共查询到20条相似文献,搜索用时 187 毫秒
1.
Closed-form solutions are derived for the steady magnetohydrodynamic (MHD) viscous flow in a parallel plate channel system
with perfectly conducting walls in a rotating frame of reference, in the presence of Hall currents, heat transfer and a transverse
uniform magnetic field. A mathematical analysis is described to evaluate the velocity, induced magnetic field and mass flow
rate distributions, for a wide range of the governing parameters. Asymptotic behavior of the solution is analyzed for large
M
2 (Hartmann number squared) and K
2 (rotation parameter). The heat transfer aspect is considered also with Joule and viscous heating effects present. Boundary
layers arise close to the channel walls for large K
2, i.e. strong rotation of the channel. For slowly rotating systems (small K
2), Hall current parameter (m) reduces primary mass flow rate (Q
x
/R
ρ
v). Heat transfer rate at the upper plate (d
θ/d
η)
η=1 decreases, while at the lower plate (d
θ/d
η)
η=−1 increases, with increase in either K
2 or m. For constant values of the rotation parameter, K
2, heat transfer rate at both plates exhibits an oscillatory pattern with an increase in Hall current parameter, m. The response of the primary and secondary velocity components and also the primary and secondary induced magnetic field
components to the control parameters is also studied graphically. Applications of the study arise in rotating MHD induction
machine energy generators, planetary and solar plasma fluid dynamics systems, magnetic field control of materials processing
systems, hybrid magnetic propulsion systems for space travel etc. 相似文献
2.
Jiří Neustupa 《Archive for Rational Mechanics and Analysis》2010,198(1):331-348
We prove the existence of a weak solution to the steady Navier–Stokes problem in a three dimensional domain Ω, whose boundary
∂Ω consists of M unbounded components Γ1, . . . , Γ
M
and N − M bounded components Γ
M+1, . . . , Γ
N
. We use the inhomogeneous Dirichlet boundary condition on ∂Ω. The prescribed velocity profile α on ∂Ω is assumed to have an L
3-extension to Ω with the gradient in L
2(Ω)3×3. We assume that the fluxes of α through the bounded components Γ
M+1, . . . , Γ
N
of ∂Ω are “sufficiently small”, but we impose no restriction on the size of fluxes through the unbounded components Γ1, . . . , Γ
M
. 相似文献
3.
The stress dependencies of the steady-state viscosity η and, particularly, that of the steady-state elastic compliance J
e of various linear isotactic polypropylenes (PP) and one long-chain branched PP are investigated using creep-recovery tests.
The creep stresses applied range from 2 to 10,000 Pa. In order to discuss the stress-dependent viscosity η and elastic compliance J
e with respect to the influence of the weight average molar mass M
w and the polydispersity factor M
w/M
n the PP are characterized by SEC–MALLS. For the linear PP, linear steady-state elastic compliances Je0J_{\rm e}^0 in the range of 10 − 5–10 − 3 Pa − 1 are obtained depending on the molar mass distribution. Je0J_{\rm e}^0 of the LCB-PP is distinctly higher and comes to lie at around 10 − 2 Pa − 1. Je0J_{\rm e}^0 is found to be independent of M
w but strongly dependent on polydispersity. η and J
e decrease with increasing stress. For the linear PP, J
e as a function of the stress τ is temperature independent. The higher M
w/M
n the stronger is the shear thinning of η and the more pronounced is the stress dependence of J
e. For the LCB-PP, the strongest stress dependence of η and J
e is observed. Furthermore, for all PP J
e reacts more sensitively to an increasing stress than η. A qualitative explanation for the stronger stress dependence of J
e compared to η is given by analyzing the contribution of long relaxation times to the viscosity and elasticity. 相似文献
4.
Oscillatory MHD Couette flow of electrically conducting fluid between two parallel plates in a rotating system in the presence
of an inclined magnetic field is considered when the upper plate is held at rest and the lower plate oscillates non-torsionally
. An exact solution of the governing equations has been obtained by using Laplace transform technique. Asymptotic behavior
of the solution is analyzed for M
2
≪1, K
2
≪1 and ω
≪1 and for large M
2, K
2 and ω. Numerical results of velocities are depicted graphically and the frictional shearing stresses are presented in tables. It
is found that a thin boundary layer is formed near the lower plate, for large values of rotation parameter K
2, Hartman number M
2 and frequency parameter ω. The thickness of this boundary layer increases with increase in inclination of the magnetic field with the axis of rotation. 相似文献
5.
