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1.
R. R. Siraev 《Fluid Dynamics》2014,49(3):369-376
Thermal vibrational convection in a saturated porous medium is theoretically studied on the basis of a thermal nonequilibrium model, in accordance with which the temperatures of the porous medium and the saturating liquid can be different. In the high-frequency vibration approximation the averaged equations of convection are derived. The dependence of the vibration force direction on the interphase heat transfer coefficient and the vibration frequency is established. Vibrational convection in a cylindrical layer is studied. It is shown that, depending on the interphase heat transfer coefficient, the flows of two types differing in the liquid circulation direction can exist. 相似文献
2.
The problem of melting from a vertical flat plate embedded in a porous medium is studied. The main focus is to determine the effect of mixed convection flow in the liquid phase on the melting phenomenon. Both aiding and opposing flows are considered. The conservation equations that govern the problem are reduced to a system of nonlinear ordinary differential equations. The governing equations are solved numerically. Numerical results are obtained for the temperature and flow fields in the melting region. The melting phenomenon decreases the local Nusselt number at the solid–liquid interface. 相似文献
3.
M. M. Ramazanov 《Fluid Dynamics》2005,40(4):613-622
The steady-state convection of a fluid in a thin porous vertical ring located in a heat-conducting half-plane is considered. For this problem approximate equations are derived. For a circular ring an analytic solution is obtained. For an elliptic ring a numerical-analytic solution is found. The Nusselt number and the fluid flow rate as functions of the Rayleigh number, the aspect ratio, and the contour depth are investigated.Many studies have been devoted to fluid convection in a porous ring [1–3]. In [1] two-dimensional convection with an isothermal internal boundary was considered when a temperature stratification is given on the outer boundary. A feature of this problem is the fact that the ring is located inside an impermeable heat-conducting medium in which a thermal gradient directed vertically downward is specified at a large distance from the ring. In [2, 3] two-dimensional convection in an annular ring occupied by a porous medium was investigated. From the results obtained in these studies it follows that in the formulation considered the hydraulic approximation can be used with satisfactory accuracy. In the present study this question is discussed more concretely and the necessary estimates are found. The results obtained could be useful for investigating hydrothermal convection in the Earth's crust, which has important geophysical applications [4–6]. 相似文献
4.
S. M. Zen’kovskaya T. N. Rogovenko 《Journal of Applied Mechanics and Technical Physics》1999,40(3):379-385
The effect of high-frequency translational vibrations on the occurrence of filtration convection in a plane horizontal layer
of a viscous incompressible liquid saturating a porous medium is studied. Constant temperature is maintained at the boundaries
of the layer. It is established that for any vibration direction different from the vertical (transverse) direction, convection
in gravity and thermal gravitational convection under both heating from above and heating from below can arise. In the case
of reduced gravity, values of the vibration parameter that lead to transition to zero gravity are established. The results
are obtained from an analysis of the averaged equations of filtration convection, derived for an arbitrary region.
This work was presented at the joint X European and VI Russian Symposium on Physical Sciences in Microgravity (St. Petersburg,
June 15–20, 1997).
Rostov State university, Rostov-on-Don 344090. Rostov State Academy of Building, Rostov-on-Don 344022. Translated from Prikladnaya
Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 22–29, May–June, 1999. 相似文献
5.
Thermohaline convection occurs in hypersaline geothermal systems due to thermal and salinity effects on liquid density. Because of its importance in oceanography, thermohaline convection in viscous liquids has received more attention than thermohaline convection in porous media. The fingered and layered convection patterns observed in viscous liquid thermohaline convection have been hypothesized to occur also in porous media. However, the extension of convective dynamics from viscous liquid systems to porous media systems is complicated by the presence of the solid matrix in porous media. The solid grains cause thermal retardation, hydrodynamic dispersion, and permeability effects. We present simulations of thermohaline convection in model systems based on the Salton Sea Geothermal System, California, that serve to point out the general dynamics of porous media thermohaline convection in the diffusive regime, and the effects of porosity and permeability, in particular. We use the TOUGH2 simulator with residual formulation and fully coupled solution technique for solving the strongly coupled equations governing thermohaline convection in porous media. We incorporate a model for brine density that takes into account the effects of NaCl and CaCl2. Simulations show that in forced convection, the increased pore velocity and thermal retardation in low-porosity regions enhances brine transport relative to heat transport. In thermohaline convection, the heat and brine transport are strongly coupled and enhanced transport of brine over heat cannot occur because buoyancy caused by heat and brine together drive the flow. Random permeability heterogeneity has a limited effect if the scale of flow is much larger than the scale of permeability heterogeneity. For the system studied here, layered thermohaline convection persists for more than one million years for a variety of initial conditions. Our simulations suggest that layered thermohaline convection is possible in hypersaline geothermal systems provided the vertical permeability is smaller than the horizontal permeability, as is likely in sedimentary basins such as the Salton Trough. Layered thermohaline convection can explain many of the observations made at the Salton Sea Geothermal System over the years. 相似文献
6.
