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1.
The mixed convection caused when a horizontal circular cylinder is suddenly heated is investigated in the situation when the initial flow past the cylinder is uniform and its direction either upwards or downwards. An analytical series solution, which is valid at small times, is obtained using the matched asymptotic expansions technique. A numerical solution, which is valid at all times and for any values of the Rayleigh and Péclet numbers, is also obtained using a fully implicit finite-difference method. Three different regimes, when either the free or forced convection is dominant or when they have the same order of magnitude, are considered. In the free convection dominated regime, two vortices develop near the sides of the cylinder in both situations of an upward or downward external flow. Comparisons between the analytical and numerical results at small times, as well as a detailed discussion of the evolution of the numerical solution are presented. The numerical results obtained for large Rayleigh, Ra, and Péclet Pe, numbers show that a thermal boundary-layer forms adjacent to the cylinder for any value of the ratio Ra/e. The steady state boundary-layer analysis, similar to that performed by Cheng and Merkin, is analysed in comparison to the numerical solution obtained for large values of Ra and Pe at very large times. 相似文献
2.
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
3.
We analyse the convection flow of a viscous fluid through a horizontal channel enclosing a fully saturated porous medium. The Galerkin finite element analysis is used to discuss the flow and heat transfer through the porous medium using serendipity elements. The velocity, the temperature distributions and the rate of heat transfer are analysed for variations in the governing parameters. The profiles at different vertical levels are asymmetric curves, exhibiting reversal flow everywhere except on the midplane. In a given porous medium, for fixed G or N, the temperature in the fluid region at any position in fluids with a higher Prandtl number, is much higher than in fluids with a lower Prandtl number. Likewise, other parameters being fixed, lesser the permeability of the medium, lower the temperature in the flow field. Nu reduces across the flow at all axial positions, while it enhances along the axial direction of the channel. Nu reduces with decrease in the Darcy parameter D, and thus lesser the permeability of the medium, lesser the rate of heat transfer across the boundary at any axial position of the channel. 相似文献
4.
The paper deals with a steady coupled dissipative layer, called Marangoni mixed convection boundary layer, which can be formed
along the interface of two immiscible fluids, in surface driven flows. The mixed convection boundary layer is generated when
besides the Marangoni effects there are also buoyancy effects due to gravity and external pressure gradient effects. We shall
use a model proposed by Golia and Viviani (L’ Aerotecnica missili e Spazio 64 (1985) 29–35, Meccanica 21 (1986) 200–204) wherein the Marangoni coupling condition has been included into the boundary conditions at the interface.
The similarity equations are first determined, and the pertinent equations are solved numerically for some values of the governing
parameters and the features of the flow and temperature fields as well as the interface velocity and heat transfer at the
interface are analysed and discussed. 相似文献
5.
A fully developed mixed convection flow between inclined parallel flat plates filled with a porous medium is considered through
which there is a constant flow rate and with heat being supplied to the fluid by the same uniform heat flux on each plate.
The equations governing this flow are made non-dimensional and are seen to depend on two dimensionless parameters, a mixed
convection parameter λ and the Péclet number Pe, as well as the inclination γ of the plates to the horizontal. The velocity and temperature profiles are obtained in terms of λ, Pe and γ when the channel is inclined in an upwards direction as well as for horizontal channels. The limiting cases of small and
large λ and small Pe are considered with boundary-layer structures being seen to develop on the plates for large values of λ. 相似文献
6.
The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water
close to its maximum density is considered for uniform wall temperature and outer flow. The problem can be reduced to similarity
form and the resulting equations are examined in terms of a mixed convection parameter λ and a parameter δ which measures
the difference between the ambient temperature and the temperature at the maximum density. Both assisting (λ > 0) and opposing
flows (λ < 0) are considered. A value δ0 is found for which there are dual solutions for a range λc < λ < 0 of λ (the value of λc dependent on δ) and single solutions for all λ ≥ 0. Another value of δ1 of δ, with δ1 > δ0, is found for which there are dual solutions for a range 0 < λ < λc of positive values of λ, with solutions for all λ≤ 0. There is also a range δ0 < δ < δ1 where there are solutions only for a finite range of λ, with critical points at both positive and negative values of λ, thus
putting a finite limit on the range of existence of solutions. 相似文献
7.
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
8.
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
9.