Laminar mixed convection from a continuously moving vertical surface with suction or injection 总被引:1,自引:0,他引:1
The boundary layer flow over a uniformly moving vertical surface with suction or injection is studied when the buoyancy forces
assist or oppose the flow. Similarity solutions are obtained for the boundary layer equations subject to power law temperature
and velocity boundary conditions. The effect is of various governing parameters, such as Prandtl number Pr, temperature exponent
n, injection parameter d, and the mixed convection parameter λ=Gr/Re2, which determine the velocity and temperature distributions and the heat transfer coefficient, are studied. The heat transfer
coefficient increases as λ assisting the flow for all d at Pr=0.72 however, for n=−1 it decreases sharply with λ. On the other hand, increasing λ has no effect on heat transfer coefficient for Pr=10 at n=0, and 1 for almost all values of d studied. However, for n=−1 it has similar effect as for Pr=0.72. It is also found that Nusselt number increases as n increases for fixed λ and d.
Received on 26 March 1997 相似文献
6.
The steady flow in a parallel plate channel rotating with an angular velocity Ω and subjected to a constant transverse magnetic
field is analysed. An exact solution of the governing equations is obtained. The solution in the dimensionless form contains
two parameters: the Hartmann number, M
2, and K
2 which is the reciprocal of the Ekman number. The effects of these parameters on the velocity and magnetic field distributions
are studied. For large values of the parameters, there arise thin boundary layers on the walls of the channel. 相似文献
7.
Tzer-Ming Jeng Sheng-Chung Tzeng Yen-Chan Wang Chao-Hsien Lin 《Heat and Mass Transfer》2008,44(5):527-533
This work experimentally investigates the heat transfer characteristics in the annulus with an inner rotating rib-roughness
cylinder, whose flow and thermal behaviors are associated with Taylor number (Ta) and centrifugal buoyancy parameter (Gr
Ω/Ta). The operating range of Ta is from 4.90 × 102 to 5.80 × 105, while the surface of the inner cylinder is heated up with several constant heat fluxes (279, 425 and 597 W/m2) to obtain various values of Gr
Ω/Ta. Besides, three modes of the inner cylinder without/with longitudinal ribs are considered. The end of the annular channel
is connected to a side chamber to fit practical applications (such as in the rotary blade coupling of a four-wheel-drive vehicle).
The experimental results show that the average Nusselt number
was almost constant at low Ta, but increased rapidly with Ta when Ta exceeded some critical value (3,000–5,200 for present study). Additionally, the Gr
Ω/Ta effect on the heat transfer was negligible herein. Furthermore, by comparing with the inner cylinder without longitudinal
ribs, stalling ribs on the inner cylinder increases the transport of heat by a factor of 1.22 at 105 < Ta < 106, and embedding cavities into the ribs increases the transport of heat by a factor of 1.16 at 105 < Ta < 106. Finally, the relationships between the and the Ta for various modes of test sections were proposed. 相似文献
8.
Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries 总被引:3,自引:0,他引:3
This paper analyzes the convective heat transfer enhancement mechanism of microencapsulated phase change material slurries based on the analogy between convective heat transfer and thermal conduction with thermal sources. The influence of each factor affecting the heat transfer enhancement for laminar flow in a circular tube with constant wall temperature is analyzed using an effective specific heat capacity model. The model is validated with results available in the literature. The analysis and the results clarify the heat transfer enhancement mechanism and the main factors influencing the heat transfer. In addition, the conventional Nusselt number definition of phase change slurries for internal flow is modified to describe the degree of heat transfer enhancement of microencapsulated phase change material slurries. The modification is also consistent evaluation of the convective heat transfer of internal and external flows.c volumetric concentration of microcapsules - cm mass concentration of microcapsules - cp specific heat, kJ kg–1 K–1 - hfs phase change material heat of fusion, kJ kg–1 - hm* modified convective heat transfer coefficient, W m–2 K–1 - k thermal conductivity, W m–1 K–1 - ke effective thermal conductivity of slurry, W m–1 K–1 - kb slurry bulk thermal conductivity, W m–1 K–1 - ML dimensionless initial subcooling - Mr dimensionless phase change temperature range - Nu conventional Nusselt number - Nu* improved Nusselt number - qwn wall heat flux, Wm–2 - Pe Peclet number - Pr Prandtl number - Re Reynolds number - r radial coordinate, m - r0 duct radius, m - r1 dimensionless radial coordinate - Ste Stefan number - T temperature, K - T1 lower phase change temperature limit, K - T2 upper phase change temperature limit, K - Ti slurry inlet temperature, K - u axial velocity, m/s - v radial velocity, m/s - x axial coordinate, m - x1 dimensionless axial coordinate - thermal diffusivity, m2/s - dimensionless temperature - dynamic viscosity, N·s/m2 - kinematic viscosity, m2/s - t width of thermal boundary, m - degree of heat transfer enhancement, = hm*/(hm*)single - b bulk fluid (slurry) - b0 slurry without phase change - l liquid - m mean - s solid - f suspending fluid - p microcapsule particles - w wall - single single-phase fluid 相似文献
9.
