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1.
S. Govender 《Transport in Porous Media》2006,63(3):489-502
The linear stability theory is used to investigate analytically the effects of gravity modulation on convection in a homogeneous
cylindrical porous layer heated from below. The linear stability results show that increasing the frequency of vibration stabilizes
the convection. In addition the aspect ratio of the porous cylinder is shown to influence the stability of convection for
all frequencies analysed. It was also observed that only synchronous solutions are possible in cylindrical porous layers,
with no transition to subharmonic solutions as was the case in Govender (2005a) [Transport Porous Media 59(2), 227–238] for rectangular layers or cavities. 相似文献
2.
Colin Smith 《Transport in Porous Media》2006,63(1):223-237
An analytical study is made of the convective flow field produced when a warm cylinder maintained at a fixed temperature above
freezing is buried in saturated frozen porous medium. The flow field is shown to have a double cell pattern due to the density
inversion of water at ~ 4°C, with downward convection of heat dominating at cylinder temperatures of below ~ 10°C and upward
heat convection dominating at temperatures greater than this. The analysis uses a perturbation technique to determine the
first-order convective correction to the flow and temperature fields around the cylinder for a quasi-static case. It demonstrates
that the porous medium permeability and the cylinder temperature are the dominant factors in determining the point at which
convection heat transfer becomes significant, with convection expected to be insignificant for Darcy permeabilies lower than
10−5 m/s. The analysis also gives an indication of the rates of thawing occurring in different directions without resorting to
numerical methods. The practical implications of a thawing pattern significantly different to that predicted by conduction
theory only are discussed briefly with respect to the problem of differential thaw settlement of arctic pipelines. 相似文献
3.
The effects of viscous dissipation on unsteady free convection from an isothermal vertical flat plate in a fluid saturated
porous medium are examined numerically. The Darcy–Brinkman–Forchheimer model is employed to describe the flow field. A new
model of viscous dissipation is used for the Darcy–Brinkman–Forchheimer model of porous media. The simultaneous development
of the momentum and thermal boundary layers are obtained by using a finite difference method. Boundary layer and Boussinesq
approximation have been incorporated. Numerical calculations are carried out for various parameters entering into the problem.
Velocity and temperature profiles as well as local friction factor and local Nusselt number are shown graphically. It is found
that as time approaches infinity, the values of friction factor and heat transfer coefficient approach steady state. 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.
A linear stability analysis determining the critical Rayleigh number R
c for onset of convection in a bounded vertical cylinder containing a fluid-saturated porous medium is performed for insulated sidewalls, isothermal top surface, and bottom surface heated by forced convection. This Newtonian heating of the bottom surface involves a Biot number Bi that allows consideration of the continuum of boundary conditions ranging from constant heat flux, with global minimum R
min=27.096 found as Bi→0, to isothermal, with global minimum R
min=4π2 found as Bi→ ∞. In both cases and for most cylinder aspect ratios, incipient convection sets in as an asymmetric mode, though islands of aspect ratio exist where the onset mode is symmetric. Sample three-dimensional renderings of disturbance temperature distributions showing preferred modes at onset of convection for fixed Bi are provided and an analytical fit to R
min as a function of Bi is given. 相似文献
6.
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
7.
A. Pantokratoras 《Heat and Mass Transfer》2000,36(4):351-360
In most studies concerning laminar natural convection along a vertical isothermal cylinder a linear relationship between
fluid density and temperature has been used and kinematic viscosity and thermal diffusivity have been considered constant
calculated at ambient temperature. However, it is known that the density–temperature relationship for water is non-linear
at low temperatures and kinematic viscosity and thermal diffusivity are functions of temperature. In this study the problem
of laminar natural convection of pure and saline water along a vertical isothermal cylinder has been investigated in the temperature
range between 20 and 0 ∘C taking into account the temperature dependence of ν, α and ρ. The results are obtained with the numerical solution of the
boundary layer equations. The variation of ν, α and ρ with temperature has a strong influence on free convection characteristics.
Received on 17 May 1999 相似文献
8.
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
9.
In this study, we carried out a numerical simulation of transient heat transfer in a composite passive system consisting of
air–phase change material–air, arranged as a rectangular enclosure. The vertical boundaries of the enclosure are isothermal
and the horizontal ones adiabatic. The enthalpy formulation with a fixed grid is used to study the process of phase change
with liquid–solid interface zone controlled by natural convection. The flow in this zone is simulated by a model based on
the Darcy porous medium. The numerical solution of the mathematical model is done using finite difference–control volume algorithm.
The influence of the geometrical and thermal parameters is studied. It is found that subcooling coefficient is the most important
parameter influencing heat transfer, and for a given subcooling, there is an optimum phase change partition thickness. 相似文献
10.
The onset of thermal convection in a vertical porous cylinder in three dimensions is investigated analytically. Top and bottom
of the cylinder are set to be perfectly heat conducting and impermeable, and is uniformly heated from below. The convection
problem is solved for a cylinder wall that is partly conducting and partly penetrative. The expressions for semi-conduction
and semi-penetration are based on a porous medium separated from its surroundings by a thin wall. The eigenvalue problem is
split into two Helmholtz equations, and the results are expressed by Bessel functions in the radial direction. Comparisons
are made with existing solutions for the limit cases of a closed cylinder wall that is either conducting or insulating. Two
different models are compared for the kinematic limit condition of an open boundary. 相似文献
11.
The natural convection of a gas-particle suspension inside a two-dimensional square region is investigated within the framework
of a two-velocity two-temperature model of the medium with allowance for phase relaxation and particle deposition.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 46–52, March–April, 1994. 相似文献
12.