L. B. Maslov 《Mechanics of Solids》2012,47(2):221-233
The paper deals with theoretical problems of analysis of forced harmonic vibrations in liquid-saturated porous structures.
The differential equations of motion written for the vector of the solid phase displacements and the liquid phase pressure
are derived from the equations of phase component dynamics and the constitutive equations of anisotropic continuum. An example
of transverse vibrations of a porous framing is used to study the influence of material constants on the dynamic characteristics
of a poroelastic system. It is shown that an increase in the excitation frequency significantly increases the effect of inertial
interaction between the phases of the poroelastic material, especially for the amplitudes of the liquid pressure in the pores.
Thus, to obtain exact solutions of problems of poroelastic material dynamics, it is necessary to take into account all types
of interaction between the solid and liquid phases of heterogenous materials. 相似文献
7.
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
8.
The onset of convection in a system of two horizontal layers (a pure liquid and a porous medium saturated with the same liquid) heated from below under the action of vertical vibration is investigated. For describing the free thermal convection, in the liquid layer the Boussinesq approximation and in the porous layer the Darcy-Boussinesq approximation are used. In the limiting case of a thin liquid layer, effective boundary conditions on the upper boundary of the porous layer with account for convection in the liquid layer are obtained and it is shown that vibration has a stabilizing effect, whereas the presence of a liquid layer leads to destabilization. For an arbitrary liquid to porous layer thickness ratio the onset of convection is investigated numerically. In the case of a thin liquid layer there are two (short-and long-wave) unstable modes. In the case of thick layers the neutral curves are unimodal. Vibration has a stabilizing effect on perturbations with any wave number but affects short-wave perturbations much more strongly than long-wave ones. 相似文献
9.
Rasool Alizadeh Asghar B. Rahimi Nader Karimi Ahmad Alizadeh 《Transport in Porous Media》2017,120(3):579-604
This paper extends the existing studies of heat convection by an external flow impinging upon a flat porous insert to that on a circular cylinder inside a porous medium. The surface of the cylinder is subject to constant temperature and can include uniform or non-uniform transpiration. These cylindrical configurations are introduced in the analyses of stagnation-point flows in porous media for the first time. The equations governing steady transport of momentum and thermal energy in porous media are reduced to simpler nonlinear differential equations and subsequently solved numerically. This reveals the dimensionless velocity and temperature fields of the stagnation-point flow, as well as the Nusselt number and shear stress on the surface of the cylinder. The results show that transpiration on the surface of the cylinder and Reynolds number of the external flow dominate the fluid dynamics and heat transfer problems. In particular, non-uniform transpiration is shown to significantly affect the thermal and hydrodynamic responses of the system in the circumferential direction. However, the permeability and porosity of the porous medium are found to have relatively smaller influences. 相似文献
10.
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
11.
Free flow channel confined by porous walls is a feature of many of the natural and industrial settings. Viscous flows adjacent
to saturated porous medium occur in cross-flow and dead-end filtrations employed primarily in pharmaceutical and chemical
industries for solid–liquid or gas–solid separations. Various mathematical models have been put forward to describe the conjugate
flow dynamics based on theoretical grounds and experimental evidence. Despite this fact, there still exists a wide scope for
extensive research in numerical solutions of these coupled models when applied to problems with industrial relevance. The
present work aims towards the numerical analysis of coupled free/porous flow dynamics in the context of industrial filtration
systems. The free flow dynamics has been expressed by the Stokes equations for the creeping, laminar flow regime whereas the
flow behaviour in very low permeability porous media has been represented by the conventional Darcy equation. The combined
free/porous fluid dynamical behaviour has been simulated using a mixed finite element formulation based on the standard Galerkin
technique. A nodal replacement technique has been developed for the direct linking of Stokes and Darcy flow regimes which
alleviates specification of any additional constraint at the free/porous interface. The simulated flow and pressure fields
have been found for flow domains with different geometries which represent prototypes of actual industrial filtration equipment.
Results have been obtained for varying values of permeability of the porous medium for generalised Newtonian fluids obeying
the power law model. A series of numerical experiments has been performed in order to validate the coupled flow model. The
developed model has been examined for its flexibility in dealing with complex geometrical domains and found to be generic
in delivering convergent, stable and theoretically consistent results. The validity and accuracy of the simulated results
has been affirmed by comparing with available experimental data. 相似文献
12.
13.
