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1.
The problem of steady mixed convection boundary layer flow over a vertical impermeable flat plate in a porous medium saturated
with water at 4°C (maximum density) when the temperature of the plate varies as x
m
and the velocity outside boundary layer varies as x
2 m
, where x measures the distance from the leading edge of the plate and m is a constant is studied. Both cases of the assisting and the opposing flows are considered. The plate is aligned parallel
to a free stream velocity U
∞ oriented in the upward or downward direction, while the ambient temperature is T
∞ = T
m (temperature at maximum density). The mathematical models for this problem are formulated, analyzed and simplified, and further
transformed into non-dimensional form using non-dimensional variables. Next, the system of governing partial differential
equations is transformed into a system of ordinary differential equations using the similarity variables. The resulting system
of ordinary differential equations is solved numerically using a finite-difference method known as the Keller-box scheme.
Numerical results for the non-dimensional skin friction or shear stress, wall heat transfer, as well as the temperature profiles
are obtained and discussed for different values of the mixed convection parameter λ and the power index m. All the numerical solutions are presented in the form of tables and figures. The results show that solutions are possible
for large values of λ and m for the case of assisting flow. Dual solutions occurred for the case of opposing flow with limited admissible values of λ
and m. In addition, separation of boundary layers occurred for opposing flow, and separation is delayed for the case of water at
4°C (maximum density) compared to water at normal temperature. 相似文献
2.
A Pantokratoras 《Heat and Mass Transfer》2005,41(12):1085-1094
The steady laminar boundary layer flow along a flat plate is studied taking into account the variation of fluid viscosity and fluid Prandtl number with temperature. In the forced convection case the plate moves with constant velocity and its temperature varies in power law with x. In the mixed convection case the plate temperature is constant and the fluid moves upwards due to an external free stream and due to buoyancy forces. The results are obtained with the direct numerical solution of the boundary layer equations. The study concerns the wall heat transfer, the wall shear stress and velocity and temperature profiles across the boundary layer. The results of the present work are different from those existing in the literature, which have been obtained with the assumption of constant Pr number. 相似文献
3.
M. Mosaad 《Heat and Mass Transfer》1999,35(5):371-375
Coupled heat transfer between laminar forced convection along and conduction inside a flat plate wall is theoretically studied.
The laminar convective boundary layer is analyzed by employing the integral technique. The energy equations for the fluid
and the plate wall are combined under the condition of the continuity in the temperature and heat flux at the fluid-solid
interface. The analysis results in a simple formal solution. Expressions have been obtained for calculating local Nusselt
number, wall heat flux and temperature along the plate, all are functions of the local Brun number, Br
x
, which is a measure of the ratio of the thermal resistance of the plate to that of the convective boundary layer. The results
indicate that for Br
x
≥0.15, neglecting the plate resistance will results in an error of more than 5% in Nusselt number. Comparison of the present
solution with other previous studies has been made. The solution may be of a considerable theoretical and practical interest.
Received on 19 August 1998 相似文献
4.
Measurements and scaling of wall shear stress fluctuations 总被引:2,自引:0,他引:2
Measurements of velocity and wall shear stress fluctuations were made in an external turbulent boundary layer developed over
a towed surface-piercing flat plate. An array of eight flush-mounted wall shear stress sensors was used to compute the space-time
correlation function. A methodology for in situ calibration of the sensors for ship hydrodynamic applications is presented.
The intensity of the wall shear stress fluctuations, τ
rms/τ
avg was measured as 0.25 and 0.36 for R
θ
=3,150 and 2,160 respectively. The probability density is shown to exhibit positive skewness, and lack of flow reversals at
the wall. Correlations between velocity and wall shear stress fluctuations are shown to collapse with outer boundary layer
length and velocity scales, verifying the existence of large-scale coherent structures which convect and decay along the wall
at an angle of inclination varying from 10 to 13° over the range of Reynolds numbers investigated. The wall shear stress convection
velocity determined from narrow band correlation measurements is shown to scale with outer variables. The space-time correlation
of the wall shear is shown to exhibit a well-defined convective ridge, and to decay 80% over approximately 3δ for R
θ
=3,150.
Published online: 7 November 2002 相似文献
5.
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
6.
In this study, the mixed convection of water at 4°C along a wedge in a porous medium is investigated numerically using finite
difference method. In order to explore the effect of mixed convection, both forced and free convection-dominated regimes are
considered. Non-similarity solutions are obtained for the variable wall flux boundary condition. Velocity and temperature
profiles as well as local dimensionless skin friction and Nusselt number are obtained and compared with the available numerical
results for various values of different parameters. The wedge angle geometry parameter m and mixed convection parameter ξ are ranged from 0 to 1 in both regimes whereas different values of λ are considered for the purpose of comparison of heat transfer results. 相似文献
7.
