共查询到20条相似文献,搜索用时 531 毫秒
1.
Double-diffusive convection due to a cylindrical source submerged in a salt-stratified solution is numerically investigated
in this study. For proper simulation of the vortex generated around the cylinder, a computational domain with irregular shape
is employed. Flow conditions depend strongly on the thermal Rayleigh number, Ra
T
, and the buoyancy ratio, R
ρ. There are two types of onset of instability existing in the flow field. Both types are due to either the interaction of
the upward temperature gradient and downward salinity gradient or the interaction of the lateral temperature gradient and
downward salinity gradient. The onset of layer instability due to plume convection is due to the former, whereas, the onset
of layer instability of layers around the cylinder is due to the latter. Both types can be found in the flow field. The transport
mechanism of layers at the top of the basic plume belongs to former while that due to basic plume and layer around the cylinder
are the latter. The increase in Ra
T
reinforces the plume convection and reduces the layer numbers generated around the cylinder for the same buoyancy ratio.
For the same Ra
T
, the increase of R
ρ suppresses the plume convection but reinforces the layers generated around the cylinder. The profiles of local Nusselt number
reflects the heat transfer characteristics of plume convection and layered structure. The profiles of averaged Nusselt number
are between the pure conduction and natural convection modes and the variation is due to the evolution of layers.
Received on 13 September 1996 相似文献
2.
K. A. Yih 《Heat and Mass Transfer》2001,37(1):53-57
The radiation effect on the mixed convection flow of an optically dense viscous fluid adjacent to an isothermal cone embedded
in a saturated porous medium with Rosseland diffusion approximation is numerically investigated. The entire regime of the
mixed convection is included, as the mixed convection parameter of χ varies from 0 (pure free convection) to 1 (pure forced
convection). The transformed nonlinear system of equations is solved by using an implicit finite difference method. Numerical
results are given for the dimensionless temperature profiles and the local Nusselt number for various values of the mixed
convection parameter χ, the cone angle parameter m, the radiation-conduction parameter R
d
and the surface temperature parameter H. The local Nusselt number decreases initially, reaches a minimum in the intermediate value of χ and then increases gradually.
It is apparent that increasing the cone angle parameter m enhances the local Nusselt number. The local Nusselt number is significantly increased for the large values of the radiation-conduction
parameter R
d
and the surface temperature parameter H, i.e., radiation effect becomes pronounced.
Received on 25 October 1999 相似文献
3.
Robert McKibbin 《Transport in Porous Media》1986,1(3):271-292
The theory describing the onset of convection in a homogeneous porous layer bounded above and below by isothermal surfaces
is extended to consider an upper boundary which is partly permeable. The general boundary condition p + λ ∂p/∂n = constant is applied at the top surface and the flow is investigated for various λ in the range 0 ⩽ λ < ∞. Estimates of the magnitude and horizontal distribution of the vertical mass and heat fluxes at the surface, the horizontally-averaged
heat flux (Nusselt number) and the fraction of the fluid which recirculates within the layer are found for slightly supercritical
conditions. Comparisons are made with the two limiting cases λ → ∞, where the surface is completely impermeable, and λ = 0, where the surface is at constant pressure. Also studied are the effects of anisotropy in permeability, ξ = K
H
/K
V
, and anisotropy is thermal conductivity, η = k
H
/k
V
, both parameters being ratios of horizontal to vertical quantities. Quantitative results are given for a wide variety of
the parameters λ, ξ and η. In the limit ξ/η → 0 there is no recirculation, all fluid being converted out of the top surface, while in the limit ξ/η → ∞ there is full recirculation. 相似文献
4.
The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water
at 4°C (maximum density) when the surface heat flux varies as x
m
and the velocity outside the boundary layer varies as x
(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions
of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions
when the mixed convection parameter λ is greater than some critical value λ
c
(dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > −1 being required for solutions. The nature of the critical point λ
c
is considered as well as various limiting forms; the forced convection limit (λ = 0), the free convection limit (λ → ∞) and
the limits as m → ∞ and as m → −1. 相似文献
5.
Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second
grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time
t=0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis. The solutions that have
been obtained are presented under series form in terms of the generalized G-functions. The similar solutions for ordinary second grade and Newtonian fluids are obtained from general solution for β→1, respectively, β→1 and α
1→0. Finally, the influences of the pertinent parameters on the fluid motion, as well as a comparison between models, is underlined
by graphical illustrations. 相似文献
6.
The combined effect of a vertical AC electric field and the boundaries on the onset of Darcy–Brinkman convection in a dielectric
fluid saturated porous layer heated either from below or above is investigated using linear stability theory. The isothermal
bounding surfaces of the porous layer are considered to be either rigid or free. It is established that the principle of exchange
of stability is valid irrespective of the nature of velocity boundary conditions. The eigenvalue problem is solved exactly
for free–free (F/F) boundaries and numerically using the Galerkin technique for rigid–rigid (R/R) and lower-rigid and upper-free
(F/R) boundaries. It is observed that all the boundaries exhibit qualitatively similar results. The presence of electric field
is emphasized on the stability of the system and it is shown that increasing the AC electric Rayleigh number R
ea is to facilitate the transfer of heat more effectively and to hasten the onset of Darcy–Brinkman convection. Whereas, increase
in the ratio of viscosities Λ and the inverse Darcy number Da
−1 is to delay the onset of Darcy–Brinkman electroconvection. Besides, increasing R
ea and Da
−1 as well as decreasing Λ are to reduce the size of convection cells. 相似文献
7.
Experiments have been performed to assess the impact of an extended surface on the heat transfer enhancement for axisymmetric,
turbulent liquid jet impingement on a heated round disk. The disk, with an array of integral radial fins mounted on its surface,
is placed at the bottom of an open vertical circular cavity. Hydrodynamic and heat transfer data were obtained for a dielectric
fluorocarbon liquid FC-77. For a fixed circular heater of diameter D=22.23 mm, several geometric parameters were tested: the nozzle diameter (4.42≤d≤9.27 mm), the confining wall diameter of the vertical cavity (22.23≤D
c≤30.16 mm), and the nozzle-to-heater spacing (0.5≤S/d≤5.0). The FC-77 flow rates varied from =0.2 to 11.0 l/min producing Reynolds numbers in the wide interval 700≤Re
d
≤44,000. For d=4.42 mm, the heat transfer response to the separation distance S/d was small but increased gradually with increasing nozzle diameter up to d=9.27 mm. The thermal resistance R
th increased with the confining wall diameter D
c and also with the nozzle diameter d. A minimum value of the thermal resistance of R
th,min=0.4 cm2 K/W was attained for a combination of d=4.42 mm, D
c=22.23 mm, S/d=1, and =7.5 l/min. Based on a simplified heat transfer model, reasonable agreement was obtained between measured values of
the thermal resistance and the R
th-predictions. The total fin effectiveness ɛf was shown to increase with increasing nozzle diameter, but was invariant with the flow rate (or the jet exit velocity). More
than a three-fold heat transfer enhancement was realized through the addition of the array of integral radial fins on the
heated round disk.
Received on 30 August 2000 / Published online: 29 November 2001 相似文献
8.
The onset of convective instability in an initially quiescent, stably stratified fluid layer between two horizontal plates
is analyzed with linear theory. The bottom boundary is heated suddenly from below, subjected to a step change in surface temperature.
The critical time t
c to mark the onset of Rayleigh-Bénard convection is predicted by propagation theory. This theory uses the length scaled by
, where α denotes thermal diffusivity. Under the normal mode analysis the dimensionless disturbance equations are obtained
as a function of τ(=αt/d
2) and ζ(=Z/), where d is the fluid layer depth and Z is the vertical distance. The resulting equations are transformed to self-similar ones by using scaling and finally fixing
τ as τc under the frame of coordinates τ and ζ. For a given γ, Pr and τc, the minimum value of Ra is obtained from the marginal stability curve. Here γ denotes the temperature ratio to represent the degree of stabilizing
effect, Pr is the Prandtl number and Ra is the Rayleigh number. With γ=0, the minimum Ra value approaches the well-known value of 1708 as τc increases. However, it is inversely proportional to τc
3/2 as τc decreases. With increasing γ, the system becomes more stable. It is interesting that in the present system, propagation theory
produces the stability criteria to bound the available experimental data over the whole domain of time.
