共查询到20条相似文献,搜索用时 0 毫秒
1.
B. S. Dandapat A. Kitamura B. Santra 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,45(11):623-635
In this paper we have studied a non-planar thin liquid film flow on a planar stretching surface. The stretching surface is
assumed to stretch impulsively from rest and the effect of inertia of the liquid is considered. Equations describing the laminar
flow on the stretching surface are solved analytically. It is observed that faster stretching causes quicker thinning of the
film on the stretching surface. Velocity distribution in the liquid film and the transient film profile as functions of time
are obtained. 相似文献
2.
The flow of a heated ferrofluid over a linearly stretching sheet is studied in the pres-
ence of an applied magnetic field due to a magnetic dipole. It is assumed that the applied
magnetic field is sufficiently strong to saturate the ferrofluid and the variation of magnetization
with temperature can be approximated by a non linear function of temperature difference. By
introducing appropriate non dimensional variables the problem is described by a coupled and
non linear system of ordinary differential equations with its boundary conditions which is solved
numerically by applying an efficient numerical technique based on the common finite difference
method. The obtained results are presented graphically for different values of the parameters
entering into the problem under consideration and the dependence of the flow field from these
parameters is discussed. A comparative study, with a similar problem which has already been
solved and documented in literature, is also made wherever necessary, emphasizing the impor-
tance of the non-linear variation of magnetization with temperature. Emphasis is also given in
the obtained results for Prandtl number equal to 21 and critical exponent = 0.368 which are
important and interesting in Biomagnetic Fluid Dynamics. 相似文献
3.
P. D. Weidman A. M. J. Davis D. G. Kubitschek 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(2):313-332
The simultaneous effects of transpiration through and tangential movement of a semi-infinite flat plate on the self-similar
boundary layer flow driven by uniform shear in the far field is considered. Difficulties with standard shooting techniques
are overcome using Crocco variables which also serve to better elucidate the solution structure. The stabilities of dual,
triple and even quadruple steady flow solutions encountered in different ranges of plate stretching and wall stress are determined
using a linear temporal stability analysis for the self-similar flow.
相似文献
4.
Lie group method is investigated for solving the problem of heat transfer in an unsteady, three-dimensional, laminar, boundary-layer flow of a viscous, incompressible and electrically conducting fluid over inclined permeable surface embedded in porous medium in the presence of a uniform magnetic field and heat generation/absorption effects. A uniform magnetic field is applied in the y-direction and a generalized flow model is presented to include the effects of the macroscopic viscous term and the microscopic permeability of porous medium. The infinitesimal generators accepted by the equations are calculated and the extension of the Lie algebra for the problem is also presented. The restrictions imposed by the boundary conditions on the generators are calculated. The investigation of the three-independent-variable partial differential equations is converted into a two-independent-variable system by using one subgroup of the general group. The resulting equations are solved numerically with the perturbation solution for various times. Velocity, temperature and pressure profiles, surface shear stresses, and wall-heat transfer rate are discussed for various values of Prandtl number, Hartmann number, Darcy number, heat generation/absorption coefficient, and surface mass-transfer coefficient. 相似文献
5.
M. Günther 《Journal of Differential Equations》2008,245(10):2802-2845
In the free boundary problem of Stokes flow driven by surface tension, we pass to the limit of small layer thickness. It is rigorously shown that in this limit the evolution is given by the well-known thin film equation. The main techniques are appropriate scaling and uniform energy estimates in Sobolev spaces of sufficiently high order, based on parabolicity. 相似文献
6.
Short-time existence, uniqueness, and regularity results are shown for the moving boundary problem of a free drop of liquid governed by the Stokes equations and driven by surface tension. The value of the surface tension coefficient is variable, not necessarily strictly positive, and transported with the flow on the moving surface.By a perturbation of identity approach, the problem is transformed into a nonlinear, nonlocal first order degenerate parabolic evolution equation on a fixed reference manifold. Its solvability is proved by deriving a priori estimates and using Galerkin approximations. 相似文献
7.
Two-dimensional boundary value problems of flow of a viscous micropolar fluid are investigated in the case of linearization by Oseen's method. 相似文献
8.
Stokes flow between corrugated plates in microdomains has been analyzed using a perturbation method. This approach used the incompressible Navier-Stokes equations, but the velocity-slip is present along the solid-fluid interface. For the slip flow regime, if we introduce Knudsen number (K
n) herein, 0.01 K
n 0.1, the total flow rate is increasing as a ratio of 1 + 6K
nto no-slip Stokes flow. If we consider fixedK
ncases, the corrugations still decrease the flow rate, consideringO(2) terms, and the decrease is maximum as the phase shift becomes 180 °. 相似文献
9.
We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects into account. This leads to a coupled system of Navier–Stokes and Mullins–Sekerka type parts that coincides with the asymptotic limit of a diffuse interface model. We prove the long-time existence of weak solutions, which is an open problem for the classical two-phase model. We show that the phase interfaces have in almost all points a generalized mean curvature. 相似文献
10.
