-477
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 convection effect and to the viscous dissipation effect. A linear stability analysis of the basic solution
is carried out in order to determine the conditions for the onset of convective rolls. The critical values of the wave number
and of the Darcy–Rayleigh number are determined numerically by the fourth-order Runge–Kutta method. It is shown that, although
generally weak, the effect of viscous dissipation yields an increase of the critical value of the Darcy–Rayleigh number for
downward throughflow and a decrease in the case of upward throughflow. Finally, the limiting case of a vanishing boundary
temperature difference is discussed. 相似文献
4.
J. C. Umavathi 《Transport in Porous Media》2013,98(1):59-79
The effect of time-periodic temperature modulation at the onset of convection in a Boussinesq porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. The perturbation method is applied for computing the critical Rayleigh and wave numbers for small amplitude temperature modulation. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation, concentration Rayleigh number, porosity, Lewis number, and thermal capacity ratio. It has been shown that it is possible to advance or delay the onset of convection by time-periodic modulation of the wall temperature. The nanofluid is found to have more stabilizing effect when compared to regular fluid. Low frequency is destabilizing, while high frequency is always stabilizing for symmetric modulation. Asymmetric modulation and only lower wall temperature modulation is stabilizing for all frequencies when concentration Rayleigh number is greater than one. 相似文献
5.
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
6.
It is well known that the onset of convection in an inclined porous layer heated from below takes the form of longitudinal
vortices when Darcy’s law is valid. In this paper we consider briefly how the onset criterion alters when form drag, as modelled
by the Forchheimer terms, is significant. In general, the critical Rayleigh number increases substantially as form drag effects
strengthen, but the wavenumber rises by only a small amount. This numerical study is supplemented by a brief asymptotic analysis
of the case when the Forchheimer terms dominate and it is shown that the critical Rayleigh number increases in direct proportion
with the form drag parameter. 相似文献
7.
The onset of convective rolls instability in a horizontal porous layer subject to a basic temperature gradient inclined with
respect to gravity is investigated. The basic velocity has a linear profile with a non-vanishing mass flow rate, i.e., it
is the superposition of a Hadley-type flow and a uniform flow. The influence of the viscous heating contribution on the critical
conditions for the onset of the instability is assessed. There are four governing parameters: a horizontal Rayleigh number
and a vertical Rayleigh number defining the intensity of the inclined temperature gradient, a Péclet number associated with
the basic horizontal flow rate, and a Gebhart number associated with the viscous dissipation effect. The critical wave number
and the critical vertical Rayleigh number are evaluated for assigned values of the horizontal Rayleigh number, of the Péclet
number, and of the Gebhart number. The linear stability analysis is performed with reference either to transverse or to longitudinal
roll disturbances. It is shown that generally the longitudinal rolls represent the preferred mode of instability. 相似文献
8.
A. S. Gupta 《Applied Scientific Research》1960,9(1):319-333
Summary An analysis is made for the laminar free convection and heat transfer of a viscous electrically conducting fluid from a hot
vertical plate in the case when the induced field is negligible compared to the imposed magnetic field. It is found that similar
solutions for velocity and temperature exist when the imposed magnetic field (acting perpendicular to the plate) varies inversely
as the fourth root of the distance from the lowest end of the plate. Explicit expressions for velocity, temperature, boundary
layer thickness and Nusselt number are obtained and the effect of a magnetic field on them is studied. It is found that the
effect of the magnetic field is to decrease the rate of heat transfer from the wall. In the second part, the method of characteristics
is employed to obtain solutions of the time-dependent hydromagnetic free convection equations (hyperbolic) of momentum and
energy put into integral form. The results yield the time required for the steady flow to be established, and the effect of
the magnetic field on this time is studied. 相似文献
9.
This paper investigates the effect of non-uniform temperature gradient and magnetic field on Marangoni convection in a horizontal fluid layer heated from below and cooled from above with a constant heat flux. A linear stability analysis is performed. The influence of various parameters on the convection onset is analyzed. Six non-uniform basic temperature profiles are considered, and some general conclusions about their desta- bilizing effects are presented. 相似文献
10.