An exact solution is presented for the hydromagnetic natural convection boundary layer flow past an infinite vertical flat
plate under the influence of a transverse magnetic field with magnetic induction effects included. The transformed ordinary
differential equations are solved exactly, under physically appropriate boundary conditions. Closed-form expressions are obtained
for the non-dimensional velocity (u), non-dimensional induced magnetic field component (B
x
) and wall frictional shearing stress i.e. skin friction function (τ
x
) as functions of dimensionless transverse coordinate (η), Grashof free convection number (G
r
) and the Hartmann number (M). The bulk temperature in the boundary layer (Θ) is also evaluated and shown to be purely a function of M. The Rayleigh flow distribution (R) is derived and found to be a function of both Hartmann number (M) and the buoyant diffusivity parameter (ϑ
*). The influence of Grashof number on velocity, induced magnetic field and wall shear stress profiles is computed. The response
of Rayleigh flow distribution to Grashof numbers ranging from 2 to 200 is also discussed as is the influence of Hartmann number
on the bulk temperature. Rayleigh flow is demonstrated to become stable with respect to the width of the boundary layer region
and intensifies with greater magnetic field i.e. larger Hartman number M, for constant buoyant diffusivity parameter ϑ
*. The induced magnetic field (B
x
), is elevated in the vicinity of the plate surface with a rise in free convection (buoyancy) parameter G
r
, but is reduced over the central zone of the boundary layer regime. Applications of the study include laminar magneto-aerodynamics,
materials processing and MHD propulsion thermo-fluid dynamics. 相似文献
8.
This paper describes a numerical method for the study of combined natural convection and radiation in a rectangular, two-dimensional cavity containing a non-participating (i.e. transparent) fluid. One wall of the cavity is isothermal, being heated either by solar radiation or independently. The opposite wall is partially transparent, permitting radiation exchanges between the cavity and its surroundings and/or the Sun; that wall also exchanges heat by convection from its external surface to the surroundings. The other two walls are adiabatic: convection and radiation there are balanced, so that there is no heat transfer through those walls. The equations of motion and energy are solved by finite difference methods. Coupled to these equations are the radiative flux boundary conditions which are used to determine the temperature distribution along the non-isothermal walls. A two-band radiation model has been employed. Results are presented for a square cavity with a vertical hot wall at 150 °C, the ambient at 20 °C and 104 ? Ra ? 3 × 105, in the absence of direct insolation. The effects on the flow and heat transfer in the cavity of radiation and external convection have been examined. More extensive results will be presented in subsequent papers. 相似文献
9.
This work presents a numerical analysis of the effects of thermal boundary conditions, fluid variable viscosity and wall conduction
on transient laminar natural convection of a high Prandtl number (Pr=4×104) fluid (Golden Syrup) in a cubical cavity. The simulations consider physical situations realizable at laboratory scale using
a cavity with Plexiglas walls of 1 cm of thickness, and inside dimension of L=20 cm. The initial Rayleigh (Ra) number is 106. The cavity is initially full of fluid at rest and at constant temperature (T
i
=45°C) higher than the temperature of the walls (T
w
=25°C). The time evolution of the flow patterns, the temperature contours, the mean temperature of the fluid and the Nusselt
number (Nu) of eight different cases of cooling are presented and analyzed. 相似文献
10.
Density Maximum Effect on Double-diffusive Natural Convection in a Porous Cavity with Variable Wall Temperature 总被引:1,自引:0,他引:1
The effect of density maximum of water on double-diffusive natural convection in a two-dimensioned cavity filled with a water
saturated isotropic porous medium is studied numerically. The horizontal walls of the cavity are insulated. The opposing vertical
walls are kept at different temperatures θ
h
(linearly varies with height) and θ
c
(θ
c
≤ θ
h
). The concentration levels at cold wall and hot wall are, respectively, c
1 and c
2 with c
1 > c
2. Brinkman-Forchheimer extended Darcy model is used to investigate the average heat and mass transfer rates. The non-dimensional
equations for momentum, energy, and concentration are solved by finite volume method with power law scheme for convection
and diffusion terms. The results are presented in the form of streamlines, isotherms, and isoconcentration lines for various
values of Grashof numbers, Schmidt number, porosity, and Darcy numbers. It is observed that the density maximum of water has
profound effect on the thermosolutal convection. The effects of different parameters on the velocity, temperature, and species
concentrations are also shown graphically. 相似文献
11.