The existence and uniqueness of local in time strong solution with large initial data for the three-dimensional compressible viscoelastic flow is established. The strong solution has weaker regularity than the classical solution. The Lax-Milgram theorem and the Schauder-Tychonoff fixed-point argument are applied. 相似文献
11.
In the simplest case of a linearly degenerate mobility, we view the thin-film equation as a classical free boundary problem. Our focus is on the regularity of solutions and of their free boundary in the “complete wetting” regime, which prescribes zero slope at the free boundary. In order to rule out of the analysis possible changes in the topology of the positivity set, we zoom into the free boundary by looking at perturbations of the stationary solution. Our strategy is based on a priori energy-type estimates which provide “minimal” conditions on the initial datum under which a unique global solution exists. In fact, this solution turns out to be smooth for positive times and to converge to the stationary solution for large times. As a consequence, we obtain smoothness and large-time behavior of the free boundary. 相似文献
12.
Blanca Climent-Ezquerra Francisco Guillén-González Marko Rojas-Medar 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):984-998
In this paper we prove existence of weak solution with the reproductivity in time property, for a penalized PDE’s system related
to a nematic liquid crystal model.
This problem is relatively explict when time-independent Dirichlet boundary conditions are imposed for the orientation of
crystal molecules. Nevertheless, for the time-dependent case, the treatment of the problem is completely different. The verification
of a maximum principle for weak reproductive solutions is fundamental in the argument.
Finally, the relation between reproductive and periodic in time (regular) solutions will be pointed out, differenting the
2D and 3D cases. Basically, in two-dimensional domains every reproductive solution is regular and time periodic, whereas the problem
remains open for three-dimensional domains. 相似文献
13.
14.
Yun Zhao Libo ZhangYongluo Cao 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):5015-5022
Given a continuous dynamical system (X,T) with the specification property, and a sequence of asymptotically additive continuous functions, we consider the irregular set for it and show that this set is either empty or carries full asymptotically additive topological pressure. 相似文献
15.
This paper furthers the study of Adhikari et al. (2010) [2] on the global regularity issue concerning the 2D Boussinesq equations with vertical dissipation and vertical thermal diffusion. It is shown here that the vertical velocity v of any classical solution in the Lebesgue space Lq with 2?q<∞ is bounded by C1q for C1 independent of q. This bound significantly improves the previous exponential bound. In addition, we prove that, if v satisfies , then the associated solution of the 2D Boussinesq equations preserve its smoothness on [0,T]. In particular, implies global regularity. 相似文献
16.
Bo Einarsson 《BIT Numerical Mathematics》1988,28(3):383-390
The importance of using analytical methods is taught through the discussion of an example, where the analytical treatment of a partial differential equation provides not only a suitable time scale and an asymptotic solution, but also information important for the accuracy of the numerical solution.Dedicated to Peter Naur on the occasion of his 60th birthday 相似文献
17.
Habib Marzougui 《Journal of Differential Equations》2009,247(10):2681-2687
The aim of this paper is to prove a Morse conjecture; in particular it is shown that a topologically transitive analytic flow on a compact surface is metrically transitive. We also build smooth topologically transitive flows on surfaces which are not metrically transitive. 相似文献
18.
H. H. Sherif M. S. Faltas E. I. Saad 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(2):293-312
The Stokes axisymmetrical flow caused by a sphere translating in a micropolar fluid perpendicular to a plane wall at an arbitrary
position from the wall is presented using a combined analytical-numerical method. A linear slip, Basset type, boundary condition
on the surface of the sphere has been used. To solve the Stokes equations for the fluid velocity field and the microrotation
vector, a general solution is constructed from fundamental solutions in both cylindrical, and spherical coordinate systems.
Boundary conditions are satisfied first at the plane wall by the Fourier transforms and then on the sphere surface by the
collocation method. The drag acting on the sphere is evaluated with good convergence. Numerical results for the hydrodynamic
drag force and wall effect with respect to the micropolarity, slip parameters and the separation distance parameter between
the sphere and the wall are presented both in tabular and graphical forms. Comparisons are made between the classical fluid
and micropolar fluid.
相似文献
19.
We study the blowing-up behavior of solutions of a class of nonlinear integral equations of Volterra type that is connected with parabolic partial differential equations with concentrated nonlinearities. We present some analytic results and, in the case of the kernel of Abel-kind with power nonlinearity and fixed initial data, we give a numerical approximation by using one-point collocation methods. 相似文献
20.
Yong Zhou 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(3):384-392
In this paper we establish a Serrin’s type regularity criterion on the gradient of pressure for weak solutions to the Navier–Stokes
equations in
It is proved that if the gradient of pressure belongs to Lα, γ with
then the weak solution actually is regular and unique.
Received: May 4, 2004 相似文献