An analytical solution is obtained for forced convection in a circular tube occupied by a core–sheath-layered saturated porous
medium with counterflow produced by pulsating pressure gradients. The case of the constant heat-flux boundary conditions is
considered, and the Brinkman model is employed for the porous medium. A perturbation approach is used to obtain analytical
expressions for the velocity, temperature distribution, and transient Nusselt number for convection produced by an applied
pressure gradient that fluctuates with small amplitude harmonically in time about a non-zero mean. It is shown that the fluctuating
part of the Nusselt number alters in magnitude and phase as the dimensionless frequency increases. The magnitude increases
from zero, goes through a peak, and then decreases to zero. The height of the peak depends on the values of various parameters.
The phase (relative to that of the steady component) decreases from π/2 to − π/2 as the frequency increases. 相似文献
14.
S. P. Suma Y. H. Gangadharaiah R. Indira I. S. Shivakumara 《Transport in Porous Media》2012,95(1):91-110
The effect of vertical throughflow on the onset of penetrative convection simulated via internal heating in a two-layer system in which a layer of fluid overlies and saturates a layer of porous medium is studied. Flow in the porous medium is governed by Forchheimer-extended Darcy equation, and Beavers?CJoseph slip condition is applied at the interface between the fluid and the porous layers. The boundaries are considered to be rigid, however permeable, and insulated to temperature perturbations. The eigenvalue problem is solved using a regular perturbation technique with wave number as a perturbation parameter. The ratio of fluid layer thickness to porous layer thickness, ??, the direction of throughflow, and the presence of volumetric internal heat source in fluid and/or porous layer play a decisive role on the stability characteristics of the system. In addition, the influence of Prandtl number arising due to throughflow is also emphasized on the stability of the system. It is observed that both stabilizing and destabilizing factors can be enhanced because of the simultaneous presence of a volumetric heat source and vertical throughflow so that a more precise control (suppress or augment) of thermal convective instability in a layer of fluid or porous medium is possible. 相似文献
15.
This work is focused on the numerical modeling of steady, laminar, heat and mass transfer by MHD mixed convection from a semi-infinite,
isothermal, vertical and permeable surface immersed in a uniform porous medium in the presence of thermal radiation and Dufour
and Soret effects. A mixed convection parameter for the entire range of free-forced-mixed convection is employed and the governing
equations are transformed into non-similar equations. These equations are solved numerically by an efficient, implicit, iterative,
finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem
and are found to be in excellent agreement. A parametric study illustrating the influence of the thermal radiation coefficient,
magnetic field, porous medium inertia parameter, concentration to thermal buoyancy ratio, and the Dufour and Soret numbers
on the fluid velocity, temperature and concentration as well as the local Nusselt and the Sherwood numbers is conducted. The
obtained results are shown graphically and the physical aspects of the problem are discussed. 相似文献
16.
Gorla Rama Subba Reddy Mansour M. A. Hassanien I. A. Bakier A. Y. 《Transport in Porous Media》1999,36(2):245-254
In the present work, the effect of mixed convection about vertical surfaces on the phenomenon of melting process in a fluid-saturated porous medium is analyzed on the basis of boundary layer approximations. Similarity solutions are obtained for aiding external flow. The final similarity equations are integrated numerically by use of the fourth-order Runge–Kutta method. Results are reported for the flow and thermal fields in the melt region. The melting phenomenon decreases the local Nusselt number at the solid–liquid interface. 相似文献
17.
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
18.
Abstract Aim of the paper is to investigate the effects of linearly varying thermal conductivity, viscous dissipation and
Ohmic heating on steady free convection flow of a viscous incompressible electrically conducting liquid having low Prandtl
number along an inclined isothermal non-conducting porous plate in the presence of transverse magnetic field. The governing
equations of continuity, momentum and energy are transformed into ordinary differential equations using similarity transformation.
The resulting coupled and non-linear ordinary differential equations are solved using Runge-Kutta fourth order method and
shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction
coefficient and Nusselt number at the plate are derived, discussed and their numerical values for various values of physical
parameters are presented through tables. 相似文献
19.
Mahmoud Jourabian Mousa Farhadi Ahmad Ali Rabienataj Darzi 《Heat and Mass Transfer》2013,49(4):555-565
Heat transfer and fluid flow processes of natural convection melting of a phase change material are simulated numerically inside a partially heated square cavity. The momentum and energy equations are solved by using enthalpy-based lattice Boltzmann method combined with multi distribution function model. In this communication, the dependence of liquid fraction, temperatures of vertical nodes and average Nusselt number on the positions of heated plates is investigated quantitatively. 相似文献
20.
An analytical study is made for wall effects in non-Darcy mixed convection from vertical impermeable surfaces embedded in
a saturated porous medium. The governing equations are transformed into a dimensionless form by non-similar transformation
to cover both forced and natural convection dominated regimes. Two different dimensionless parameters that measure the strength
of mixed convection were found in both regimes. The parameters of forced convection dominated regime can be related to those
of natural convection dominated regime. An approximate analytical solution for the governing equations was obtained. Temperature
and velocity profiles for both regimes are presented.
Received on 9 September 1997 相似文献