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1.
2.
This investigation explores the mass/heat transfer from a wall-mounted block in a rectangular fully developed channel flow.
The naphthalene sublimation scheme was used to measure the level of local mass transfer from the block’s surfaces. The heat
transfer coefficient can be obtained by analogy between heat and mass transfer. The effects of the Reynolds number on the
local mass transfer from the block’s surfaces have been widely discussed. Results showed that, owing to the flow complexity
induced by vortices around the block, the block’s surfaces appeared four different spatial Sherwood number distributions,
termed “Wave type”, “U type”, “Slant type”, and “Pit type”. A change in the Reynolds number significantly altered the spatial Sherwood number distributions on the block’s surfaces.
Besides, four correlations between the Reynolds number and the surface-averaged Sherwood number were presented for the front,
top, side, and rear surfaces of the block at a given block’s height, for the purpose of practical applications. 相似文献
3.
Positivity and Almost Positivity of Biharmonic Green’s Functions under Dirichlet Boundary Conditions
Hans-Christoph Grunau Frédéric Robert 《Archive for Rational Mechanics and Analysis》2010,195(3):865-898
In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped
plate boundary value problem, neither a maximum principle nor a comparison principle or—equivalently—a positivity preserving
property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem
from being reasonably written as a system of second order boundary value problems. It is shown that, on the other hand, for
bounded smooth domains
W ì \mathbbRn{\Omega \subset\mathbb{R}^n} , the negative part of the corresponding Green’s function is “small” when compared with its singular positive part, provided
n\geqq 3{n\geqq 3} . Moreover, the biharmonic Green’s function in balls
B ì \mathbbRn{B\subset\mathbb{R}^n} under Dirichlet (that is, clamped) boundary conditions is known explicitly and is positive. It has been known for some time
that positivity is preserved under small regular perturbations of the domain, if n = 2. In the present paper, such a stability result is proved for
n\geqq 3{n\geqq 3} . 相似文献
4.
Lawrence Markus 《Journal of Dynamics and Differential Equations》2007,19(1):133-154
In a celebrated theorem H?lder proved that the Euler Γ-function is differential transcendental, i.e. Γ(z) is not a solution of any (non-trivial) algebraic ordinary differential equation with coefficients that are complex numbers; and we extend his methods to the Riemann ζ-function. Moreover, we conjecture that Γ and ζ are differential independent, i.e. Γ(z) is not a solution of any such algebraic differential equation—even allowing coefficients that are differential polynomials in ζ(z). However, we are able to demonstrate only the partial result that Γ(z) and ζ(sin 2πz) are differential independent. 相似文献
5.
We investigated the influence of elastic material compressibility on parameters of an expanding spherical stress wave. The
material compressibility is represented by Poisson’s ratio, ν, in this paper. The stress wave is generated by a pressure produced inside a spherical cavity surrounded by the isotropic
elastic material. The analytical closed form formulae determining the dynamic state of the mechanical parameters (displacement,
particle velocity, strains, stresses, and material density) in the material have been derived. These formulae were obtained
for surge pressure p(t) = p
0 = const inside the cavity. From analysis of these formulae, it is shown that the Poisson’s ratio substantially influences
the course of material parameters in space and time. All parameters intensively decrease in space together with an increase
of the Lagrangian coordinate, r. On the contrary, these parameters oscillate versus time around their static values. These oscillations decay in the course
of time. We can mark out two ranges of parameter ν values in which vibrations of the parameters are “damped” at a different rate. Thus, Poisson’s ratio in the range below about
0.4 causes intense decay of parameter oscillations. On the other hand in the range 0.4 < ν < 0.5, i.e. in quasi-incompressible materials, the “damping” of parameter vibrations is very low. In the limiting case when
ν = 0.5, i.e. in the incompressible material, “damping” vanishes, and the parameters harmonically oscillate around their static
values. The abnormal behaviour of the material occurs in the range 0.4 < ν < 0.5. In this case, an insignificant increase of Poisson’s ratio causes a considerable increase of the parameter vibration
amplitude and decrease of vibration “damping”.
相似文献
6.
7.
Modeling heat transfer and fluid flow in materials with complicated micro-structures is a major challenge to numerical methods
due to their multiscale and multiphysics nature. A relatively novel numerical technique—the meshless smoothed particle hydrodynamics
(SPH) method has the potential of making a significant contribution to this research field. In the present SPH modeling effort,
a 2D modeling system is devised for the prediction of the effective thermal conductivity in heterogeneous materials containing
two or three different components. The microscopic component configuration inside the materials is constructed in the SPH
methodology by randomly assigning particles as a certain component to meet the required macroscopic composition. For heterogeneous
two-component materials, the effective thermal conductivity predicted by the modified effective medium theory model with the
so-called “flexible” factor f equal to 4.5 agrees well with the SPH data. On the basis of a simple “step-process” concept, the effective thermal conductivity
of a heterogeneous multi-component material can be derived from the corresponding “degenerate” materials which consist of
fewer components. 相似文献
8.
