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1.
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
2.
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
3.
Stability of a flat layer with a free boundary in the model of microconvection is studied in the linear approximation of equilibrium. The most important physical case is considered, where the Boussinesq parameter and the Rayleigh number depend linearly on the Marangoni number. It is shown that longwave disturbances always decay. Neutral curves for a wide range of dimensionless parameters are constructed numerically; new (as compared to the Oberbeck–Boussinesq model) growing disturbances are found, which are caused by fluid compressibility. Based on numerical results, the areas of applicability of the microconvection, Oberbeck–Boussinesq, and viscous heatconducting fluid models are established. 相似文献
4.
Combined forced and free convection flow in a fluid saturated inclined plane channel is investigated by taking into account
the effect of viscous dissipation. Steady parallel flow is considered assuming that the temperature gradient in the parallel
flow direction is constant, and the channel walls are subject to uniform symmetric heat fluxes. Two possible formulations
of the Darcy–Boussinesq scheme are considered, based on two different choices of the reference temperature for modelling buoyancy.
The first choice is a constant temperature, while the second is a streamwise changing temperature. It is shown that both approaches
substantially agree in the formulation of the balance equations for the range of values of the Darcy–Rayleigh number such
that viscous dissipation is important. The boundary value problem is solved analytically for any tilt angle, revealing that
it admits dual solutions for assigned values of the governing parameters. The rather important effect of viscous dissipation
in the special case of adiabatic channel walls is outlined.
E. Magyari is on leave from Institute of Building Technology, ETH—Zürich 相似文献
5.
J. Prathap Kumar J. C. Umavathi I. Pop Basavaraj M. Biradar 《Transport in Porous Media》2009,80(1):117-135
An analysis of fully developed combined free and forced convective flow in a fluid saturated porous medium channel bounded
by two vertical parallel plates is presented. The flow is modeled using Brinkman equation model. The viscous and Darcy dissipation
terms are also included in the energy equation. Three types of thermal boundary conditions such as isothermal–isothermal,
isoflux–isothermal, and isothermal–isoflux for the left–right walls of the channel are considered. Analytical solutions for
the governing ordinary differential equations are obtained by perturbation series method. In addition, closed form expressions
for the Nusselt number at both the left and right channel walls are derived. Results have been presented for a wide range
of governing parameters such as porous parameter, ratio of Grashof number and Reynolds number, viscosity ratio, width ratio,
and conductivity ratio on velocity, and temperature fields. It is found that the presence of porous matrix in one of the region
reduces the velocity and temperature. 相似文献
6.
Viscous dissipation effect on heat transfer characteristics of a rectangular microchannel is studied. Flow is governed by the Navier–Stokes equations with the slip flow and temperature jump boundary conditions. Integral transform technique is applied to derive the temperature distribution and Nusselt number. The velocity distribution is taken from literature. The solution method is verified for the case where viscous dissipation is neglected. It is found that, the viscous dissipation is negligible for gas flows in microchannels, since the contribution of this effect on Nu number is about 1%. However, this effect should be taken into account for much more viscous flows, such as liquid flows. Neglecting this effect for a flat microchannel with an aspect ratio of 0.1 for Br=0.04 underestimates the Nu number about 5%. 相似文献
7.
E. Magyari 《Transport in Porous Media》2009,80(2):389-395
In a recent article by Barletta and Nield (Transport in Porous Media, DOI , 2009), the title problem for the fully developed parallel flow regime was considered assuming isoflux/isothermal wall conditions.
For the limiting cases of the forced and the free convection, analytical solutions were reported; for the general case, numerical
solutions were reported. The aim of the present note is (i) to give an analytical solution for the full problem in terms of
the Weierstrass elliptic P-function, (ii) to illustrate this general approach by two easily manageable examples, and (iii) to rise a couple of questions
of basic physical interest concerning the interplay between the viscous dissipation and the pressure work. In this context,
the concept of “eigenflow” introduced by Barletta and Nield is discussed in some detail. 相似文献
8.
Flow driven by an externally imposed pressure gradient in a vertical porous channel is analysed. The combined effects of viscous dissipation and thermal buoyancy are taken into account. These effects yield a basic mixed convection regime given by dual flow branches. Duality of flow emerges for a given vertical pressure gradient. In the case of downward pressure gradient, i.e. upward mean flow, dual solutions coincide when the intensity of the downward pressure gradient attains a maximum. Above this maximum no stationary and parallel flow solution exists. A nonlinear stability analysis of the dual solution branches is carried out limited to parallel flow perturbations. This analysis is sufficient to prove that one of the dual solution branches is unstable. The evolution in time of a solution in the unstable branch is also studied by a direct numerical solution of the governing equation. 相似文献
9.
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
10.
