共查询到20条相似文献,搜索用时 31 毫秒
1.
Bidyut Santra Bhabani S. Dandapat 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,80(11):688-700
A thin viscous liquid film flow is developed over a stretching sheet under different nonlinear stretching velocities. An evolution
equation for the film thickness, is derived using long-wave approximation of thin liquid film and is solved numerically by
using the Newton–Kantorovich method. A comparison is made with the analytic solution obtained in [B. S. Dandapat, A. Kitamura,
B. Santra, “Transient film profile of thin liquid film flow on a stretching surface”, ZAMP, 57, 623-635 (2006)]. It is observed that all types of stretching produce film thinning but non-monotonic stretching produces
faster thinning at small distance from the origin. The velocity u along the stretching direction strongly depends on the distance along the stretching direction and the Froude number. 相似文献
2.
B. S. Dandapat Bidyut Santra S. K. Singh 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,46(2):685-695
A thin viscous liquid film flow is developed over a stretching sheet under different non-linear stretching velocities in presence
of uniform transverse magnetic field. Evolution equation for the film thickness is derived using long-wave approximation of
thin liquid film and is solved numerically by using the Newton–Kantorovich method. It is observed that all types of stretching
produces film thinning, but non-monotonic stretching produces faster thinning at small distance from the origin. Effect of
the transverse magnetic field is to slow down the film thinning process. Observed flow behavior is explained physically. 相似文献
3.
B. S. Dandapat Bidyut Santra S. K. Singh 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,61(4):685-695
A thin viscous liquid film flow is developed over a stretching sheet under different non-linear stretching velocities in presence of uniform transverse magnetic field. Evolution equation for the film thickness is derived using long-wave approximation of thin liquid film and is solved numerically by using the Newton–Kantorovich method. It is observed that all types of stretching produces film thinning, but non-monotonic stretching produces faster thinning at small distance from the origin. Effect of the transverse magnetic field is to slow down the film thinning process. Observed flow behavior is explained physically. 相似文献
4.
《Quaestiones Mathematicae》2013,36(1):137-151
Abstract In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated. The Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered. The boundary layer equations are derived for the two-dimensional flow of an incompressible Sisko fluid. Similarity transformations are used to reduce the governing nonlinear equations and then solved analytically using the homotopy analysis method. In addition, closed form exact analytical solutions are provided for n = 0 and n = 1. Effects of the pertinent parameters on the boundary layer flow are shown and solutions are contrasted with the power-law fluid solutions. 相似文献
5.
This paper presents a mathematical analysis of MHD flow and heat transfer to a laminar liquid film from a horizontal stretching surface. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of non-linear ordinary differential equations. Numerical solution of resulting non-linear differential equations is found by using efficient shooting technique. Boundary layer thickness is explored numerically for some typical values of the unsteadiness parameter S and Prandtl number Pr, Eckert number Ec and Magnetic parameter Mn. Present analysis shows that the combined effect of magnetic field and viscous dissipation is to enhance the thermal boundary layer thickness. 相似文献
6.
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
7.
B. S. Dandapat A. Kitamura B. Santra 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):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.
(Received: May 4, 2004; revised: February 2/August 24, 2005) 相似文献
8.
Our aim in this article is to investigate numerically the unsteady two‐dimensional mixed convection flow along a vertical semi‐infinite stretching sheet in a parallel free stream with a power‐law wall temperature and concentration distributions of the form T w (x) = T∞ + Ax2m?1 and Cw (x) = C∞ + Bx2m?1, where A, B and m are constants. The unsteadiness in the flow is caused by the time dependent stretching sheet as well as by the free stream velocity. The governing nonlinear partial differential equations in the velocity, temperature and concentration fields are written in nondimensional form using suitable transformations. The final set of resulting coupled nonlinear partial differential equations is solved using an implicit finite‐difference scheme in combination with a quasi‐linearization technique. The effects of various governing parameters on the velocity, temperature and concentration profiles as well as on the skin friction coefficient, local Nusseltnumber and local Sherwood number are presented and discussed in details. The computed numerically results are compared with previously reported work and are found to be in excellent agreement. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
9.
J. H. Merkin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):543-564
The free convection boundary-layer flow on a vertical surface in a porous medium with local heat generation proportional to
(T – T∞)p, where T is the local temperature and T∞ is the ambient temperature, is considered when the surface is thermally insulated. The way in which the flow develops from
the leading edge is seen to depend critically on the exponent p. For p ≤ 2 there is a boundary-layer flow for all x > 0, where x measures distance from the leading edge, with the internal heating having a significant effect at large x. For p ≥ 5 there is also a boundary-layer flow to large x but now the internal heating has an increasingly weaker effect as x increases. For 2 < p < 5 the boundary-layer solution breaks down at a finite x, with a singularity developing leading to thermal runaway at a finite distance along the surface. 相似文献
10.
11.
We consider a new way of establishing Navier wall laws. Considering a bounded domain Ω of R
N
, N=2,3, surrounded by a thin layer Σ
ε
, along a part Γ2 of its boundary ∂Ω, we consider a Navier-Stokes flow in Ω∪∂Ω∪Σ
ε
with Reynolds’ number of order 1/ε in Σ
ε
. Using Γ-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier
law involving a matrix of Borel measures having the same support contained in the interface Γ2. We then consider two special cases where we characterize this matrix of measures. As a further application, we consider
an optimal control problem within this context. 相似文献
12.
