共查询到20条相似文献,搜索用时 46 毫秒
1.
An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic (MHD) flow is obtained for a special
case, namely, the sink flow with a velocity power index of −1. The solution is given in a closed form. Multiple solution branches
are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles
are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan
MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan
equation and provide better understanding of this equation. 相似文献
2.
S. Vantieghem X. Albets-Chico B. Knaepen 《Theoretical and Computational Fluid Dynamics》2009,23(6):525-533
We present numerical simulations without modeling of an incompressible, laminar, unidirectional circular pipe flow of an electrically
conducting fluid under the influence of a uniform transverse magnetic field. Our computations are performed using a finite-volume
code that uses a charge-conserving formulation [called current-conservative formulation in references (Ni et al J Comput Phys
221(1):174–204, 2007, Ni et al J Comput Phys 227(1):205–228, 2007)]. Using high resolution unstructured meshes, we consider
Hartmann numbers up to 3000 and various values of the wall conductance ratio c. In the limit c << Ha-1{c{\ll}{\rm Ha}^{-1}} (insulating wall), our results are in excellent agreement with the so-called asymptotic solution (Shercliff J Fluid Mech
1:644–666, 1956). For higher values of the wall conductance ratio, a discrepancy with the asymptotic solution is observed
and we exhibit regions of velocity overspeed in the Roberts layers. We characterise these overspeed regions as a function
of the wall conductance ratio and the Hartmann number; a set of scaling laws is derived that is coherent with existing asymptotic
analysis. 相似文献
3.
The combined effect of rotation and magnetic field is investigated for the axisymmetric flow due to the motion of a sphere
in an inviscid, incompressible electrically conducting fluid having uniform rotation far upstream. The steady-state linearized
equations contain a single parameter α=1/2βR
m, β being the magnetic pressure number and R
m the magnetic Reynolds number. The complete solution for the flow field and magnetic field is obtained and the distribution
of vorticity and current density is found. The induced vorticity is O(α4) and the current density is O(R
m) on the sphere. 相似文献
4.
Transient convection of an incompressible viscous fluid in a square cavity is investigated. The temperature at the top lid
is higher than that at the bottom wall, producing a stably stratified overall configuration. The vertical sidewalls are insulated.
Flow is initiated by an impulsive start of the sliding motion of the top lid. The transient features of the mixed convection
are delineated by procuring numerical solutions in a wide range of parameters, i.e., 400≤Re≤4,000, 1.6×105≤Gr≤1.6×107. Flows and heat transfer characteristics are described both in the interior core and boundary-layer regions. In the large-time
limit, the steady state features are depicted. Parallel experimental efforts are made by employing the particle image velocimetry
(PIV) to visualize the steady state flow and thermal fields, together with thermocouple measurements. 相似文献
5.
An analysis has been carried out to determine the development of momentum and heat transfer occurring in the laminar boundary
layer of an incompressible viscous electrically conducting fluid in the stagnation region of a rotating sphere caused by the
impulsive motion of the free stream velocity and the angular velocity of the sphere. At the same time the wall temperature
is also suddenly increased. This analysis includes both short and long-time solutions. The partial differential equations
governing the flow are solved numerically using an implicit finite-difference scheme. There is a smooth transition from the
short-time solution to the long-time solution. The surface shear stresses in the longitudinal and rotating directions and
the heat transfer are found to increase with time, magnetic field, buoyancy parameter and the rotation parameter.
Received on 27 January 2000 相似文献
6.
Shear and extensional viscosities and wall slip are determined simultaneously under extrusion processing conditions using
an on-line rheometer. Because it is not possible to independently control flow rate and temperature, classical methods for
interpretation of capillary data cannot be used with on-line rheometry. This limitation is overcome using computational optimization
to fit parameters in a flow model. This consists of three parts, representing shear viscosity, extensional viscosity, and
wall slip. Three-parameter, power law forms, based on local instantaneous deformation rates and including temperature dependence,
are used for each, and analytic solutions applied for entry flow and flow in the capillary. For entry flow, the Cogswell–Binding
approach is used, and for developed flow in the capillary a solution incorporating wall slip is derived. The rheometer, with
interchangeable capillaries, is mounted in place of the die on a rubber profile extrusion line. Pressure drops and temperatures
for extrusion of an EPDM rubber through 2 mm diameter capillaries of length 0, 2, 3, 4, and 5 mm are logged and flow rates
determined for a range of extruder speeds (5 to 20 rpm). Pressures ranged from 60 to 75 bar and temperatures from 86 to 116 °C.
Mean flow velocity in the capillaries was between 5 × 10−3 and 5 × 10−1 m s−1. The nine material parameters are optimized for best fit of the analytic pressure drops to experimental data, using about
100 data points, with the Levenberg–Marquardt method. It is concluded that flow is dominated by extension and wall slip. Shear
flow appears to play little part. The slip model indicates that slip velocity increases much more rapidly than the wall shear
stress (in the range 0.5–1 MPa) and decreases with temperature for a given stress level. Results for the (uniaxial) extensional
viscosity represent an engineering approximation to this complex phenomenon at the high strains (approximately 200) and high
extension rates (up to 800 s−1) applying in the extrusion. Results indicate a slight extension hardening and a decrease with temperature. Results are put
into the context of the available studies in the literature, which, particularly with regard to wall-slip and extensional
flow, consider conditions far removed from those applying in industrial extrusion. The present methods provide a powerful
means for flow characterization under processing conditions, providing data suitable for use in computer simulations of extrusion
and optimization of die design. 相似文献
7.