The stability of infinitestimal steady and oscillatory motions and finite amplitude steady motions of a conducting fluid through porous media with free boundaries which is heated from below and cooled from above is investigated in the presence of a uniform magnetic field. Infinitesimal steady motions are investigated using Liapunov method and its is shown that the principle of exchange of stability is valid only when Pm/Pr≤1 with a restricted value of the Hartmann number. It is shown that overstable motions are due to the zonal current induced by the magnetic field. Finite amplitude steady motions are investigated using Veronis [1] analysis and it is shown that for a restricted range of Hartmann numbers and porous parameter Pl, steady finite-amplitude motions can exist for values of the Rayleigh number smaller than that value corresponding to oscillatory motions. Since the Busse number is greater than the wave number the horizontal scale of the steady finite-amplitude motions is larger than that of the overstable motions. 相似文献
11.
V. M. Soundalgekar 《Applied Scientific Research》1965,12(1):151-156
Summary Hydromagnetic flow of a viscous incompressible fluid due to uniformly accelerated motion of an infinite flat plate in the presence of a magnetic field fixed relative to the plate, is discussed. It is assumed that the induced magnetic field is negligible compared to the imposed magnetic field. It is observed under these conditions that the velocity at any point and at any instant decreases when the strength of the magnetic field is increased. 相似文献
12.
《International Journal of Non》1996,31(3):371-376
The combined effect of viscous and ohmic dissipations on magnetoconvection in a vertical enclosure heated at the vertical side walls in the presence of applied electric field parallel to gravity and magnetic field normal to gravity is investigated. The coupled non-linear equations governing the motion are solved both analytically valid for small buoyancy parameter N and numerically valid for large N. Solutions for large N reveal a marked change in velocity profile, mass flow rate, skin friction and rate of heat transfer. These results are presented for various Hartmann number M, electric field loading parameter E and buoyancy parameter N. It is shown in the case of open circuit (i.e. E ≠ 0) that the effect of magnetic field is to increase both the velocity and temperature in contrast with the short circuit case (i.e. E = 0). The results for the case when the walls are maintained at the same temperatures (i.e. T1 = T2) are obtained as a particular case. 相似文献
13.
Mallikarjunaiah S. Muddamallappa Dambaru Bhatta Daniel N. Riahi 《Transport in Porous Media》2009,79(2):301-317
In this article, an investigation is conducted to analyze the marginal stability with and without magnetic field in a mushy
layer. During alloy solidification, such mushy layer, which is adjacent to the solidification front and composed of solid
dendrites and liquid, is known to produce vertical chimneys. Here, we carry out numerical investigation for particular range
of parameter values, which cover those of available experimental studies, to determine the convective flow at the onset of
motion. The governing coupled non-linear partial differential equations are non-dimensionalised and solved to get the steady
basic-state solution. The thickness of the mushy layer is determined as a part of the solution. Using multiple shooting technique,
we determine the steady-state solutions in a range of critical Rayleigh number. We analyse the effect of several parameters,
Chandrasekhar number Q, and Robert’s number τ on the problem. It was found that an increase in Q has a stabilizing effect on solidification and the critical Rayleigh number increases on increasing Q. It was also found that for moderate or small values of Robert’s number τ the critical Rayleigh number is mostly insensitive. 相似文献
14.
In this paper, the effects of Prandtl number on the steady magneto-convection around a centrally located adiabatic body inside
a square enclosure are numerically investigated. Two-dimensional nonlinear governing equations are discretized using the control
volume method and hybrid scheme. The equations are solved using SIMPLER algorithm. The results are displayed in the form of
streamlines and isotherms when the Rayleigh number varies between 103 and 106, the Hartmann number changes between 0 and 100 and the Prandtl number ranges between 0.005 and 0.1. The ratio of the buoyancy
force to the Lorentz force (Ra/Ha
2) is introduced as an index to compare the contribution of natural convection and magnetic field strength on heat transfer.
The results obtained from numerical modeling show that the Prandtl number has not considerable effect on heat transfer at
low Rayleigh numbers. The effect of magnetic field strength on convection is increased by increasing Prandtl number. The effect
of Prandtl number on the average Nusselt number in the presence of a magnetic field is less than the case without a magnetic
field. 相似文献
15.