Received 5 November 2001 and accepted 29 March 2002 Published online: 2 October 2002
RID="*"
ID="*" This work has been supported by both SK Chemicals Co. Ltd. and LG Chemical Ltd., Seoul under the Brain Korea 21 Project
of the Ministry of Education.
Communicated by H.J.S. Fernando 相似文献
9.
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
10.
The Darcy Model with the Boussinesq approximation is used to study natural convection in a horizontal annular porous layer
filled with a binary fluid, under the influence of a centrifugal force field. Neumann boundary conditions for temperature
and concentration are applied on the inner and outer boundary of the enclosure. The governing parameters for the problem are
the Rayleigh number, Ra, the Lewis number, Le, the buoyancy ratio, j{\varphi } , the radius ratio of the cavity, R, the normalized porosity, e{\varepsilon } , and parameter a defining double-diffusive convection (a = 0) or Soret induced convection (a = 1). For convection in a thin annular layer (R → 1), analytical solutions for the stream function, temperature and concentration fields are obtained using a concentric
flow approximation and an integral form of the energy equation. The critical Rayleigh number for the onset of supercritical
convection is predicted explicitly by the present model. Also, results are obtained from the analytical model for finite amplitude
convection for which the flow and heat and mass transfer are presented in terms of the governing parameters of the problem.
Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement
is observed between the analytical model and the numerical simulations. 相似文献
11.
Non-Darcy mixed convection in a porous medium from horizontal surfaces with variable surface heat flux of the power-law distribution
is analyzed. The entire mixed convection regime is divided into two regions. The first region covers the forced convection
dominated regime where the dimensionless parameter ζ
f
=Ra*
x
/Pe2
x
is found to characterize the effect of buoyancy forces on the forced convection with K
′
U
∞/ν characterizing the effect of inertia resistance. The second region covers the natural convection dominated regime where
the dimensionless parameter ζ
n
=Pe
x
/Ra*1/2
x
is found to characterize the effect of the forced flow on the natural convection, with (K
′
U
∞/ν)Ra*1/2
x
/Pe
x
characterizing the effect of inertia resistance. To obtain the solution that covers the entire mixed convection regime the
solution of the first regime is carried out for ζ
f
=0, the pure forced convection limit, to ζ
f
=1 and the solution of the second is carried out for ζ
n
=0, the pure natural convection limit, to ζ
n
=1. The two solutions meet and match at ζ
f
=ζ
n
=1, and R
*
h
=G
*
h
.
Also a non-Darcy model was used to analyze mixed convection in a porous medium from horizontal surfaces with variable wall
temperature of the power-law form. The entire mixed convection regime is divided into two regions. The first region covers
the forced convection dominated regime where the dimensionless parameter ξ
f
=Ra
x
/Pe
x
3/2 is found to measure the buoyancy effects on mixed convection with Da
x
Pe
x
/ɛ as the wall effects. The second region covers the natural convection dominated region where ξ
n
=Pe
x
/Ra
x
2/3 is found to measure the force effects on mixed convection with Da
x
Ra
x
2/3/ɛ as the wall effects. Numerical results for different inertia, wall, variable surface heat flux and variable wall temperature
exponents are presented.
Received on 8 July 1996 相似文献
12.