Natural convection in a partially filled porous square cavity is numerically investigated using SIMPLEC method. The Brinkman-Forchheimer
extended model was used to govern the flow in the porous medium region. At the porous-fluid interface, the flow boundary condition
imposed is a shear stress jump, which includes both the viscous and inertial effects, together with a continuity of normal
stress. The thermal boundary condition is continuity of temperature and heat flux. The results are presented with flow configurations
and isotherms, local and average Nusselt number along the cold wall for different Darcy numbers from 10−1 to 10−6, porosity values from 0.2 to 0.8, Rayleigh numbers from 103 to 107, and the ratio of porous layer thickness to cavity height from 0 to 0.50. The flow pattern inside the cavity is affected
with these parameters and hence the local and global heat transfer. A modified Darcy–Rayleigh number is proposed for the heat
convection intensity in porous/fluid filled domains. When its value is less than unit, global heat transfer keeps unchanged.
The interfacial stress jump coefficients β
1 and β
2 were varied from −1 to +1, and their effects on the local and average Nusselt numbers, velocity and temperature profiles
in the mid-width of the cavity are investigated. 相似文献
12.
In this study, laminar boundary layer flow over a flat plate embedded in a fluid-saturated porous medium in the presence of
viscous dissipation, inertia effect and suction/injection is analyzed using the Keller box finite difference method. The flat
plate is assumed to be held at constant temperature. The non-Darcian effects of convection, boundary and inertia are considered.
Results for the local heat transfer parameter and the local skin friction parameter as well as the velocity and temperature
profiles are presented for various values of the governing parameters. The non-Darcian effects are shown to decrease the velocity
and to increase the temperature. It is also shown that the local heat transfer parameter and the local skin friction parameter
increase due to suction of fluid while injection reverses this trend. It is disclosed that the effect of the viscous dissipation
for negative values of Ec (T
w
< T
∞) is to enhance the heat transfer coefficient while the opposite is true for positive values of Ec (T
w
> T
∞). The results are compared with those available in the existing literature and an excellent agreement is obtained. 相似文献
13.
The problem of mixed convection about non-isothermal vertical surfaces in a saturated porous medium is analysed using boundary layer approximations. The analysis is made assuming that the surface temperature varies as an arbitrary function of the distance from the origin. A perturbation technique has been applied to obtain the solutions. Using the differentials of the wall temperature, which are functions of distance along the surface, as perturbation elements, universal functions are derived for various values of the governing parameter Gr/Re. Both aiding and opposing flows are considered. The universal functions obtained can be used to estimate the heat transfer and fluid velocity inside the boundary layer for any type of wall temperature variation. As a demonstration of the method, heat transfer results have been presented for the case of the wall temperature varying as a power function of the distance from the origin. The results have been studied for various combinations of the parameters Gr/Re and the power index m, taking both aiding and opposing flows into consideration. On comparing these results with those obtained by a similarity analysis, the agreement is found to be good. 相似文献
14.
An experimental study had been carried out to investigate the buoyancy-opposed mixed convection from an upward flow of hot
air to a vertical pipe with a cooled surface. The investigation covered a wide range of flow regime, ranging from the “free
convection significant” to the “forced convection significant” conditions. Reynolds number of the flow extended from 966 to
14780, whereas the Buoyancy parameter, Ω [=Grd/(Red)2], varied from 0.008 to 2.77.
A steady stream of hot air at a moderate pressure and a Prandtl number of 0.707 was arranged to flow upward through a vertical
steel pipe, whose external wall was cooled uniformly by ambient air at 20°C. Test section of the vertical pipe was 1625 mm
long with an internal diameter of 156 mm and an external diameter of 166 mm. Air temperature at inlet of the test section
was varied from 40°C to 70°C. Both radial temperature and velocity profiles of the airflow were measured at inlet and exit
of the test section respectively. Temperatures along the pipe wall were also measured. Non-dimensional expression for the
prediction of the average heat transfer coefficient of the mixed convection from an upward flow of hot air to a vertical pipe
with a cooled surface was developed from the experimental results. Convection heat transfer was found to impair when the flow
is laminar and was enhanced for turbulent flow condition.
Received on 20 July 1998 相似文献
15.
