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1.
The combined effects of the magnetic field, permeable walls, Darcy velocity, and slip parameter on the steady flow of a fluid in a channel of uniform width are studied. The fluid flowing in the channel is assumed to be homogeneous, incompressible,and Newtonian. Analytical solutions are constructed for the governing equations using Beavers-Joseph slip boundary conditions. Effects of the magnetic field, permeability,Darcy velocity, and slip parameter on the axial velocity, slip velocity, and shear stress are discussed in detail. It is shown that the Hartmann number, Darcy velocity, porous parameter, and slip parameter play a vital role in altering the flow and in turn the shear stress. 相似文献
2.
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
3.
The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated.The plate exchanges heat with an external fluid.Both conditions of equal and different reference temperatures of the external fluid are considered.First,the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically.Then,the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter.To relax the conditions on the perturbation parameter,the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique.The velocity,temperature,skin friction,and Nusselt numbers at the plates are discussed numerically and presented through graphs. 相似文献
4.
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
5.
A. Ali S. Saba S. Asghar D. N. Khan 《Journal of Applied Mechanics and Technical Physics》2017,58(6):990-996
The heat and mass transfer effects on the flow of a conducting third-grade fluid over an oscillating vertical porous plate with chemical reactions are considered. Highly nonlinear governing equations of the third-grade fluid are solved analytically by using a multi-parameter perturbation technique and compared with the numerical results obtained by the parallel shooting method. The fluid flow velocity, temperature, and concentration are analyzed as functions of the Hartmann number, suction parameter, Prandtl and Schmidt numbers, and chemical reaction parameter. 相似文献
6.
The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases. 相似文献
7.
This paper presents an analytical study of laminar fully developed free-convection flow between two vertical walls partially
filled with porous matrix and partially with a clear fluid having interface vertically. The momentum transfer in porous medium
is described by the Brinkman-extended Darcy model and the two regions are coupled by equating the velocity and shear stress
at the interface. The governing equations having non-linear nature have been solved by using perturbation method. It has been
found that effect of Brinkman term is in entire porous domain for large values of Darcy number while its effect is confined
nearer to interface and wall for small values of Darcy number.
Received on 19 March 1997 相似文献
8.
The verified Darcy–Brinkman model and boundary perturbation method are used to study the Brinkman flow in a tube with a bumpy surface, assuming the amplitude of the bumps is small compared to the mean tube radius. This study is important to understand the abnormal flow conditions caused by the boundary irregularities in diseased vessels. The mean rate flow is found, up to second-order correction, as a function of circumferential and longitudinal wave numbers and the permeability parameter of the porous medium. Numerical results displaying the velocity components and bumpiness functions are obtained for various values of the physical parameters of the problem. The results are tabulated and represented graphically for various physical parameters. It is found that, for every permeability parameter and for given bump area, there exists a circumferential wave number, for which the flow resistance is minimized. The limiting cases of Stokes and Darcy’s flows of the bumpiness function are discussed and compared with the available results in the literature. 相似文献
9.
Tiziana Tosco Daniele L. Marchisio Federica Lince Rajandrea Sethi 《Transport in Porous Media》2013,96(1):1-20
Flow of non-Newtonian fluids through porous media at high Reynolds numbers is often encountered in chemical, pharmaceutical and food, as well as petroleum and groundwater engineering, and in many other industrial applications. Under the majority of operating conditions typically explored, the dependence of pressure drops on flow rate is non-linear and the development of models capable of describing accurately this dependence, in conjunction with non-trivial rheological behaviors, is of paramount importance. In this work, pore-scale single-phase flow simulations conducted on synthetic two-dimensional porous media are performed via computational fluid dynamics for both Newtonian and non-Newtonian fluids and the results are used for the extension and validation of the Darcy?CForchheimer law, herein proposed for shear-thinning fluid models of Cross, Ellis and Carreau. The inertial parameter ?? is demonstrated to be independent of the viscous properties of the fluids. The results of flow simulations show the superposition of two contributions to pressure drops: one, strictly related to the non-Newtonian properties of the fluid, dominates at low Reynolds numbers, while a quadratic one, arising at higher Reynolds numbers, is dependent on the porous medium properties. The use of pore-scale flow simulations on limited portions of the porous medium is here proposed for the determination of the macroscale-averaged parameters (permeability K, inertial coefficient ?? and shift factor ??), which are required for the estimation of pressure drops via the extended Darcy?CForchheimer law. The method can be applied for those fluids which would lead to critical conditions (high pressures for low permeability media and/or high flow rates) in laboratory tests. 相似文献
10.