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
8.
Laminar two-dimensional stagnation flow of a viscous and electrically conducting fluid obliquely impinging on a flat plate
in the presence of a uniform applied magnetic field is formulated as a similarity solution of the Navier-Stokes equations.
The relative importance of this flow is measured by the dimensionless strain rate and magnetohydrodynamic parameters γ and M. The viscous problem is reduced to a coupled pair of ordinary differential equations governed by γ and M. It is found that the parameter M causes a shift in the position of the point of zero skin friction along the wall. 相似文献
9.
The flow-induced microstructure of a mesophase pitch was studied within custom-made dies for changing wall shear rates from
20 to 1,100 s − 1, a flow scenario that is typically encountered during fiber spinning. The apparent viscosity values, measured at the nominal
wall shear rates ranging from 500 to 2,500 s − 1 using these dies, remain fairly constant. The microstructure was studied in two orthogonal sections: r–θ (cross section) and r–z (longitudinal mid plane). In these dies, the size of the microstructure gradually decreases toward the wall (to as low as
a few micrometers), where shear rate is highest. Furthermore, as observed in the r–θ plane of the capillary, for a significant fraction of the cross section, discotic mesophase has a radial orientation. Thus,
the directors of disc-like molecules were aligned in the vorticity (θ) direction. As confirmed from the microstructure in the r–z plane, most of the discotic molecules remain nominally in the flow plane. Orientation of the pitch molecules in the shear
flow conditions is consistent with that observed in controlled low-shear rheometric experiments reported earlier. Microstructral
investigation suggests that the radial orientation of carbon fibers obtained from a mesophase pitch originates during flow
of pitch through the die. 相似文献
10.
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
11.
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
12.
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
13.
The present paper focuses on the analysis of unsteady flow and heat transfer regarding an axisymmetric impinging synthetic
jet on a constant heat flux disc. Synthetic jet is a zero net mass flux jet that provides an unsteady flow without any external
source of fluid. Present results are validated against the available experimental data showing that the SST/k − ω turbulence model is more accurate and reliable than the standard and low-Re k − ε models for predicting heat transfer from an impinging synthetic jet. It is found that the time-averaged Nusselt number
enhances as the nozzle-to-plate distance is increased. As the oscillation frequency in the range of 16–400 Hz is increased,
the heat transfer is enhanced. It is shown that the instantaneous Nu distribution along the wall is influenced mainly by the interaction of produced vortex ring and wall boundary layer. Also,
the fluctuation level of Nu decreases as the frequency is raised. 相似文献
14.
We consider the magnetohydrodynamic flow that is laminar and steady of a viscous, incompressible, and electrically conducting fluid in a semi‐infinite duct under an externally applied magnetic field. The flow is driven by the current produced by a pressure gradient. The applied magnetic field is perpendicular to the semi‐infinite walls that are kept at the same magnetic field value in magnitude but opposite in sign. The wall that connects the two semi‐infinite walls is partly non‐conducting and partly conducting (in the middle). A BEM solution was obtained using a fundamental solution that enables to treat the magnetohydrodynamic equations in coupled form with general wall conductivities. The inhomogeneity in the equations due to the pressure gradient was tackled, obtaining a particular solution, and the BEM was applied with a fundamental solution of coupled homogeneous convection–diffusion type partial differential equations. Constant elements were used for the discretization of the boundaries (y = 0, ?a ? x ? a) and semi‐infinite walls at x = ±a, by keeping them as finite since the boundary integral equations are restricted to these boundaries due to the regularity conditions as y → ∞ . The solution is presented in terms of equivelocity and induced magnetic field contours for several values of Hartmann number (M), conducting length (l), and non‐conducting wall conditions (k). The effect of the parameters on the solution is studied. Flow rates are also calculated for these values of parameters. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
Donald D. Gray 《Applied Scientific Research》1977,33(5-6):437-457
The dynamics of a buoyant plume rising above a horizontal line heat source in a transverse, horizontal magnetic field is investigated.
Similarity is shown to occur when the magnetic field strength varies as the −2/5 power of vertical distance from the source.
The plume depends on two parameters — the Prandtl number (Pr) and the Lykoudis number (Z
L). Families of exact closed form solutions are derived for Pr=5/9 and Pr≥2. A family of numerical integrations for Pr=0.01 (typical of liquid metals) is also reported. The magnetic field is shown to affect the profiles of velocity and temperature
by altering the similarity functions, the coefficients, and the value of the independent similarity variable corresponding
to a fixed physical position. An approximate closed form solution valid for low Pr and high Z
L is presented. Possible experimental tests of the theory are proposed.