Florian J. Stadler Christian Piel Joachim Kaschta Sascha Rulhoff Walter Kaminsky Helmut Münstedt 《Rheologica Acta》2006,45(5):755-764
Linear high-density polyethylenes with molar masses M
w between 240 and 1,000,000 g/mol, obtained by metallocene catalysts, were characterized in shear using oscillatory and creep tests. The polydispersities of the molar mass distributions (MMDs) lay between 1 and 16. The resulting zero shear-rate viscosities η0 covered a range from 2.5×10−3 to around 108 Pas. Above a critical molar mass of M
c≈2,900 g/mol, the experimental results can be described by the relation η0 ∼ M
w3.6, independently of the MMD. The oscillatory data were fitted with a Carreau–Yasuda equation. The resulting parameters were correlated to molecular structure. The parameter a, being a quantity for the width of the transition between the Newtonian and the non-Newtonian regime, showed a dependence on the molar mass M
w but not on M
w/M
n. The parameter λ of the Carreau-Yasuda equation was found to be the reciprocal crossover frequency for all samples with a log-Gaussian MMD. λ depends on the molar mass M
w and also on M
w/M
n.
相似文献
Helmut MünstedtEmail: Phone: +49-9131-8527604Fax: +49-9131-8528321 |
10.
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
11.
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
12.
An analysis is made for the steady two-dimensional magneto-hydrodynamic flow of an incompressible viscous and electrically
conducting fluid over a stretching vertical sheet in its own plane. The stretching velocity, the surface temperature and the
transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The transformed boundary layer
equations are solved numerically for some values of the involved parameters, namely the magnetic parameter M, the velocity exponent parameter m, the temperature exponent parameter n and the buoyancy parameter λ, while the Prandtl number Pr is fixed, namely Pr = 1, using a finite difference scheme known as the Keller-box method. Similarity solutions are obtained in the presence of
the buoyancy force if n = 2m−1. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed
and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter
M increases for fixed λ and m. For m = 0.2 (i.e. n = −0.6), although the sheet and the fluid are at different temperatures, there is no local heat transfer at the surface of
the sheet except at the singular point of the origin (fixed point). 相似文献
13.
This paper presents the results of an experimental study of convective heat transfer between three parallel vertical plates
symmetrically spaced with and without bubble agitation to ascertain the degree of augmentation of the heat transfer coefficients
due to agitation. The centre plate was electrically heated, while the other side plates were water-cooled forming two successive
parallel vertical rectangular channels of dimensions 20 cm × 3.5 cm × 35 cm (length W, gap L, height H) each. At the bottom of the hot and cold plates air spargers were fitted. Water/ethylene glycol (100%) was used to fill the
channels. The superficial gas velocity ranged from 0.0016 to 0.01 m/s. Top, bottom and sides of the channels were open to
the water/ethylene glycol in the chamber which is the novel aspect of this study. Experimental data have been correlated as
under: Natural convective heat transfer: Nu = 0.60 Gr
0.29, r = 0.96, σ = 0.186, 1.17 E6 < Gr < 1.48 E7; Bubble agitated heat transfer: St = 0.11(ReFrPr
2)−0.23, r = 0.82, σ = 0.002, 1.20 E−2 < (ReFrPr
2) < 1.36 E2. 相似文献
14.