P. I. Kolykhalov 《Fluid Dynamics》1986,21(6):854-860
The viscous dissipative instability of two flows with continuous spectrum of neutrally-stable perturbations in the absence
of dissipation is investigated. Ranges of wave numbers in which viscosity leads to flow destabilization are determined for
a shear discontinuity in a smoothly-stratified fluid. A shear flow with a velocity in the transition layer that depends linearly
on the coordinate has a continuum of neutral modes even in the case of an unstratified fluid. When viscosity is present in
one of the layers with constant velocity, one of the branches of the spectrum becomes unstable. When the viscosity is the
same above and below the shear layer, dissipation only leads to the damping of the perturbations.
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 14–19, November–December, 1986. 相似文献
11.
Natalia Strong 《Journal of Mathematical Fluid Mechanics》2008,10(4):488-502
The present paper examines the effect of vertical harmonic vibration on the onset of convection in an infinite horizontal
layer of fluid saturating a porous medium. A constant temperature distribution is assigned on the rigid boundaries, so that
there exists a vertical temperature gradient. The mathematical model is described by equations of filtration convection in
the Darcy–Oberbeck–Boussinesq approximation. The linear stability analysis for the quasi-equilibrium solution is performed
using Floquet theory. Employment of the method of continued fractions allows derivation of the dispersion equation for the
Floquet exponent σ in an explicit form. The neutral curves of the Rayleigh number Ra versus horizontal wave number α for the
synchronous and subharmonic resonant modes are constructed for different values of frequency Ω and amplitude A of vibration. Asymptotic formulas for these curves are derived for large values of Ω using the method of averaging, and,
for small values of Ω, using the WKB method. It is shown that, at some finite frequencies of vibration, there exist regions
of parametric instability. Investigations carried out in the paper demonstrate that, depending on the governing parameters
of the problem, vertical vibration can significantly affect the stability of the system by increasing or decreasing its susceptibility
to convection.
相似文献
12.
The problem of the onset of convective roll instabilities in a horizontal porous layer with isothermal boundaries at unequal
temperatures, well known as the Horton–Rogers–Lapwood problem, is revisited including the effect of pressure work and viscous
dissipation in the local energy balance. A linear stability analysis of rolls disturbances is performed. The analysis shows
that, while the contribution of viscous dissipation is ineffective, the contribution of the pressure work may be important.
The condition of marginal stability is investigated by adopting two solution procedures: method of weighted residuals and
explicit Runge–Kutta method. The pressure work term in the energy balance yields an increase of the value of the Darcy–Rayleigh
number at marginal stability. In other words, the effect of pressure work is a stabilizing one. Furthermore, while the critical
value of the Darcy– Rayleigh number may be considerably affected by the pressure work contribution, the critical value of
the wave number is affected only in rather extreme cases, i.e. for very high values of the Gebhart number. A nonlinear stability
analysis is also performed pointing out that the joint effects of viscous dissipation and pressure work result in a reduction
of the excess Nusselt number due to convection, when the Darcy–Rayleigh number is replaced by the superadiabatic Darcy–Rayleigh
number. 相似文献
13.
We consider the asymptotic limit for the complete Navier–Stokes–Fourier system as both Mach and Froude numbers tend to zero.
The limit is investigated in the context of weak variational solutions on an arbitrary large time interval and for the ill-prepared
initial data. The convergence to the Oberbeck–Boussinesq system is shown.
相似文献
14.
Maxim A. Olshanskii 《国际流体数值方法杂志》2012,69(5):983-994
We study numerically a recently introduced formulation of incompressible Newtonian fluid equations in vorticity–helical density and velocity–Bernoulli pressure variables. Unlike most numerical methods based on vorticity equations, the current approach provides discrete solutions with mass conservation, divergence‐free vorticity, and accurate kinetic energy balance in a simple and natural way. The method is applied to compute buoyancy‐driven flows in a differentially heated cubic enclosure in the Boussinesq approximation for Ra ∈ {104,105,106}. The numerical solutions on a finer grid are of benchmark quality. The computed helical density allows quantification of the three‐dimensional nature of the flow. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
We investigate a sequence of low-dimensional models of turbulent channel flows. These models are based on the extraction of
the Karhunen–Loève (KL) eigenfunctions from a large-scale simulation in a wide channel with R
*=180 (based on the friction velocity). KL eigenfunctions provide an optimal coordinate system in which to represent the dynamics
of the turbulent flow. The hierarchy of KL modes identifies the most energetic independent phenomena in the system. A series
of Galerkin projections is then used to derive a dynamical approximation to flows. In order to capture essential aspects of
the flow in a low-dimensional system, a careful selection of modes is carried out. The resulting models satisfy momentum and
energy conservation as well as yielding the amount of viscous dissipation found in the exact system. Their dynamics includes
modes which characterize the flux, rolls, and propagating waves. Unlike previous treatments the instantaneous streamwise flow
is time dependent and represented by KL flux modes. The rolls correspond to the streaks observed in experiments in the viscous
sublayer. Propagating waves which first appear in the model flow at low Reynolds number (R
*∼ 60) persist through the chaotic regime that appears as the Reynolds number is increased. Statistical measures of the chaotic
flows which have been generated by the models compare favorably with those found in full-scale simulations.
