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1.
An analytical study of viscous dissipation effect on the fully developed forced convection Couette flow through a parallel
plate channel partially filled with porous medium is presented. A uniform heat flux is imposed at the moving plate while the
fixed plate is insulated. In the fluid-only region the flow field is governed by Navier–Stokes equation while the Brinkman-extended
Darcy law relationship is considered in the fully saturated porous medium. The interface conditions are formulated with an
empirical constant β due to the stress jump boundary condition. Fluid properties are assumed to be constant and the longitudinal
heat conduction is neglected. A closed-form solution for the velocity and temperature distributions and also the Nusselt number
in the channel are obtained and the viscous dissipation effect on these profiles is briefly investigated. 相似文献
2.
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
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.
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
5.
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
6.
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
7.
An analytical study is performed on steady, laminar, and fully developed forced convection heat transfer in a parallel plate
channel with asymmetric uniform heat flux boundary conditions. The channel is filled with a saturated porous medium, and the
lower and upper walls are subjected to different uniform heat fluxes. The dimensionless form of the Darcy–Brinkman momentum
equation is solved to determine the dimensionless velocity profile, while the dimensionless energy equation is solved to obtain
temperature profile for a hydrodynamically and thermally fully developed flow in the channel. Nusselt numbers for the lower
and upper walls and an overall Nusselt number are defined. Analytical expressions for determination of the Nusselt numbers
and critical heat flux ratio, at which singularities are observed for individual Nusselt numbers, are obtained. Based on the
values of critical heat flux ratio and Darcy number, a diagram is provided to determine the direction of heat transfer between
the lower or upper walls while the fluid is flowing in the channel. 相似文献
8.
J.C. Umavathi 《International Journal of Non》2005,40(1):91-101
The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε. 相似文献
9.
Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated
numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered:
isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic
Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not
the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the
value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered. 相似文献
10.
The effect of buoyancy forces on laminar convection with viscous dissipation in a vertical channel 总被引:1,自引:0,他引:1
The interaction of the viscous dissipation effect with the presence of buoyancy forces is investigated for laminar-flow heat
transfer in a parallel-plate vertical channel. One of the channel walls is considered as isothermal with a prescribed temperature,
while the other wall is considered as insulated. The velocity field is assumed to be parallel. The velocity field, the temperature
field and the Nusselt number are obtained by a perturbation series method which employs the ratio between the Grashof number
and the Reynolds number as the perturbation parameter. The radius of convergence of the perturbation series is estimated.
Received on 10 December 1997 相似文献
11.
Combined, forced, and free flow in a vertical circular duct filled with a porous medium is investigated according to the Darcy–Boussinesq
model. The effect of viscous dissipation is taken into account. It is shown that a thermal boundary condition compatible with
fully developed and axisymmetric flow is either a linearly varying wall temperature in the axial direction or, only in the
case of uniform velocity profile, an axial linear-exponential wall temperature change. The case of a linearly varying wall
temperature corresponds to a uniform wall heat flux and includes the uniform wall temperature as a special case. A general
analytical solution procedure is performed, by expressing the seepage velocity profile as a power series with respect to the
radial coordinate. It is shown that, for a fixed thermal boundary condition, i.e., for a prescribed slope of the wall temperature,
and for a given flow rate, there exist two solutions of the governing balance equations provided that the flow rate is lower
than a maximum value. When the maximum value is reached, the dual solutions coincide. When the flow rate is higher than its
maximum, no axisymmetric solutions exist.
E. Magyari is on leave from the Institute of Building Technology, ETH—Zürich. 相似文献
12.
Based on the two-energy equation model, taking into account viscous dissipation due to the interaction between solid skeleton and pore fluid flow, temperature expressions of the solid skeleton and pore fluid flow are obtained analytically for the thermally developing forced convection in a saturated porous medium parallel plate channel, with walls being at constant temperature. It is proved that the temperatures of the two phases for the local thermal nonequilibrium approach to the temperature derived from the one-energy equation model for the local thermal equilibrium when the heat exchange coefficient goes to infinite. The temperature profiles are shown in figures for different dimensionless parameters and the effects of the parameters on the local thermal nonequilibrium are revealed by parameter study. 相似文献
13.
The stability of a fluid-saturated horizontal rotating porous layer subjected to time-periodic temperature modulation is investigated
when the condition for the principle of exchange of stabilities is valid. The linear stability analysis is used to study the
effect of infinitesimal disturbances. A regular perturbation method based on small amplitude of applied temperature field
is used to compute the critical values of Darcy–Rayleigh number and wavenumber. The shift in critical Darcy–Rayleigh number
is calculated as a function of frequency of modulation, Taylor number, and Darcy–Prandtl number. It is established that the
convection can be advanced by the low frequency in-phase and lower-wall temperature modulation, where as delayed by the out-of-phase
modulation. The effect of Taylor number and Darcy–Prandtl number on the stability of the system is also discussed. We found
that by proper tuning of modulation frequency, Taylor number, and Darcy–Prandtl number it is possible to advance or delay
the onset of convection. 相似文献
14.