We study theoretically and computationally the incompressible, non-conducting, micropolar, biomagnetic (blood) flow and heat
transfer through a two-dimensional square porous medium in an (x,y) coordinate system, bound by impermeable walls. The magnetic field acting on the fluid is generated by an electrical current
flowing normal to the x–y plane, at a distance l beneath the base side of the square. The flow regime is affected by the magnetization B
0 and a linear relation is used to define the relationship between magnetization and magnetic field intensity. The steady governing
equations for x-direction translational (linear) momentum, y-direction translational (linear) momentum, angular momentum (micro-rotation) and energy (heat) conservation are presented.
The energy equation incorporates a special term designating the thermal power per unit volume due to the magnetocaloric effect.
The governing equations are non-dimensionalized into a dimensionless (ξ,η) coordinate system using a set of similarity transformations. The resulting two point boundary value problem is shown to
be represented by five dependent non-dimensional variables, f
ξ
(velocity), f
η
(velocity), g (micro-rotation), E (magnetic field intensity) and θ (temperature) with appropriate boundary conditions at the walls. The thermophysical parameters controlling the flow are the
micropolar parameter (R), biomagnetic parameter (N
H
), Darcy number (Da), Forchheimer (Fs), magnetic field strength parameter (Mn), Eckert number (Ec) and Prandtl number (Pr). Numerical solutions are obtained using the finite element method and also the finite difference method for Ec=2.476×10−6 and Prandtl number Pr=20, which represent realistic biomagnetic hemodynamic and heat transfer scenarios. Temperatures are shown to be considerably
increased with Mn values but depressed by a rise in biomagnetic parameter (N
H
) and also a rise in micropolarity (R). Translational velocity components are found to decrease substantially with micropolarity (R), a trend consistent with Newtonian blood flows. Micro-rotation values are shown to increase considerably with a rise in
R values but are reduced with a rise in biomagnetic parameter (N
H
). Both translational velocities are boosted with a rise in Darcy number as is micro-rotation. Forchheimer number is also
shown to decrease translational velocities but increase micro-rotation. Excellent agreement is demonstrated between both numerical
solutions. The mathematical model finds applications in blood flow control devices, hemodynamics in porous biomaterials and
also biomagnetic flows in highly perfused skeletal tissue.
Dedicated to Professor Y.C. Fung (1919-), Emeritus Professor of Biomechanics, Bioengineering Department, University of California
at San Diego, USA for his seminal contributions to biomechanics and physiological fluid mechanics over four decades and his
excellent encouragement to the authors, in particular OAB, with computational biofluid dynamics research. 相似文献
15.
We report on velocity fluctuations and the fluctuation-driven radial transport of angular momentum in turbulent circular Couette
flow. Our apparatus is short (cylinder height to gap width ratio Γ ~ 2) and of relatively high wall curvature (ratio of cylinder
radii η ~ 0.35). Fluctuation levels and the mean specific angular momentum are found to be roughly constant over radius, in
accordance with previous studies featuring narrower gaps. Synchronized dual beam Laser Doppler Velocimetry (2D LDV) is used
to directly measure the r − θ Reynolds stress component as a function of Reynolds number (Re), revealing approximate scalings in the non-dimensional angular momentum transport that confirm previous measurements of
torque in similar flows. 2D LDV further allows for a decomposition of the turbulent transport to assess the relative roles
of fluctuation intensity and r − θ cross-correlation. We find that the increasing angular momentum transport with Re is due to intensifying absolute fluctuation levels accompanied by a slightly weakening cross-correlation. 相似文献
16.
K. A. Yih 《Heat and Mass Transfer》1998,34(1):55-61
A boundary layer analysis is used to investigate the heat and mass transfer characteristics of mixed convection about a vertical
flat plate embedded in a saturated porous medium under the coupled effects of thermal and mass diffusion. The plate is maintained
at prescribed surface temperature/concentration (PST/PSC) or prescribed heat/mass flux (PHF/PMF). The nonsimilar governing
equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results for the local
heat transfer rate and the local mass transfer rate are presented for various parameters. The local heat and mass transfer
rates increase with increasing n and m and buoyancy parameter ξ. When buoyancy parameter ξ is very small (large) the value of local Nusselt and the local Sherwood
number correspond with the pure forced (free) convection, respectively. Increasing buoyancy ratio N (or N
*) increases the local heat and mass transfer rates. It is apparent that Lewis number has a pronounced effect on the local
mass transfer rate than it does on the local heat transfer rate. Furthermore, increasing Lewis number decreases (increases)
the local heat (mass) transfer rate.
