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1.
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
2.
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
3.
Ali J. Chamkha S. Abbasbandy A. M. Rashad K. Vajravelu 《Transport in Porous Media》2012,91(1):261-279
The problem of steady, laminar, mixed convection boundary-layer flow over an isothermal vertical wedge embedded in a porous
medium saturated with a nanofluid is studied, in the presence of thermal radiation. The model used for the nanofluid incorporates
the effects of Brownian motion and thermophoresis with Rosseland diffusion approximation. The wedge surface is maintained
at a constant temperature and a constant nanoparticle volume fraction. The resulting governing equations are non-dimensionalized
and transformed into a non-similar form and then solved by Keller box method. A comparison is made with the available results
in the literature, and our results are in very good agreement with the known results. A parametric study of the physical parameters
is made, and a representative set of numerical results for the velocity, temperature, and volume fraction, the local Nusselt
and Sherwood numbers are presented graphically. The salient features of the results are analyzed and discussed. 相似文献
4.
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
5.
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
6.
Adopting a two-temperature and two-velocity model, appropriate to a bidisperse porous medium (BDPM) proposed by Nield and
Kuznetsov (2008), the classical steady, mixed convection boundary layer flow about a horizontal, isothermal circular cylinder
embedded in a porous medium has been theoretically studied in this article. It is shown that the boundary layer analysis leads
to expressions for the flow and heat transfer characteristics in terms of an inter-phase momentum parameter, a thermal diffusivity
ratio, a thermal conductivity ratio, a permeability ratio, a modified thermal capacity ratio, and a buoyancy or mixed convection
parameter. The transformed partial differential equations governing the flow and heat transfer in the f-phase (the macro-pores)
and the p-phase (the remainder of the structure) are solved numerically using a very efficient implicit finite-difference
technique known as Keller-box method. A good agreement is observed between the present results and those known from the open
literature in the special case of a traditional Darcy formulation (monodisperse system). 相似文献
7.
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
8.
Numerical analysis is performed to examine laminar free convective of a nanofluid along a vertical wavy surface saturated
porous medium. In this pioneering study, we have considered the simplest possible boundary conditions, namely those in which
both the temperature and the nanoparticle fraction are constant along the wall. Non-similar transformations are presented
for the governing equations and the obtained PDE are then solved numerically employing a fourth order Runge–Kutta method with
shooting technique. A detailed parametric study (nanofluid parameters) is performed to access the influence of the various
physical parameters on the local Nusselt number and the local Sherwood number. The results of the problem are presented in
graphical forms and discussed. 相似文献
9.
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
10.
John H. Merkin Azizah Mohd Rohni Syakila Ahmad Ioan Pop 《Transport in Porous Media》2012,94(1):133-147
A problem derived previously (Rohni et?al., Transp Porous Media 92:1?C14, 2012) for unsteady mixed convection flow in a porous medium involving a ??temperature slip?? boundary condition and fluid transfer through the boundary is considered. It is shown that the solution to this problem can be directly related to the solution of the corresponding problem for a prescribed surface temperature, involving a mixed convection parameter ??, an unsteadiness parameter A and transpiration parameter s. This latter problem is discussed in detail, particular attention being given to the steady analogue, A?=?0, allowing for fluid transfer through the surface, and to the unsteady problem, A?>?0, for an impermeable surface, s?=?0. Asymptotic results are obtained for large fluid transfer rates, ${s \gg 1}$ and ${s <0 , |s| \gg 1}$ and for large A. Particular attention is given to deriving asymptotic results for the critical points which determine the range of existence of solutions. 相似文献
11.
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
12.
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
13.
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
14.
The natural convection boundary-layer flow on a surface embedded in a fluid-saturated porous medium is discussed in the case
when the wall heat flux is related to the wall temperature through a power-law variation. The flow within the porous medium
is assumed to be described by Darcy’s law and the Boussinesq approximation is assumed for the density variations. Two cases
are discussed, (i) stagnation-point flow and (ii) flow along a vertical surface. The possible steady states are considered
first with the governing partial equations reduced to ordinary differential equations by similarity transformations and these
latter equations further transformed to previously studied free-convection problems. This identifies values of the exponent
N in the power-law wall temperature variation, N = 3/2 for stagnation-point flows and 3/2 ≤ N ≤ 3 for the vertical surface, where similarity solutions do not exist. Time development for stagnation-point flows is seen
to depend on N, for N < 3/2 the steady state is approached at large times, for N ≥ 3/2 a singularity develops at finite time leading to thermal runaway. Numerical solutions for the vertical surface, where
the temperature-dependent boundary condition becomes more significant as the solution develops, show that, for N < 3/2, the corresponding similarity solution is approached, whereas for N > 3/2 the solution breaks down at a finite distance along the surface. 相似文献
15.