Steady mixed convection boundary layer flow from an isothermal horizontal circular cylinder embedded in a porous medium filled
with a nanofluid has been studied for both cases of a heated and cooled cylinder. The resulting system of nonlinear partial
differential equations is solved numerically using an implicit finite-difference scheme. The solutions for the flow and heat
transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle
volume fraction φ and the mixed convection parameter λ. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It is found that for each particular nanoparticle, as the nanoparticle volume fraction φ increases, the magnitude of the skin friction coefficient decreases, and this leads to an increase in the value of the mixed
convection parameter λ which first produces no separation. On the other hand, it is also found that of all the three types
of nanoparticles considered, for any fixed values of φ and λ, the nanoparticle Cu gives the largest values of the skin friction coefficient followed by TiO2 and Al2O3. Finally, it is worth mentioning that heating the cylinder (λ > 0) delays separation of the boundary layer and if the cylinder
is hot enough (large values of λ > 0), then it is suppressed completely. On the other hand, cooling the cylinder (λ < 0) brings
the boundary layer separation point nearer to the lower stagnation point and for a sufficiently cold cylinder (large values
of λ < 0) there will not be a boundary layer on the cylinder. 相似文献
13.
An analytical solution to the problem of condensation by natural convection over a thin porous substrate attached to a cooled
impermeable surface has been conducted to determine the velocity and temperature profiles within the porous layer, the dimensionless
thickness film and the local Nusselt number. In the porous region, the Darcy–Brinkman–Forchheimer (DBF) model describes the
flow and the thermal dispersion is taken into account in the energy equation. The classical boundary layer equations without
inertia and enthalpyterms are used in the condensate region. It is found that due to the thermal dispersion effect, the increasing
of heat transfer is significant. The comparison of the DBF model and the Darcy–Brinkman (DB) one is carried out. 相似文献
14.
The onset of convection in a horizontal porous layer is investigated theoretically. The permeability of the porous medium
is a continuous periodic function of the horizontal x coordinate. Floquet theory has been employed to determine the favoured two-dimensional mode of convection. For a wide range
of periods of the permeability variation, a matrix eigenvalue technique with eighth order accuracy has been employed to find
the critical Darcy– Rayleigh number. This is supplemented by a multiple-scales analysis of the large-period limit, and a brief
consideration of the anisotropic limit for very short periods. 相似文献
15.
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
16.
A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered
with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous
medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate
averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects
of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered.
The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly
and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds
number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with
the increase of Reynolds number. 相似文献
17.
A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces
is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman–Forchheimer-extended
Darcy equations. The two boundaries are considered as isothermal–isothermal, isoflux–isothermal and isothermal–isoflux for
the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are
solved numerically by finite difference method with Southwell–Over–Relaxation technique for extended Darcy model and analytically
using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter,
inertia effect, product of Brinkman number and Grashof number and the ratio of Grashof number and Reynolds number for equal
and different wall temperatures. Nusselt number at the walls is also determined for three types of thermal boundary conditions.
The viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of
upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree
very well for the Darcian model.
An erratum to this article is available at . 相似文献
18.
A linear stability analysis is performed for mono-diffusive convection in an anisotropic rotating porous medium with temperature-dependent
viscosity. The Galerkin variant of the weighted residual technique is used to obtain the eigen value of the problem. The effect
of Taylor–Vadasz number and the other parameters of the problem are considered for stationary convection in the absence or
presence of rotation. Oscillatory convection seems highly improbable. Some new results on the parameters’ influence on convection
in the presence of rotation, for both high and low rotation rates, are presented. 相似文献
19.
A numerical investigation of the steady-state, laminar, axi-symmetric, mixed convection heat transfer in the annulus between
two concentric vertical cylinders using porous inserts is carried out. The inner cylinder is subjected to constant heat flux
and the outer cylinder is insulated. A finite volume code is used to numerically solve the sets of governing equations. The
Darcy–Brinkman–Forchheimer model along with Boussinesq approximation is used to solve the flow in the porous region. The Navier–Stokes
equation is used to describe the flow in the clear flow region. The dependence of the average Nusselt number on several flow
and geometric parameters is investigated. These include: convective parameter, λ, Darcy number, Da, thermal conductivity ratio,
K
r, and porous-insert thickness to gap ratio (H/D). It is found that, in general, the heat transfer enhances by the presence of porous layers of high thermal conductivity
ratios. It is also found that there is a critical thermal conductivity ratio on which if the values of Kr are higher than
the critical value the average Nusselt number starts to decrease. Also, it found that at low thermal conductivity ratio (K
r ≈ 1) and for all values of λ the porous material acts as thermal insulation. 相似文献
20.
Quasi-steady solidification between two vertical flat plates filled with a saturated porous medium has been investigated.
The medium is homogeneous and isotropic. The convection flow of liquid takes place in the porous medium in the variable space
between the two walls. One of the vertical walls is set to a temperature lower than the solidification temperature of the
medium and therefore a frozen crust is formed on this wall. The second wall has a high temperature then the fusion temperature
of the medium. The problem has been simplified by assuming laminar flow and the Brinkman and the Oberbeck–Bousinesq’s approximations.
The results are presented in terms of the velocity for different properties of the porous medium. Various velocities are displayed
in dependence of the Rayleigh and Darcy numbers. The study indicates that asymmetric boundary conditions have an important
effect on the temperature and flow field. In addition, the growth of the thickness of the frozen layer with time has been
derived from a simple analytical solution of the interface energy equation. 相似文献