A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing. 相似文献
11.
Convective flow and heat transfer in an inclined channel bounded by two rigid plates held at constant different temperatures with one region filled with porous matrix saturated with a viscous fluid and another region with a clear viscous fluid different from the fluid in first region is studied analytically. The coupled nonlinear governing equations are solved using regular perturbation method. It is found that the presence of porous matrix in one of the region reduces the velocity and temperature. Results have been presented for a wide range of governing parameters such as Grashof number, porous parameter, angle of inclination, ratio of heights of the two layers and also the ratio of viscosities. 相似文献
12.
S. P. V. ANANTH B. N. HANUMAGOWDA S. V. K. VARMA C. S. K. RAJU I. KHAN P. RANA 《应用数学和力学(英文版)》2023,44(2):307-324
The heat and mass transfer of two immiscible fluids in an inclined channel with thermal diffusion, vicious, and Darcy dissipation is studied. The first region consists of a clear fluid, and the second one is filled with a nanofluid saturated with a porous medium. The behaviors of Cu-H2O, In-H2O, and Au-H2O nanofluids are analyzed. The transport properties are assumed to be constant. The coupled non-linear equations of the flow model are transformed into the dimensionless form, and the solutions for the velocity, temperature, and concentration are obtained by the regular perturbation technique. Investigations are carried out on the flow characteristics for various values of the material parameters. The results show that the velocity and temperature of the fluids enhance with the thermal Grashof number, solutal Grashof number, and Brinkman number while decrease with the porosity parameter and solid volume fraction. 相似文献
13.
A numerical study is performed to analyse heat and mass transfer phenomena due to natural convection in a composite cavity
containing a fluid layer overlying a porous layer saturated with the same fluid. The flow in the porous region is modelled
using Brinkman–Forchheimer-extended Darcy model that includes both the effect of macroscopic shear (Brinkman effect) and flow
inertia (Forchheimer effect). The vertical walls of the two-dimensional enclosure are isothermal whilst the horizontal walls
are adiabatic. The two regions are coupled by equating the velocity and stress components at the interface. The resulting
coupled equations in non-dimensional form are solved by an alternating direction implicit method by transforming them into
parabolic form by the addition of false transient terms. The numerical results show that the amount of fluid penetration into
the porous layer depends strongly upon the Darcy, thermal and solutal Rayleigh numbers. Average Nusselt number decreases while
average Sherwood number increases with an increase of the Lewis number. The transfer of heat and mass on the heated wall near
the interface depends strongly on the Darcy number.
Received on 11 May 1998 相似文献
14.
M. A. Ezzat A. A. El-Bary A. S. Hatem 《Journal of Applied Mechanics and Technical Physics》2014,55(4):660-671
A technique of the state space approach and the inversion of the Laplace transform method are applied to dimensionless equations of an unsteady one-dimensional boundary-layer flow due to heat and mass transfer through a porous medium saturated with a viscoelastic fluid bounded by an infinite vertical plate in the presence of a uniform magnetic field is described. Complete analytical solutions for the temperature, concentration, velocity, and induced magnetic and electric fields are presented. The inversion of the Laplace transforms is carried out by using a numerical approach. The proposed method is used to solve two problems: boundary-layer flow in a viscoelastic fluid near a vertical wall subjected to the initial conditions of a stepwise temperature and concentration and viscoelastic fluid flow between two vertical walls. The solutions are found to be dependent on the governing parameters including the Prandtl number, the Schmidt number, the Grashof number, reaction rate coefficient, viscoelastic parameter, and permeability of the porous medium. Effects of these major parameters on the transport behavior are investigated methodically, and typical results are illustrated to reveal the tendency of the solutions. Representative results are presented for the velocity, temperature, concentration, and induced magnetic and electric field distributions, as well as the local skin-friction coefficient and the local Nusselt and Sherwood numbers. 相似文献
15.
研究了非稳态分数阶Oldroyd-B流体在多孔介质中通过楔形拉伸板的驻点流动问题。基于分数阶Oldroyd-B流体的本构模型建立了动量方程,并在其中引入了浮升力和驻点流动特征。此外,考虑了具有热松弛延迟时间的修正的分数阶Fourier定律,并将其应用于能量方程和对流换热边界条件。接着,采用与L1算法相结合的有限差分法求解控制偏微分方程。最后,分析了相关物理参数对流动的影响。结果表明,随着楔角参数的增加,流体受到的浮升力增大,导致速度加快;达西数越大,介质的孔隙度变大,流体的流动越快;此外,温度分布先略有上升后明显下降,这表明Oldroyd-B流体具有热延迟特性。 相似文献
16.