Temperature and velocity measurements are performed to clarify the effects of sub-millimeter-bubble injection on the transition
to turbulence in the natural convection boundary layer along a vertical plate in water. In particular, we focus on the relationship
between the bubble injection position L and the transition to turbulence in the natural convection boundary layer. The bubble injection positions used in our experiments
are L = 1.6 and 3.6 mm. Bubble injection at L = 1.6 mm delays the transition to turbulence in the natural convection boundary layer, while that at L = 3.6 mm accelerates the transition to turbulence in the boundary layer. In the case of L = 1.6 mm, the appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated
section is restricted to near the wall, although the peak of the liquid velocity fluctuation is high. In contrast, in the
case of L = 3.6 mm, the relatively large liquid velocity fluctuation is distributed widely over the laminar boundary layer width. These
results suggest that the effect of the liquid velocity fluctuation on the laminar boundary layer is quite different between
L = 1.6 and 3.6 mm. It is therefore expected that the transition to turbulence in the natural convection boundary layer for
the case with bubble injection is dependent on the magnitude and appearance region of the liquid velocity fluctuation in the
bubble-induced upward flow in the upstream unheated section. 相似文献
16.
A. Pantokratoras 《Heat and Mass Transfer》2000,36(4):351-360
In most studies concerning laminar natural convection along a vertical isothermal cylinder a linear relationship between
fluid density and temperature has been used and kinematic viscosity and thermal diffusivity have been considered constant
calculated at ambient temperature. However, it is known that the density–temperature relationship for water is non-linear
at low temperatures and kinematic viscosity and thermal diffusivity are functions of temperature. In this study the problem
of laminar natural convection of pure and saline water along a vertical isothermal cylinder has been investigated in the temperature
range between 20 and 0 ∘C taking into account the temperature dependence of ν, α and ρ. The results are obtained with the numerical solution of the
boundary layer equations. The variation of ν, α and ρ with temperature has a strong influence on free convection characteristics.
Received on 17 May 1999 相似文献
17.
Turbulence measurements are reported on the three-dimensional turbulent boundary layer along the centerline of the flat endwall
in a 30° bend. Profiles of mean velocities and Reynolds stresses were obtained down to y
+≈2 for the mean flow and y
+≈8 for the turbulent stresses. Mean velocity data collapsed well on a simple law-of-the-wall based on the magnitude of the
resultant velocity. The turbulence intensity and turbulent shear stress magnitude both increased with increased three-dimensionality.
The ratio of these two quantities, the a
1 structure parameter, decreased in the central regions of the boundary layer and showed profile similarity for y
+<50. The shear stress vector angle lagged behind the velocity gradient vector angle in the outer region of the boundary layer,
however there was an indication that the shear stress vector tends to lead the velocity gradient vector close to the wall.
Received: 16 July 1996/Accepted: 14 July 1997 相似文献
18.
A new approach on MHD natural convection boundary layer flow from a finite flat plate of arbitrary inclination in a rotating
environment, is presented. This problem plays a significant role on boundary layer flow control. It is shown that taking into
account the pressure rise region at the leading edge of the plate leads to avoid separation and the back flow is reduced by
the strong magnetic field. It is also shown that the frictional drag at the leading edge of the plate is reduced when the
inclination angle α=π/4. In the case of isothermal flat plate, the bulk temperature becomes identical for any value of Gr (Grashof number) when the value of M
2 (Hartmann number) and K
2 (rotation parameter) are kept fixed. 相似文献
19.
M. Yahya Salam 《Applied Scientific Research》1986,43(1):23-38
Experiments were conducted in a turbulent boundary layer near separation along a flat plate. The pressure gradient in flow
direction was varied such that three significant boundary layer configurations could be maintained. The flow in the test section
thus had simultaneously a region of favourable pressure gradient, a region of strong adverse pressure gradient with boundary
layer separation and a region of reattached boundary layer. Specially designed fine probes facilitated the measurements of
skin friction and velocity distribution very close to the wall. Bulk flow parameters such as skin friction coefficient C
f, Reynold's number Reδ2 and shape factors H and G, which are significant characteristics of wall boundary layers were evaluated. The dependence of these parameters on the
Reynolds number and along the test section was explored and the values were compared with other empirical and analytical formulae
known in the literature. 相似文献
20.
A linear stability analysis is used to study the conditions marking the onset of secondary flow in the form of longitudinal
vortices for plane Poiseuille flow of water in the thermal entrance region of a horizontal parallel-plate channel by a numerical
method. The water temperature range under consideration is 0∼30°C and the maximum density effect at 4°C is of primary interest.
The basic flow solution for temperature includes axial heat conduction effect and the entrance temperature is taken to be
uniform at far upstream location jackie=−∞ to allow for the upstream heat penetration through thermal entrance jackie=0. Numerical results for critical Rayleigh number are obtained for Peclet numbers 1, 10, 50 and thermal condition parameters
(λ
1, λ
2) in the range of −2.0≤λ
1≤−0.5 and −1.0≤λ
2≤1.4. The analysis is motivated by a desire to determine the free convection effect on freezing or thawing in channel flow
of water. 相似文献