Received 13 July 1998 and accepted 8 January 1999 相似文献
16.
L. A. Kovaleva V. N. Kireev A. A. Musin 《Journal of Applied Mechanics and Technical Physics》2009,50(1):80-85
Results of numerical simulations of the thermal action on a high-viscosity hydrocarbon fluid with temperature-dependent viscosity
and thermal conductivity are presented. A system of equations of thermal convection in the Boussinesq approximation is used
as the constitutive equations to describe the convection of the hydrocarbon fluid. The dynamics of the temperature field and
convective structures in the fluid is studied. The spatial motion of the fluid is found to be locally nonuniform; the motion
is accompanied by vortex flows; as a result, two regions with significantly different temperatures are formed in the medium.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 95–100, January–February, 2009. 相似文献
17.
The transient character of the jet issuing from an upward nozzle centered at the bottom of a vertical cylindrical tank into
bulk liquid of a different density was measured using flow visualization and PIV for varying densimetric Froude numbers by
varying the jet Reynolds numbers and the ratios of fluid densities. Positively buoyant jets penetrate to the free surface,
driven by both momentum and buoyancy in the upward direction. The lighter jet fluid stratifies in a layer above the bulk liquid.
Upon starting, a negatively buoyant jet has three stages. First the jet penetrates to its maximum height in the tank. Then
the jet penetration decreases due to the downward backflow of heavier fluid surrounding the jet, which reduces the jet’s upward
momentum. Finally the jet penetration height fluctuates around a mean value about 70% the maximum height of penetration. For
small negative Froude numbers, the flow is fountain-like. The downward flow turns radially outward as it reaches the bottom
of the tank and eventually an annular recirculation zone forms at the bottom of the tank with vortical motion opposite the
vorticity of the jet. For large negative Froude numbers, the spreading of the jet extends far enough so the annular downward
flow is along the walls of the tank resulting in a large annular recirculation zone. The penetration depth, h, and time, t, scale with buoyancy flux, F, and the jet momentum flux, M, as hM
-3/4∣F∣1/2 and t∣F∣/M to collapse the transient jet penetration height data onto a single curve over a wide range of Froude numbers for either
positively or negatively buoyant jets.
Received: 8 June 1998/Accepted: 3 February 1999 相似文献
18.
Yu. Ya. Trifonov 《Journal of Applied Mechanics and Technical Physics》2007,48(1):91-100
The linear and nonlinear stability of downward viscous film flows on a corrugated surface to freesurface perturbations is
analyzed theoretically. The study is performed with the use of an integral approach in ranges of parameters where the calculated
results and the corresponding solutions of Navier-Stokes equations (downward wavy flow on a smooth wall and waveless flow
along a corrugated surface) are in good agreement. It is demonstrated that, for moderate Reynolds numbers, there is a range
of corrugation parameters (amplitude and period) where all linear perturbations of the free surface decay. For high Reynolds
numbers, the waveless downward flow is unstable. Various nonlinear wavy regimes induced by varying the corrugation amplitude
are determined.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 110–120, January–February, 2007. 相似文献
19.
The concepts of subcritical and supercritical flows are introduced for the long-wave approximation model describing stationary
free-boundary rotational flows of an ideal incompressible fluid. Shear flows of a fluid layer above an uneven bottom are analyzed.
Exact solutions describing different flow regimes are constructed, and the flow properties are studied as a function of the
flow regime. Flows with backward streamlines are considered.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 26–38, July–August, 2006.
An erratum to this article is available at . 相似文献
20.
Creeping channel flows of compressible fluids subject to wall slip are widely encountered in industries. This paper analyzes
such flows driven by pressure in planar as well as circular channels. The analysis elucidates unsteady flows of Newtonian
fluids subject to the Navier slip condition, followed by steady flows of viscoplastic fluids, in particular, Herschel–Bulkley
fluids and their simplifications including power law and Newtonian fluids, that slip at wall with a constant coefficient or
a coefficient inversely proportional to pressure. Under the lubrication assumption, analytical solutions are derived, validated,
and discussed over a wide range of parameters. Analysis based on the derived solutions indicates that unsteadiness alters
cross-section velocity profiles. It is demonstrated that compressibility of the fluids gives rise to a concave pressure distribution
in the longitudinal direction, whereas wall slip with a slip coefficient that is inversely proportional to pressure leads
to a convex pressure distribution. Energy dissipation resulting from slippage can be a significant portion in the total dissipation
of such a flow. A distinctive feature of the flow is that, in case of the pressure-dependent slip coefficient, the slip velocity
increases rapidly in the flow direction and the flow can evolve into a pure plug flow at the exit. 相似文献