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1.
Mixed Convection in a Vertical Porous Channel 总被引:1,自引:1,他引:0
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.
Combined free and forced convection flow in a parallel plate vertical channel filled with porous matrix is analyzed in the fully developed region with boundary conditions of third kind. The flow is modeled using the Brinkman?CForchheimer-extended Darcy equations. The plates exchange heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. Governing equations are solved numerically by shooting technique that uses classical explicit Runge?CKutta scheme and Newton?CRaphson method as a correction scheme and analytically using perturbation series method for Darcy model. The velocity field, the temperature field and Nusselt numbers are obtained for governing parameters such as porous parameter, inertia term and perturbation parameter for equal and unequal Biot numbers and are displayed graphically. The dimensionless mean velocity and bulk temperature are also determined. It is found that the numerical solutions agree for small values of the perturbation parameter in the absence of the inertial forces. 相似文献
4.
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
5.
We study scalar diffusion, both from Eulerian and Lagrangian perspectives, advected by two dimensional flows. Emphasis is devoted to the problem of scalar diffusion under a synthetic turbulent flow. We present numerical and analytical results for the turbulent diffusion coefficient either from the influence of the turbulent synthetic field and a periodic array of eddies. Preliminary results concerning Lagrangian dispersion are also reported. 相似文献
6.
Mansour M. A. Abd El-Hakiem M. Abd El-Gaid S. Subba Reddy Gorla Rama 《Transport in Porous Media》1997,28(3):307-317
Mixed convection in power-law type non-Newtonian fluids along an isothermal vertical cylinder in porous media is studied. The problem is solved by means of a finite difference method for the case of uniform wall temperature. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5–1.5. 相似文献
7.
Kalabin et al. (Numer. Heat Transfer A 47, 621-631, 2005) studied the unsteady natural convection for the sinusoidal oscillating wall temperature on one side wall
and constant average temperature on the opposing side wall. The present article is on the unsteady natural convective heat
transfer in an inclined porous cavity with similar temperature boundary conditions as those of Kalabin et al. The inclined
angle of the cavity is varied from 0° to 80°. The flow field is modeled with the Brinkman-extended Darcy model. The combined effects
of inclination angle of the enclosure and oscillation frequency of wall temperature are studied for Ra* = 103, Da = 10−3, , and Pr=1. Some results are also obtained with the Darcy–Brinkman–Forchheimer model and Darcy’s law and are compared with the present
Brinkman-extended Darcy model. The maximal heat transfer rate is attained at the oscillating frequency f = 46.7π and the inclined angle . 相似文献
8.
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
9.
The effect of surface melting on the dual solutions that can arise in the problem of the mixed convection boundary-layer flow past a vertical surface embedded in a non-Darcian porous medium is considered. The problem is described by M, melting parameter, \(\lambda \), mixed convection parameter, and \(\gamma \), the flow inertia coefficient, numerical results being obtained in terms of these three parameters. It is seen that the melting phenomenon reduces the heat transfer rate and enhances the boundary-layer separation at the solid–liquid interface. Asymptotic solutions for the forced convection, \(\lambda =0\), and free convection, large \(\lambda \), limits are derived. 相似文献
10.
Azizah Mohd Rohni Syakila Ahmad John H. Merkin Ioan Pop 《Transport in Porous Media》2013,96(2):237-253
The steady mixed convection boundary-layer flow on a vertical circular cylinder embedded in a porous medium filled by a nanofluid is studied for both cases of a heated and a cooled cylinder. The governing system of partial differential equations is reduced to ordinary differential equations by assuming that the surface temperature of the cylinder and the velocity of the external (inviscid) flow vary linearly with the axial distance x measured from the leading edge. Solutions of the resulting ordinary differential equations for the flow and heat transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle volume fraction ${\phi}$ , the mixed convection or buoyancy parameter ?? and the curvature parameter ??. Results are presented for the specific case of copper nanoparticles. A critical value ?? c of ?? with ?? c <?0 is found, with the values of | ?? c| increasing as the curvature parameter ?? or nanoparticle volume fraction ${\phi}$ is increased. Dual solutions are seen for all values of ?? >??? c for both aiding, ?? >?0 and opposing, ?? <?0, flows. Asymptotic solutions are also determined for both the free convection limit ${(\lambda \gg 1)}$ and for large curvature parameter ${(\gamma \gg 1)}$ . 相似文献
11.