Received on 8 December 1997 相似文献
17.
Control of Flow and Heat Transfer in a Porous Enclosure due to an Adiabatic Thin fin on the Hot Wall
Natural convection flow in a differentially heated square enclosure filled with porous matrix with a solid adiabatic thin
fin attached at the hot left wall is studied numerically. The Brinkman–Forchheimer-extended Darcy model is used to solve the
momentum equations, in the porous medium. The numerical investigation is done through streamlines, isotherms, and heat transfer
rates. A parametric study is carried out using the following parameters: Darcy number (Da) from 10−4 to 10−2, dimensionless thin fin lengths (L
p) 0.3, 0.5, and 0.7, dimensionless positions (S
p) 0.25, 0.5, and 0.75 with Prandtl numbers (Pr) 0.7 and 100 for Ra = 106. For Da = 10−3 and Pr = 0.7, it is observed that there is a counter clock-wise secondary flow formation around the tip of the fin for S
p = 0.5 for all lengths of L
p. Moreover when Da = 10−2 the secondary circulation behavior has been observed for S
p = 0.25 and 0.75 and there is another circulation between the top wall and the fin that is separated from the primary circulation.
However, these secondary circulations features are not observed for Pr = 100. It is also found that the average Nusselt number decreases as the length of the fin increases for all locations. However,
the rate of decrease of average Nusselt number becomes slower as the location of fin moves from the bottom wall to the top
wall. The overall heat transfer rate can be controlled with a suitable selection of the fin location and length. 相似文献
18.
S. Amir Hossein A. E. Tabatabaei Tinggang Zhao O. Bamidele Awojoyogbe Folorunsho O. Moses 《Heat and Mass Transfer》2009,45(10):1247-1251
The time dependent heating and cooling velocities are investigated in this paper. The temperature profile is found by using
a keyhole approximation for the melted zone and solving the heat transfer equation. A polynomial expansion has been deployed
to determine the cooling velocity during welding cut-off stage. The maximum cooling velocity has been estimated to be V
max ≈ 83°C s−1. 相似文献
19.
The free convective flow and heat transfer, within the framework of Boussinesq approximation, in an anisotropic fluid filled
porous rectangular enclosure subjected to end-to-end temperature difference have been investigated using Brinkman extended
non-Darcy flow model. The studies involve simultaneous consideration of hydrodynamic and thermal anisotropy. The flow and
temperature fields in general are governed by, Ra, the Rayleigh number, AR, the aspect ratio of the slab, K*, the permeability ratio and k*, the thermal conductivity ratio, and Da, Darcy number. Numerical solutions employing the successive accelerated replacement (SAR) scheme have been obtained for 100 ≤
Ra ≤ 1000, 0.5 ≤ AR ≤ 5, 0.5 ≤ K* ≤ 5, 0.5 ≤ k* ≤ 5, and 0 ≤ Da ≤ 0.1. It has been found that [`(Nu)]{\overline {Nu}}, average Nusselt number increases with increase in K* and decreases as k* increases. However, the magnitude of the change in [`(Nu)]{\overline {Nu}} depends on the parameter Da, characterizing the Brinkman extended non-Darcy flow. 相似文献
20.
Using thermocouples and a particle tracking velocimetry technique, temperature and velocity measurements are conducted to
investigate flow and heat transfer characteristics of turbulent natural convection from a vertical heated plate in water with
sub-millimeter-bubble injection. Hydrogen-bubbles generated by the electrolysis of water are used as the sub-millimeter-bubbles.
In the turbulent region, the heat transfer deterioration occurs for a bubble flow rate Q = 33 mm3/s, while the heat transfer enhancement occurs for Q = 56 mm3/s. Temperature and velocity measurements suggest that the former is caused by a delay of the transition due to the bubble-induced
upward flow. On the other hand, the latter is mainly due to two factors: one is the enhancement of the rotation of eddies
in the outer layer, and the other is the increase in the gradient of the streamwise liquid velocity at the heated wall. These
are caused by bubbles, which are located in the inner layer, rising at high speed. 相似文献