Research sponsored by the U.S. Energy Research and Development Administration under interagency agreement with Union Carbide
Corporation. 相似文献
16.
A novel carbon nanotube (CNT) sensor is being developed to measure the mean and fluctuating wall shear stress (WSS) in a turbulent
boundary layer. The CNT WSS sensor is based on the thermal principle and featured by high spatial and temporal resolutions
(in the order of nm and kHz, respectively), low power consumption (in the order of μW), and a compact fabrication process
compared with traditional WSS measurement sensors. The CNT WSS-sensing element was characterized in detail before its calibration.
The CNT sensor was operated under a constant temperature (CT) operation mode and an overheat ratio range of −0.15 to −0.19
and calibrated in a fully developed turbulent channel flow. It has been observed for the first time in a macroscopic flow
that the sensor output power is approximately proportional to the 1/3 powered WSS, as expected for a thermal-principle-based
WSS sensor, and the wall shear stress measurement is demonstrated for a low Reynolds number flow. 相似文献
17.
Non-Newtonian fluid flow through porous media is of considerable interest in several fields, ranging from environmental sciences
to chemical and petroleum engineering. In this article, we consider an infinite porous domain of uniform permeability k and porosity f{\phi} , saturated by a weakly compressible non-Newtonian fluid, and analyze the dynamics of the pressure variation generated within
the domain by an instantaneous mass injection in its origin. The pressure is taken initially to be constant in the porous
domain. The fluid is described by a rheological power-law model of given consistency index H and flow behavior index n; n, < 1 describes shear-thinning behavior, n > 1 shear-thickening behavior; for n = 1, the Newtonian case is recovered. The law of motion for the fluid is a modified Darcy’s law based on the effective viscosity μ
ef
, in turn a function of f, H, n{\phi, H, n} . Coupling the flow law with the mass balance equation yields the nonlinear partial differential equation governing the pressure
field; an analytical solution is then derived as a function of a self-similar variable η = rt
β
(the exponent β being a suitable function of n), combining spatial coordinate r and time t. We revisit and expand the work in previous papers by providing a dimensionless general formulation and solution to the problem
depending on a geometrical parameter d, valid for plane (d = 1), cylindrical (d = 2), and semi-spherical (d = 3) geometry. When a shear-thinning fluid is considered, the analytical solution exhibits traveling wave characteristics,
in variance with Newtonian fluids; the front velocity is proportional to t
(n-2)/2 in plane geometry, t
(2n-3)/(3−n) in cylindrical geometry, and t
(3n-4)/[2(2−n)] in semi-spherical geometry. To reflect the uncertainty inherent in the value of the problem parameters, we consider selected
properties of fluid and matrix as independent random variables with an associated probability distribution. The influence
of the uncertain parameters on the front position and the pressure field is investigated via a global sensitivity analysis
evaluating the associated Sobol’ indices. The analysis reveals that compressibility coefficient and flow behavior index are
the most influential variables affecting the front position; when the excess pressure is considered, compressibility and permeability
coefficients contribute most to the total response variance. For both output variables the influence of the uncertainty in
the porosity is decidedly lower. 相似文献
18.
Werner-Michael Kulicke Ulf Reinhardt Gerald G. Fuller Oliver Arendt 《Rheologica Acta》1999,38(1):26-33
Sodium carboxymethylcellulose (NaCMC) in solution represents a complex rheological system, since it forms aggregates and
associations and hence higher-level structures and, depending on the synthesis, is only found in a molecularly dispersed form
in exceptional cases. Rheo-mechanical investigations of the viscoelasticity showed that the Cox-Merz rule is not fulfilled.
The aim was therefore to examine whether rheo-optics could be employed to provide more detailed conclusions about the parameters that influence the flow behavior of NaCMC than
has hitherto been available with mechanical methods. The flow birefringence, Δn
′, rises as the degree of polymerization increases, and exhibits the same dependence on molar mass as does the viscosity: Δn
′∝M
w
3.4. As the degree of polymerization increases while the shear rate remains constant, the polymer segments become more distinctly
aligned in the direction of shear. Hence increasing the degree of polymerization also affects the solution structure, i.e.
the interaction of the molecules with one another. The stress-optical rule only applies to a limited extent for this system.
The stress-optical coefficient, C, is almost independent of the shear rate, but is strongly influenced by the concentration and attains a limiting value of
3 × 10−8 Pa−1. C was determined for a polymer in dilute solution and the curve obtained also enabled transitions in the solution structure to be recognized.
Received: 1 May 1998 Accepted: 5 October 1998 相似文献
19.
B. K. Jha 《Heat and Mass Transfer》2001,37(4-5):329-331
The combined effect of natural convection and uniform transverse magnetic field on the couette flow of an electrically conducting
fluid between two parallel plates for impulsive motion of one of the plates in discussed. Under the assumption of negligible
induced magnetic field and applied magnetic field being fixed relative to the fluid or plate, the governing equations have
been solved exactly, and the expressions for velocity and temperature field have been presented for two different cases. A
comparative study is made between the velocity field for magnetic field fixed with respect to plate and magnetic field fixed
with respect to fluid.
Received on 12 July 1999 相似文献
20.
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