A. V. Kuznetsov 《Flow, Turbulence and Combustion》1996,57(2):119-131
This paper concentrates on the analysis of the thermal nonequilibrium effects during forced convection in a parallel-plate channel filled with a fluid saturated porous medium. The flow in a channel is described by the Brinkman-Forchheimer-extended Darcy equation and the thermal nonequilibrium effects are accounted for by utilizing the two energy equations model. Applying the perturbation technique, an analytical solution of the problem is obtained. It is established that the temperature difference between the fluid and solid phases for the steady fully developed flow is proportional to the ratio of the flow velocity to the mean velocity. This results in a local thermal equilibrium at the walls of the channel if the Brinkman term which allows for the no-slip boundary condition at the walls is included into the momentum equation. 相似文献
17.
A. V. Kuznetsov 《Applied Scientific Research》1996,57(2):119-131
This paper concentrates on the analysis of the thermal nonequilibrium effects during forced convection in a parallel-plate
channel filled with a fluid saturated porous medium. The flow in a channel is described by the Brinkman-Forchheimer-extended
Darcy equation and the thermal nonequilibrium effects are accounted for by utilizing the two energy equations model. Applying
the perturbation technique, an analytical solution of the problem is obtained. It is established that the temperature difference
between the fluid and solid phases for the steady fully developed flow is proportional to the ratio of the flow velocity to
the mean velocity. This results in a local thermal equilibrium at the walls of the channel if the Brinkman term which allows
for the no-slip boundary condition at the walls is included into the momentum equation. 相似文献
18.
The effect of yield stress on the flow characteristics of a Casson fluid in a homogeneous porous medium bounded by a circular
tube is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. The
non-linear coupled implicit system of differential equations governing the flow is first transformed into suitable integral
equations and are solved numerically. Analytical solution is obtained for a Newtonian fluid in the case of constant permeability,
and the numerical solution is verified with that of the analytic solution. The effect of yield stress of the fluid and permeability
of the porous medium on shear stress and velocity distributions, plug flow radius and flow rate are examined. The minimum
pressure gradient required to start the flow is found to be independent of the permeability of the porous medium and is equal
to the yield stress of the fluid. 相似文献
19.
In this paper we investigate the combined free and forced convection of a fully developed Newtonian fluid within a vertical channel composed of porous media when viscous dissipation effects are taken into consideration. The flow is analysed in the region of a first critical Rayleigh number in order to interpret the multiple-valued solutions and discuss their validity. The governing fourth-order, ordinary differential equation, which contains the Darcy and the viscous dissipation terms, is solved analytically using perturbation techniques and numerically using D02HBF NAG Library. A detailed investigation of the governing O.D.E. is performed on both clear fluid and porous medium for various values of the viscous dissipation parameter, , when the wall temperature decreases linearly with height, and the pressure gradient is both above and below its hydrostatic value. Although mathematically the results in all cases show that there are two solution branches, producing four possible solutions, the study of the velocity and buoyancy profiles together with the Darcy effect indicate that only one of the two solutions at any value of the Rayleigh number appears to be physically acceptable. It is shown that the effect of the Darcy number decreases as the critical Rayleigh numbers increase. 相似文献
20.
K. Vajravelu K. V. Prasad Robert A. Van Gorder Jinho Lee 《Transport in Porous Media》2011,90(3):977-992
Numerical solutions for the free convection heat transfer in a viscous fluid at a permeable surface embedded in a saturated
porous medium, in the presence of viscous dissipation with temperature-dependent variable fluid properties, are obtained.
The governing equations for the problem are derived using the Darcy model and the Boussinesq approximation (with nonlinear
density temperature variation in the buoyancy force term). The coupled non-linearities arising from the temperature-dependent
density, viscosity, thermal conductivity, and viscous dissipation are included. The partial differential equations of the
model are reduced to ordinary differential equations by a similarity transformation and the resulting coupled, nonlinear ordinary
differential equations are solved numerically by a second order finite difference scheme for several sets of values of the
parameters. Also, asymptotic results are obtained for large values of | f
w|. Moreover, the numerical results for the velocity, the temperature, and the wall-temperature gradient are presented through
graphs and tables, and are discussed. It is observed that by increasing the fluid variable viscosity parameter, one could
reduce the velocity and thermal boundary layer thickness. However, quite the opposite is true with the non-linear density
temperature variation parameter. 相似文献