R.J. Weinacht 《Journal of Elasticity》1999,57(2):165-170
The linear elastostatic displacement boundary-value problem is considered for a bounded simply connected region Ω in R
n
in the case of a homogeneous isotropic medium. For n = 2 it is shown that if all solenoidal forcing terms result in solenoidal displacements, then Ω is a disk. It is likely that
the result is true for n ≥ 3 but that problem is not resolved.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
9.
Yu. G. Tynnikov N. A. Tolstokulakov V. A. Ivanov V. A. Andrianov 《Journal of Applied Mechanics and Technical Physics》1998,39(3):342-348
The reusable source of a pulsed magnetic field—a ballistic magnetocumulative generator (BMG)—is considered. Electrical engineering analysis of the efficiency of operation of the generator on an active-inductive load
is performed. A method for calculating the two-dimensional distribution of the field in the busbars of the generator is developed.
Experimental results are obtained for the operation of aBMG model on some types of load.
Central Scientific-Research Institute “Burevestnik,” Nizhnii Novgorod 603603. Translated from Prikladnaya Mekhanika i Tekhnicheskaya
Fizika, Vol. 39, No. 3, pp. 22–29, May–June, 1998. 相似文献
10.
Georg Dolzmann Bernd Kirchheim Jan Kristensen 《Archive for Rational Mechanics and Analysis》2000,154(2):93-100
We simplify and sharpen several results by K. Zhang concerning properties of quasiconvex hulls of sets and quasiconvex envelopes
of their distance functions. The approach emphasizes the underlying geometry and in particular we show that K
pc=K
c implies K
rc=K
c if and only if min{m,n}≤ 2 thus answering a question raised in [Z2].
(Accepted January 24, 2000)?Published online August 21, 2000 相似文献
11.
A. N. Guz 《International Applied Mechanics》2009,45(1):1-31
Nonclassical problems of fracture and failure mechanics that have been analyzed by the author and his collaborators at the
S. P. Timoshenko Institute of Mechanics (Kiev, National Academy of Sciences of Ukraine) during the past forty years are considered
in brief. The results of the analysis are presented in a form that would be quite informative for the majority of experts
interested in various fundamental and applied aspects of fracture and failure problems including the identification of related
mechanisms. This paper was prepared on invitation of the Editorial Board of the journal “Annals. The European Academy of Sciences”
and may be considered as an Extended Pascal Medal Lecture (The 2007 Blaise Pascal Medal in Materials Sciences of the EAS)
This is an updated edition of the author’s lecture prepared at the invitation of the Annals—The European Academy of Sciences Magazine on the occasion of awarding him the 2007 Blaise Pascal Medal in Materials Sciences by the EAS. The author’s speech
at the award ceremony at the General Assembly of the Academy has already been published in International Applied Mechanics [75]. The electronic version of the paper in Annals has been prepared; this issue of Annals is to be published as a book. The paper includes an additional section and extended list of references [41–99].
Published in Prikladnaya Mekhanika, Vol. 45, No. 1, pp. 3–40, January 2009. 相似文献
12.
M. Sugawara E. Tamura Y. Satoh Y. Komatsu M. Tago H. Beer 《Heat and Mass Transfer》2007,43(10):1009-1018
Visual observations reveal a complicated flow in the liquid melt and a melting front configuration resulting from horizontal
ice plate melting from above into a 20 wt% calcium chloride aqueous solution. The initial temperature of the ice plate and
the mixture are both −5°C. Small scale “mountain and valley” structures (∼1 mm) appear on the flat melting front just after
melting begins, which have been called “sharkskin”. Innumerable upward and downward flows appear near the sharkskin and are controlled by its “mountain and valley” structure. These typical flows will considerably promote the melting of the
ice plate to be 30% larger as compared to the numerically predicted results assuming a flat melting front (i.e., without the
sharkskin), and also by three times larger compared with the results for melting from below. 相似文献
13.
We investigate the behavior of the deformations of a thin shell, whose thickness δ tends to zero, through a decomposition technique of these deformations. The terms of the decomposition of a deformation v are estimated in terms of the L
2-norm of the distance from ∇
v to SO(3). This permits in particular to derive accurate nonlinear Korn’s inequalities for shells (or plates). Then we use this
decomposition technique and estimates to give the asymptotic behavior of the Green-St Venant’s strain tensor when the “strain energy” is of order less than δ
3/2. 相似文献
14.
S.A. Thorpe 《Theoretical and Computational Fluid Dynamics》1998,11(3-4):171-181
This is an overview of knowledge, derived mainly from observations, of turbulence in the stratified and rotating World Ocean
from the 1960s, when mesoscale motions with scales of 30–150 km and 100 days were discovered by neutrally buoyant floats,
to the present decade and the use of SF6“purposeful tracer” release study in the North Atlantic.