Ryoichi Chiba Masaaki Izumi Yoshihiro Sugano 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(1):61-74
Forced convection heat transfer in a non-Newtonian fluid flow inside a pipe whose external surface is subjected to non-axisymmetric
heat loads is investigated analytically. Fully developed laminar velocity distributions obtained by a power-law fluid rheology
model are used, and viscous dissipation is taken into account. The effect of axial heat conduction is considered negligible.
The physical properties are assumed to be constant. We consider that the smooth change in the velocity distribution inside
the pipe is piecewise constant. The theoretical analysis of the heat transfer is performed by using an integral transform
technique – Vodicka’s method. An important feature of this approach is that it permits an arbitrary distribution of the surrounding
medium temperature and an arbitrary velocity distribution of the fluid. This technique is verified by a comparison with the
existing results. The effects of the Brinkman number and rheological properties on the distribution of the local Nusselt number
are shown. 相似文献
15.
The numerical modeling of the conjugate heat transfer and fluid flow through the micro-heat sink was presented in the paper,
considering the viscous dissipation effect. Three different fluids with temperature dependent fluid viscosity are considered:
water, dielectric fluid HFE-7600 and isopropanol. The square shape of the cross-section is considered with D
h
= 50 μm with a channel length L = 50 mm. As most of the reported researches dealt with fully developed fluid flow and constant fluid properties in this paper
the thermal and hydro-dynamic developing laminar fluid flow is analyzed. Two different heat transfer conditions are considered:
heating and cooling at various Br. The influence of the viscous heating on local Nu and Po is analyzed. It was shown that
for a given geometry the local Po and Nu numbers are strongly affected by the viscous heating. Moreover the Po number attains
the fully developed value as the external heating is equal with the internal viscous heating. 相似文献
16.
This paper numerically simulates the forced convection flow in the developing region of a parallel-plate channel partially
filled with two porous substrates of equal thickness deposited at the inner walls of the channel. The major objective of the
present work is to investigate the impact of several operating and design parameters on the thermal performance of the channel
under consideration. The physical problem is simulated by using Darcy–Brinkman–Forchheimer model. For a prescribed amount
of porous material, the current investigation discusses the comparison between inserting this entire amount at one side of
the channel and inserting half of this amount at each side of the channel.
Received on 25 May 2000 / Published online: 29 November 2001 相似文献
17.
Analytical and numerical analyses have been performed for fully developed forced convection in a fluid-saturated porous medium channel bounded by two parallel plates. The channel walls are assumed to be finite in thickness. Conduction heat transfer inside the channel wall is also accounted and the full problem is treated as a conjugate heat transfer problem. The flow in the porous material is described by the Darcy–Brinkman momentum equation. The outer surfaces of the solid walls are treated as isothermal. A temperature dependent volumetric heat generation is considered inside the solid wall only. Analytical expressions for velocity, temperature, and Nusselt number are obtained after simplifying and solving the governing differential equations with reasonable approximations. Subsequent results obtained by numerical calculations show an excellent agreement with the analytical results. 相似文献
18.
An analytical study of fluid flow and heat transfer in a composite channel is presented. The channel walls are maintained at different constant temperatures in such a way that the temperatures do not allow for free convection. The upper plate is considered to be moving and the lower plate is fixed. The flow is modeled using Darcy–Lapwood–Brinkman equation. The viscous and Darcy dissipation terms are included in the energy equation. By applying suitable matching and boundary conditions, an exact solution has been obtained for the velocity and temperature distributions in the two regions of the composite channel. The effects of various parameters such as the porous medium parameter, viscosity ratio, height ratio, conductivity ratio, Eckert number, and Prandtl number on the velocity and temperature fields are presented graphically and discussed. 相似文献
19.
For a variety of fields in which micro-mechanical systems and electronic components are used, fluid flow and heat transfer
at the microscale needs to be understood and modeled with an acceptable reliability. In general, models are prepared by making
some extensions to the conventional theories by including the scaling effects that become important for microscale. Some of
these effects are; axial conduction, viscous dissipation, and rarefaction. In addition to these effects, temperature variable
thermal conductivity and viscosity may become important in microscale gas flows due to the high temperature gradients that
may exist in the fluid. For this purpose, simultaneously developing, single phase, laminar and incompressible air flow in
a microtube and in the micro gap between parallel plates is numerically analyzed. Navier–Stokes and energy equations are solved
and the variation of Nusselt number along the channel is presented in tabular and graphical forms as a function of Knudsen,
Peclet, and Brinkman numbers, including temperature variable thermal conductivity and viscosity. 相似文献
20.
Effects of Viscous Dissipation and Flow Work on Forced Convection in a Channel Filled by a Saturated Porous Medium 总被引:1,自引:3,他引:1
Fully developed forced convection in a parallel plate channel filled by a saturated porous medium, with walls held either at uniform temperature or at uniform heat flux, with the effects of viscous dissipation and flow work included, is treated analytically. The Brinkman model is employed. The analysis leads to expressions for the Nusselt number, as a function of the Darcy number and Brinkman number. 相似文献