Asterios Pantokratoras 《Transport in Porous Media》2009,76(3):309-325
A steady laminar boundary layer flowing along a vertical plate immersed in a Darcy–Brinkman porous medium saturated with water
at 4°C is studied. The plate temperature varies sinusoidally along the plate between 0 and 8°C where the density of water
varies parabolically and is almost symmetrical at about 4°C. Except for the existence of the buoyancy force, it is assumed
that either the plate moves upwards or the ambient water moves upwards (moving stream). The results are obtained with the
direct numerical solution of the boundary layer equations taking into account the temperature dependence of water thermophysical
properties (ρ, μ and c
p). Results are presented for the wall temperature gradient and the wall shear stress along the plate for free convection and
mixed convection. Temperature and velocity profiles are also presented. 相似文献
16.
The steady laminar incompressible free convective flow of a nanofluid over a permeable upward facing horizontal plate located
in porous medium taking into account the thermal convective boundary condition is studied numerically. The nanofluid model
used involves the effect of Brownian motion and the thermophoresis. Using similarity transformations the continuity, the momentum,
the energy, and the nanoparticle volume fraction equations are transformed into a set of coupled similarity equations, before
being solved numerically, by an implicit finite difference numerical method. Our analysis reveals that for a true similarity
solution, the convective heat transfer coefficient related with the hot fluid and the mass transfer velocity must be proportional
to x
−2/3, where x is the horizontal distance along the plate from the origin. Effects of the various parameters on the dimensionless longitudinal
velocity, the temperature, the nanoparticle volume fraction, as well as on the rate of heat transfer and the rate of nanoparticle
volume fraction have been presented graphically and discussed. It is found that Lewis number, the Brownian motion, and the
convective heat transfer parameters increase the heat transfer rate whilst the thermophoresis decreases the heat transfer
rate. It is also found that Lewis number and the convective heat transfer parameter enhance the nanoparticle volume fraction
rate whilst the thermophoresis parameter decreases nanoparticle volume fraction rate. A very good agreement is found between
numerical results of the present article for special case and published results. This close agreement supports the validity
of our analysis and the accuracy of the numerical computations. 相似文献
17.
A boundary layer analysis has been presented for the interaction of mixed convection with thermal radiation in laminar boundary flow from a vertical wedge in a porous medium saturated with a power-law type non-Newtonian fluid. The fluid considered is a gray medium, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. 相似文献
18.
In this investigation, we intend to present the influence of the prominent Soret effect on double-diffusive free convection heat and mass transfer in the boundary layer region of a semi-infinite inclined flat plate in a nanofluid saturated non-Darcy porous medium. The transformed boundary layer ordinary differential equations are solved numerically using the shooting and matching technique. Consideration of the nanofluid and the coupled convective process enhanced the number of non-dimensional parameters considerably thereby increasing the complexity of the present problem. A wide range of parameter values are chosen to bring out the effect of Soret parameter on the free convection process with varying angle of inclinations making the wall geometry from vertical to horizontal plate. The effects of angle of inclination and Soret parameter on the flow, heat and mass transfer coefficients are analyzed. The numerical results obtained for the velocity, temperature, volume fraction, and concentration profiles, local wall temperature, local nanoparticle concentration, and local wall concentration reveal interesting phenomenon, and some of these qualitative results are presented through the plots. 相似文献
19.
In this paper, oscillatory convection in a horizontal layer of nanofluid in porous medium is studied. For porous medium, Darcy model is applied. A linear stability theory and normal mode analysis method is used to find the solution confined between two free boundaries. The onset criterion for oscillatory convection is derived analytically and graphically. Regimes of oscillatory and non-oscillatory convection for various parameters are derived. The effects of Lewis number, concentration Rayleigh number, Prandtl?CDarcy number (Vadasz Number) and modified diffusivity ratio on the oscillatory convection are investigated graphically. We examine the validity of ??PES?? and concluded that ??PES?? is not valid for the problem. 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