The Darcy Model with the Boussinesq approximation is used to study natural convection in a shallow porous layer, with variable
permeability, filled with a binary fluid. The permeability of the medium is assumed to vary exponentially with the depth of
the layer. The two horizontal walls of the cavity are subject to constant fluxes of heat and solute while the two vertical
ones are impermeable and adiabatic. The governing parameters for the problem are the thermal Rayleigh number, R
T, the Lewis number, Le, the buoyancy ratio, φ, the aspect ratio of the cavity, A, the normalized porosity, ε, the variable permeability constant, c, and parameter a defining double-diffusive convection (a = 0) or Soret induced convection (a = 1). For convection in an infinite layer, an analytical solution of the steady form of the governing equations is obtained
on the basis of the parallel flow approximation. The onset of supercritical convection, or subcritical, convection are predicted by the present theory. A linear stability analysis of the parallel flow model is conducted and the
critical Rayleigh number for the onset of Hopf’s bifurcation is predicted numerically. Numerical solutions of the full governing
equations are found to be in excellent agreement with the analytical predictions. 相似文献
13.
Radiation-conduction interaction on mixed convection from a horizontal circular cylinder 总被引:1,自引:0,他引:1
A mixed convection flow of an optically dense viscous incompressible fluid along a horizontal circular cylinder has been
studied with the effect of radiation when the surface temperature is uniform. Using appropriate transformations, the boundary
layer equations governing the flow are reduced to local nonsimilarity form. Solutions of the governing equations are obtained
employing the implicit finite difference method. Effects of varying the pertinent parameters, such as, the Planck number,
R
w the surface temperature parameter, θw and the buoyancy parameter, α on the local skin-friction and local heat transfer coefficients are shown graphically as well
as in tabular form against the curvature parameter ξ, while taking Prandtl number Pr = 1.0. It is found that an increase of
R
d,θw or α leads to increases in the values of the local skin-friction and the local rate of heat transfer coefficients. At the
stagnation point asymptotic solutions for large value of α are also obtained and the effect of the other pertinent parameters
on the formation of the flow separation are studied.
Received on 28 July 1998 相似文献
14.
In this paper, we consider the effect of mechanical vibration on the onset of convection in porous media. The porous medium
is saturated either by a pure fluid or by a binary mixture. The importance of a transport model on stability diagrams is presented
and discussed. The stability threshold for the Darcy–Brinkman case in the Ra
Tc
-R and k
c
-R diagrams is presented (where Ra
Tc
, k
c
and R are the critical Rayleigh number, the critical wave number and the vibration parameters, respectively). It is shown that
there is a significant deviation from the Darcy model. In the thermo-solutal case with the Soret effect, the influence of
vibration on the reduction of multi-cellular convection is emphasized. A new analytical relation for obtaining the threshold
of mono-cellular convection is derived. This relation shows how the separation factor Ψ is related to the controlling parameters
of the problem, Ψ = f (R, ε*, Le), when the wave number k → 0. The importance of vibrational parameter definition is highlighted and it is shown how, by using a proper definition
for vibrational parameter, we may obtain compact relationship. It is also shown how this result may be used to increase component
separation. 相似文献
15.
The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal
and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are
included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u
w/(u
w + u
∞), where u
w and u
∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1
it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have
been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation
technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution.
For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase
with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and
the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction
decreases as the relative velocity between the surface and free stream decreases.
Received on 17 May 1999 相似文献
16.
Recently, in Diaz and Brevdo (J Fluid Mech 681: 567–596, 2011), further in the text referred to as D&B, we found an absolute/convective instability dichotomy at the onset of convection
in a flow in a saturated porous layer with either horizontal or vertical solutal and inclined thermal gradients, and horizontal
throughflow. The control parameter in D&B triggering the destabilization is the vertical thermal Rayleigh number, R
v. In this article, we treat the parameter cases considered in D&B in which the onset of convection has the character of convective
instability and occurs through longitudinal modes. By increasing the vertical thermal Rayleigh number starting from its critical
value, R
vc, we determine the value R
vt of R
v at which the transition from convective to absolute instability takes place and compute the physical characteristics of the
emerging absolutely unstable wave packet. In some cases, the value of the transitional vertical thermal Rayleigh number, R
vt, is only slightly greater than the critical value, R
vc, meaning that at the onset of convection the base convectively unstable state can be viewed as marginally absolutely unstable.
However, in several cases considered, the value of R
vt is significantly greater than the critical value, R
vc, implying that the base state is not marginally but essentially absolutely stable at the point of destabilization. 相似文献
17.