We study flow and heat transfer to a cylinder in cross flow at Re = 3,900–80,000 by means of three-dimensional transient RANS (T-RANS) simulations, employing an RNG k − ε turbulence model. Both the case of a bare solid cylinder and that of a solid cylinder surrounded at some fixed distance by
a thin porous layer have been studied. The latter configuration is a standard test geometry for measuring the insulating and
protective performance of garments. In this geometry, the flow in the space between the solid cylinder and the porous layer
is laminar but periodic, whereas the outer flow is transitional and characterized by vortex shedding in the wake of the cylinder.
The results from the T-RANS simulations are validated against data from Direct Numerical Simulations and experiments. It is
found that T-RANS is very well suited for simulating this type of flow. The transient nature of the flow underneath the porous
layer is well reproduced, as well as the influence of vortex shedding on the heat transfer in the downstream stagnation zone.
T-RANS results are found to be in much better agreement with DNS and experimental data than results from steady-state RANS. 相似文献
10.
In this note, we reply to the comments by Rees and Magyari (2007) on our article (Aydin and Kaya 2007). They mainly stated
that the thermal boundary conditions we defined at the edge of the boundary layer were incompatible with the energy equation.
This is questionable and therefore we will discuss it below. They disclosed that our results were in error. However, this
is quite misleading. Scientifically, they cannot reach such a conclusion without comparing our results with what they thought
to be correct. In fact, this misleading and unproven statement will be shown not to be correct in the following. 相似文献
11.
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
12.
The steady boundary-layer flow near the stagnation point on an impermeable vertical surface with slip that is embedded in
a fluid-saturated porous medium is investigated. Using appropriate similarity variables, the governing system of partial differential
equations is transformed into a system of ordinary differential equations. This system is then solved numerically. The features
of the flow and the heat transfer characteristics for different values of the governing parameters, namely, the Darcy–Brinkman,
Γ, mixed convection, λ, and slip, γ, parameters, are analysed and discussed in detail for the cases of assisting and opposing
flows. It is found that dual solutions exist for assisting flows, as well as those usually reported in the literature for
opposing flows. A stability analysis of the steady flow solutions encountered for different values of the mixed convection
parameter λ is performed using a linear temporal stability analysis. This analysis reveals that for γ = 0 (slip absent)
and Γ = 1 the lower solution branch is unstable while the upper solution branch is stable. 相似文献
13.
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
14.
Mixed Convection on a Horizontal Surface Embedded in a Porous Medium: the Structure of a Singularity
The mixed convection boundary-layer flow on a horizontal impermeable surface embedded in a saturated porous medium and driven by a local heat source is considered. Similarity solutions are obtained for specific outer flow variations and these are shown to have a solution only for parameter values greater than some critical value. When this is not the case the solution develops a singularity at a finite distance from the leading edge. The nature of this singularity is also discussed. 相似文献
15.
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
16.
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
17.
Calculated free convection flows and heat transfer are presented for concentric spherical annular sectors, filled with a porous medium. Two isothermal walls and an adiabatic radial wall at the sector angle define the sectors. The governing equations (in the stream function and temperature formulation) are solved numerically using ADI (alternative direction implicit) finite-difference method. Over the range of geometric parameters examined, the obtained results for spherical annuli and low Rayleigh number Ra. As Ra increases, multicellular flows develop for small values of the aspect ratio parameter . In addition, analytical solutions of the governing equations were obtained for small values of Ra (1) and it was shown that these solutions agree well with those obtained numerically. Significant differences in the local heat transfer rates on the inner and outer walls of the spherical annuli were observed from these solutions. 相似文献
18.
Analytic Series Solution for Unsteady Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium 总被引:1,自引:1,他引:0
In this paper, we solve the unsteady mixed convection flow near the stagnation point on a heated vertical flat plate embedded in a Darcian fluid-saturated porous medium by means of an analytic technique, namely the Homotopy Analysis Method. Different from previous perturbation results, our analytic series solutions are accurate and uniformly valid for all dimensionless times and for all possible values of mixed convection parameter, and besides agree well with numerical results. This provides us with a new analytic approach to investigate related unsteady problems. 相似文献
19.
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
20.
The steady boundary-layer flow near the stagnation point on a vertical flat plate embedded in a fluid-saturated porous medium
characterized by an anisotropic permeability is investigated. Using appropriate similarity transformation, the governing system
of partial differential equations is transformed into a system of ordinary differential equations. This system is then solved
numerically. The features of the flow and the heat transfer characteristics for different values of the governing parameters,
namely, the modified mixed convection parameter Λ, and the anisotropy parameter A are analyzed and discussed. It is found that dual solutions exist for both assisting and opposing flows. Moreover, the range
of Λ for which the solution exists increases with A. 相似文献