Most of the ocean is stably stratified, but it contains a rotational turbulent “continua” and isolated rotating eddies, as
well as Rossby waves, and many features similar to those of, say, planetary atmospheres. It differs however because (a) the
presence of lateral boundaries, the continental land masses, islands, and seamounts, provides constraints to the circulation and to the propagation
of eddies, and possibly substantial sources and sinks of eddy motion; (b) channels connecting the oceans to land-locked seas
(e.g., the Mediterranean; the formation of water with anomalous properties, “natural tracers”, e.g., temperature or salinity,
allows “interthermocline eddies” to be readily detected); and (c) convection and differential seasonal latitudinal forcing
introduce upper-ocean variability and intrathermocline eddies. The focus of research interest has moved from “turbulence”per se towards study of its consequences, for example towards dispersion of material particles and dissolved solutes, and the meridional
and inter-basin transfers of heat.
Received 2 December 1996 and accepted 18 September 1997 相似文献
15.
This article extends the mathematical formulation and solution procedure of the modified ‘q-based’ GEM to unsteady situations, namely to the modified unsteady ‘q-based’ GEM. Solutions that provide information on the evolution of the pressure and the flux over long time intervals are
available by incorporating the additional dimension of time into steady problems. This approach is first tested by solving
an example for which an analytical solution is available. The numerical results for this example is found to be in excellent
agreement with the analytical solution. Several problems involving geological features, such as wells and faults, are then
investigated, with different properties applying to the faults. A strong influence of the low permeability faults is in evidence
in these problems. 相似文献
16.
The exact linear three-dimensional equations for a elastically monoclinic (13 constant) plate of constant thickness are reduced
without approximation to a single 4th order differential equation for a thickness-weighted normal displacement plus two auxiliary equations for
weighted thickness integrals of a stress function and the normal strain. The 4th order equation is of the same form as in
classical (Kirchhoff) theory except the unknown is not the midsurface normal displacement. Assuming a solution of these plate
equations, we construct so-called modified Saint-Venant solutions—“modified” because they involve non-zero body and surface
loads. That is, solutions of the exact three-dimensional elasticity equations that exhibit no boundary layers and that are
subject to a special set of body and surface loads that leave the analogous plate loads arbitrary. 相似文献
17.
18.
We explore the effects of fluid films of variable depths on droplets impacting into them. Corresponding to a range of fluid
“film” depths, a non-dimensional parameter—H*, defined as the ratio of the film thickness to the droplet diameter—is varied in the range 0.1≤H*≤10. In general, the effect of the fluid film imposes a dramatic difference on the dynamics of the droplet–surface interaction
when compared to a similar impact on a dry surface. This is illustrated by the size distribution and number of the splash
products. While thin fluid films (H*≈0.1) promote splashing, thicker films (1≤H*≤10) act to inhibit it. The relative roles of surface tension and viscosity are investigated by comparison of a matrix of
fluids with low and high values of these properties. Impingement conditions, as characterized by Reynolds and Weber numbers,
are varied by velocity over a range from 1.34 to 4.22 m/s, maintaining a constant droplet diameter of 2.0 mm. The dependence
of splashing dynamics, characterized by splash product size and number, on the fluid surface tension and viscosity and film
thickness are discussed. 相似文献
19.
P. Ribeiro 《Nonlinear dynamics》2012,67(3):1761-1778
Vibrations in one plane of beams with fixed ends, vibrating in the geometrically non-linear and elasto-plastic regimes under
the influence of harmonic external forces, are studied. A p-version finite element that considers transverse and longitudinal displacements, as well as shear deformation, is employed.
The incremental theory of plasticity with isotropic hardening is followed. Numerical methods are employed to solve the differential
equations of motion and to carry out integrals where plastic terms exist. The main interest of this work is that “chaotic-like”
behavior—in the sense of unpredictable behavior of an apparently deterministic system—is discovered. This behavior is explained
by a buckling phenomenon induced by the plastic strains: no longitudinal external force, other than the boundary forces, exists
in the cases investigated. Since the plastic strains depend on the past history, the predictions of the long term behavior
are also affected by the different predictions on the brief transition phase. An eigenvalue problem is defined to compute
eigenvalues that provide an indication that a bifurcation induced by the plastic strains is likely to occur. 相似文献
20.
Xinyu He 《Journal of Mathematical Fluid Mechanics》2004,6(4):389-404
A self-similar solution of the three-dimensional (3d) incompressible Euler equations is defined byu(x,t) =U(y)/t*-t)
α, y = x/(t* ~ t)β,α,β> 0, whereU(y) satisfiesζU + βy. ΔU + U. VU + VP = 0,divU = 0. For α = β = 1/2, which is the limiting case of Leray’s self-similar Navier—Stokes equations, we prove the existence of(U,P) ε H3(Ω,R3 X R) in a smooth bounded domain Ω, with the inflow boundary data of non-zero vorticity. This implies the possibility that
solutions of the Euler equations blow up at a timet = t*, t* < +∞. 相似文献