The natural convection boundary layer flow with conduction-radiation interaction of a viscous incompressible fluid along
an isothermal horizontal surface has been studied. The equations valid in the upstream, downstream as well as in the entire
regime are obtained. Solutions of the non-similar equations governing the flow for the entire regime and the downstream regime
are obtained by employing an efficient implicit finite difference approximation together with the Keller box method, for a
Prandtl number of 0.73. Also, the effects of the pertinent parameters, R
d, the radiation-conduction parameter and θw, the surface heating parameter are shown graphically in terms of the local skin-friction and the local rate of heat transfer.
Comparison of the results obtained for the upstream and the downstream regimes shows good agreement over the entire regime.
Effects of R
d and θw are also shown on the streamlines and the isotherms.
Received on 15 December 1998 相似文献
18.
Steady thermocapillary-buoyant convection in a shallow annular pool. Part 2: Two immiscible fluids 总被引:1,自引:0,他引:1
This work is devoted to the study of steady thermocapillary-buoyant convection in a system of two horizontal superimposed immiscible liquid layers filling a lateral heated thin annular pool.The governing equations are solved using an asymptotic theory for the aspect ratios ε→ 0.Asymptotic solutions of the velocity and temperature fields are obtained in the core region away from the cylinder walls.In order to validate the asymptotic solutions,numerical simulations are also carried out and the results are compared to each other.It is found that the present asymptotic solutions are valid in most of the core region.And the applicability of the obtained asymptotic solutions decreases with the increase of the aspect ratio and the thickness ratio of the two layers.For a system of gallium arsenide (lower layer) and boron oxide (upper layer),the buoyancy slightly weakens the thermocapillary convection in the upper layer and strengthens it in the lower layer. 相似文献
19.
The effect of the surface thermal radiation in tall cavities with turbulent natural convection regime was analyzed and quantified
numerically. The parameters considered were: the Rayleigh number 109–1012, the aspect ratio 20, 40 and 80 and the emmisivity 0.0–1.0. The percentage contribution of the radiative surface to the total
heat transfer has a maximum value of 15.19% (Ra = 109, A = 20) with emissivity equal to 1.0 and a minimum of 0.5% (Ra = 1012, A = 80) with ε* = 0.2. The average radiative Nusselt number for a fixed emissivity is independent of the Rayleigh number, but for a fixed
Rayleigh number diminishes with the increase of the aspect ratio. The results indicate that the surface thermal radiation
does not modify significantly the flow pattern in the cavity, just negligible effects in the bottom and top of the cavity
were observed. Two different temperature patterns were observed a conductive regime Ra = 109 and a boundary layer regime Ra = 1012. 相似文献
20.
Nonsimilarity solutions for non-Darcy mixed convection from a vertical impermeable surface embedded in a saturated porous
medium are presented for variable surface heat flux (VHF) of the power-law form. The entire mixed convection region is divided
into two regimes. One region covers the forced convection dominated regime and the other one covers the natural convection
dominated regime. The governing equations are first transformed into a dimensionless form by the nonsimilar transformation
and then solved by a finite-difference scheme. Computations are based on Keller Box method and a tolerance of iteration of
10−5 as a criterion for convergence.
Three physical aspects are introduced. One measures the strength of mixed convection where the dimensionless parameter Ra*
x
/Pe3/2
x
characterizes the effect of buoyancy forces on the forced convection; while the parameter Pe
x
/Ra*2/3
x
characterizes the effect of forced flow on the natural convection. The second aspect represents the effect of the inertial
resistance where the parameter K′U
∞/ν is found to characterize the effect of inertial force in the forced convection dominated regime, while the parameter (K′U
∞/ν)(Ra*2/3
x
/Pe
x
) characterizes the effect of inertial force in the natural convection dominated regime. The third aspect is the effect of
the heating condition at the wall on the mixed convection, which is presented by m, the power index of the power-law form heating condition.
Numerical results for both heating conditions are carried out. Distributions of dimensionless temperature and velocity profiles
for both Darcy and non-Darcy models are presented.
Received on 26 May 1997 相似文献