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
12.
The paper presents a study of the laminar mixed convection adjacent to vertical continuously stretching sheets, taking into account the effects of variable viscosity and variable thermal diffusivity. The similarity solutions are reported for isothermal sheet moving with a velocity of the form uw=Bx0.5 and a continuous linearly stretching sheet with a linear surface temperature distribution. The equations of conservation of mass, momentum and energy, which govern the flow and heat transfer, are solved numerically by using the shooting method. The numerical results obtained for the flow and heat transfer characteristics reveal many interesting behaviors. The numerical results show that, variable viscosity, variable thermal diffusivity, the velocity exponent parameter, the temperature exponent parameter and the buoyancy force parameter have significant influences on the velocity and temperature profiles, shear stress and Nusselt number in two cases air and water. 相似文献
13.
Transport in Porous Media - 相似文献
14.
Mahesha Narayana Ahmed A. Khidir Precious Sibanda P. V. S. N. Murthy 《Transport in Porous Media》2013,96(2):419-428
The paper presents an investigation of the influence of thermal radiation and viscous dissipation on the mixed convective flow due to a vertical plate immersed in a non-Darcy porous medium saturated with a Newtonian fluid. The physical properties of the fluid are assumed to be constant. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations and solved numerically using a shooting method. The results are analyzed for the effects of various physical parameters such as viscous dissipation, thermal radiation, mixed convection parameters, and the modified Reynolds number on dynamics. The heat transfer coefficient is also tabulated for different values of the physical parameters. 相似文献
15.
A generalized differential-integral quadrature (GDQ) discretization technique was used to solve a mixed heat convection problem in a body-fit coordinate system in its primitive variables form. A special treatment of the boundary condition to satisfy the continuity and momentum equations along the boundaries with the implementation of the GDQ method was investigated. Comparisons with the experimental and numerical results of other investigators are presented and discussed. In contrast with the existing published results, this highly accurate method was able to reveal extremely weak net circulation around the outer cylinder. In the horizontal annulus with the mixed heat convection problem the combination of unbalance of buoyancy and centrifugal forces causes net circulation. The net circulation decreases and approaches to zero with the rise of Rayleigh number, and it reaches its minimum value with high eccentricity when the inclination angle of eccentricity is π. 相似文献
16.
The mixed convection boundary-layer flow on a vertical surface heated convectively is considered when a constant surface heat transfer parameter is assumed. The problem is seen to be chararterized by a mixed convection parameter $\gamma $ γ . The flow and heat transfer near the leading edge correspond to forced convection solution and numerical solutions are obtained to determine how the solution then develops. The solution at large distances is obtained and this identifies a critical value $\gamma _c$ γ c of the parameter $\gamma $ γ . For $\gamma > \gamma _c$ γ > γ c a solution at large distances is possible and this is approached in the numerical integrations. For $\gamma <\gamma _c$ γ < γ c the numerical solution breaks down at a finite distance along the surface with a singularity, the nature of which is discussed. 相似文献
17.
In this paper the problem of mixed convection on a moving vertical cylinder with suction in a moving micropolar fluid medium
has been investigated, using finite element method. The effect of important parameters, namely micropolar parameter, suction
parameter and velocity coefficient parameter have been discussed on the velocity, microrotation and temperature functions
when the velocity of the cylinder is greater than the free stream velocity. Skin friction and the Nusselt number have also
been computed, which are given in the table. The temperature distribution is effected moderately by the motion of the cylinder
as well with the buoyancy parameter. 相似文献
18.
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
19.
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
20.
The mixed convection boundary-layer flow on one face of a semi-infinite vertical surface embedded in a fluid-saturated porous medium is considered when the other face is taken to be in contact with a hot or cooled fluid maintaining that surface at a constant temperature $T_\mathrm{{f}}$ . The governing system of partial differential equations is transformed into a system of ordinary differential equations through an appropriate similarity transformation. These equations are solved numerically in terms of a dimensionless mixed convection parameter $\epsilon $ and a surface heat transfer parameter $\gamma $ . The results indicate that dual solutions exist for opposing flow, $\epsilon <0$ , with the dependence of the critical values $\epsilon _\mathrm{{c}}$ on $\gamma $ being determined, whereas for the assisting flow $\epsilon >0$ , the solution is unique. Limiting asymptotic forms for both $\gamma $ small and large and $\epsilon $ large are also discussed. 相似文献