V. I. Khonichev V. I. Yakovlev 《Journal of Applied Mechanics and Technical Physics》1974,15(5):606-612
We study vortex flows in a rotating circular cylinder of incompressible fluid resulting from the sudden turning-on of a transverse magnetic field. The investigation is performed for the initial stage when secondary flow is determined mainly by Lorentz forces, and the effect of viscosity and the convective transport of vorticity by secondary flow is negligibly small. No restrictions are imposed on the magnetic Reynolds number Rm for the basic rotational motion; the number Rm' calculated from a typical secondary flow speed is assumed small. 相似文献
16.
Numerical solutions of stability and convective flow in an infinite horizontal water layer, including density inversion, have been obtained using a finite element code. The evolution of the temperature field and flow pattern near the onset of convection are studied in detail. It is known that natural convection develops primarily in the lower unstably stratified layer. Of interest is the penetration of the convection rolls into the upper stably stratified layer and concurrent liquid entrainment as a function of the increasing Rayleigh number at different aspect ratios. Individual convection rolls may grow and expand before splitting up into two roll cells. It is shown that changing the aspect ratio influences critical Rayleigh number, flow symmetry, flow pattern, and transitions between flow patterns. Numerical results on heating from above or from below, agree well with available results in the literature. A correlation to predict critical Rayleigh numbers is given for the case of heating from above. 相似文献
17.
The effect of magnetic field dependent viscosity on thermosolutal convection in a ferromagnetic fluid saturating a porous medium is considered for a fluid layer heated and soluted from below in the presence of uniform magnetic field. Using linearized stability theory and normal mode analysis, an exact solution is obtained for the case of two free boundaries. For case of stationary convection, medium permeability has a destabilizing effect, whereas a stable solute gradient and magnetic field dependent viscosity have a stabilizing effect on the system. In the absence of magnetic field dependent viscosity, the destabilizing effect of non-buoyancy magnetization is depicted but in the presence of magnetic field dependent viscosity non-buoyancy magnetization may have a destabilizing or stabilizing effect on the onset of instability. The critical wave number and the critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of buoyancy magnetization parameter M1 and the results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of stable solute gradient. The oscillatory modes are introduced due to the presence of the stable solute gradient, which were non-existent in its absence. A sufficient condition for the non-existence of overstability is also obtained. The paper also reaffirms the qualitative findings of earlier investigations which are, in fact, limiting cases of the present study. 相似文献
18.
A. Barletta 《Transport in Porous Media》2012,92(2):419-437
The linear thermoconvective instability of the basic parallel flow in a plane and horizontal porous channel is investigated.
The boundary walls are assumed to be impermeable and subject to symmetric and uniform heat fluxes. The wall heat fluxes produce
either a net heating or a net cooling of the fluid saturated porous medium. A horizontal mass flow rate is externally impressed
leading to a stationary basic state with a temperature gradient inclined to the vertical. A region of possibly unstable thermal
stratification exists either in the lower half-channel (boundary heating), or in the upper half-channel (boundary cooling).
The convective instability of the basic flow is governed by the Rayleigh number and by the Péclet number. In the case of boundary
heating, the thermal instability arises when the Rayleigh number exceeds its critical value, that depends on the Péclet number.
The change of the critical Rayleigh number as a function of the Péclet number is determined numerically for arbitrary normal
modes oblique to the basic flow direction. The most dangerous modes are the longitudinal rolls, with a wave vector perpendicular
to the basic velocity. There exists a minimum value of the Péclet number, 19.1971, below which no linear instability is detected. 相似文献
19.
E. A. Pushkar' 《Fluid Dynamics》1983,18(2):251-260
A plane-polarized self-similar steady solution is constructed numerically for the problem of flow past a nonconducting wedge in magnetohydrodynamics when the magnetic field is not parallel to the velocity. The dependence of the form of the solution on the flow parameters — the velocity, the magnetic field intensity, and the angle ψ between the velocity and the field — is investigated. It is shown that there can be an abrupt re-arrangement of the solution at critical values of ψ, when either the characteristics merge in the flow or solutions with continuous magnetic field appear. 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