Á. G. Horváth 《Monatshefte für Mathematik》2007,150(3):211-216
This paper presents a result concerning the connection between the parallel projection P
v,H
of a parallelotope P along the direction v (into a transversal hyperplane H) and the extension P + S(v), meaning the Minkowski sum of P and the segment S(v) = {λv | −1 ≤ λ ≤ 1}. A sublattice L
v
of the lattice of translations of P associated to the direction v is defined. It is proved that the extension P + S(v) is a parallelotope if and only if the parallel projection P
v,H
is a parallelotope with respect to the lattice of translations L
v,H
, which is the projection of the lattice L
v
along the direction v into the hyperplane H. 相似文献
13.
The Blow-up Locus of Heat Flows for Harmonic Maps 总被引:5,自引:0,他引:5
Abstract
Let M and N be two compact Riemannian manifolds. Let u
k
(x, t) be a sequence of strong stationary weak heat flows from M×R
+ to N with bounded energies. Assume that u
k→u weakly in H
1, 2(M×R
+, N) and that Σt is the blow-up set for a fixed t > 0. In this paper we first prove Σt is an H
m−2-rectifiable set for almost all t∈R
+. And then we prove two blow-up formulas for the blow-up set and the limiting map. From the formulas, we can see that if the
limiting map u is also a strong stationary weak heat flow, Σt is a distance solution of the (m− 2)-dimensional mean curvature flow [1]. If a smooth heat flow blows-up at a finite time, we derive a tangent map or a weakly
quasi-harmonic sphere and a blow-up set ∪t<0Σt× {t}. We prove the blow-up map is stationary if and only if the blow-up locus is a Brakke motion.
This work is supported by NSF grant 相似文献
14.
Paolo Albano 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):273-281
In an open bounded set Ω, we consider the distance function from ∂Ω associated to a Riemannian metric with C
1,1 coefficients. Assuming that Ω is convex near a boundary point x
0, we show that the distance function is differentiable at x
0 if and only if there exists the tangent space to ∂Ω at x
0. Furthermore, if the distance function is not differentiable at x
0 then there exists a Lipschitz continuous curve, with initial point at x
0, such that the distance function is not differentiable along such a curve.
相似文献
15.
Thomas H. Solomon Brian R. Wallace Nathan S. Miller Courtney J. L. Spohn 《Communications in Nonlinear Science & Numerical Simulation》2003,8(3-4):239
We discuss experimental and numerical studies of the effects of Lagrangian chaos (chaotic advection) on the stretching of a drop of an immiscible impurity in a flow. We argue that the standard capillary number used to describe this process is inadequate since it does not account for advection of a drop between regions of the flow with varying velocity gradient. Consequently, we propose a Lagrangian-generalized capillary number CL number based on finite-time Lyapunov exponents. We present preliminary tests of this formalism for the stretching of a single drop of oil in an oscillating vortex flow, which has been shown previously to exhibit Lagrangian chaos. Probability distribution functions (PDFs) of the stretching of this drop have features that are similar to PDFs of CL. We also discuss on-going experiments that we have begun on drop stretching in a blinking vortex flow. 相似文献
16.
Tomasz Radzik 《Mathematical Programming》1996,78(1):43-58
In this paper we consider an optimization version of the multicommodity flow problem which is known as the maximum concurrent
flow problem. We show that an approximate solution to this problem can be computed deterministically using O(k(ε
−2 + logk) logn) 1-commodity minimum-cost flow computations, wherek is the number of commodities,n is the number of nodes, andε is the desired precision. We obtain this bound by proving that in the randomized algorithm developed by Leighton et al. (1995)
the random selection of commodities can be replaced by the deterministic round-robin without increasing the total running
time. Our bound significantly improves the previously known deterministic upper bounds and matches the best known randomized
upper bound for the approximation concurrent flow problem.
A preliminary version of this paper appeared inProceedings of the 6th ACM-SIAM Symposium on Discrete Algorithms, San Francisco CA, 1995, pp. 486–492. 相似文献
17.
Generalizing earlier results, it is shown that if are “large” subsets of a finite field F
q
, then the equations a + b = cd, resp. ab + 1 = cd can be solved with . Other algebraic equations with solutions restricted to “large” subsets of F
q
are also studied. The proofs are based on character sum estimates proved in Part I of the paper.
Research partially supported by the Hungarian National Foundation for Scientific Research, Grants No. T 043623, T 043631 and
T 049693. 相似文献
18.
Given a data instanced=(A, b, c) of a linear program, we show that certain properties of solutions along the central trajectory of the linear program are
inherently related to the condition number C(d) of the data instanced=(A, b, c), where C(d) is a scale-invariant reciprocal of a closely-related measure ρ(d) called the “distance to ill-posedness”. (The distance to ill-posedness essentially measures how close the data instanced=(A,b,c) is to being primal or dual infeasible.) We present lower and upper bounds on sizes of optimal solutions along the central
trajectory, and on rates of change of solutions along the central trajectory, as either the barrier parameter μ or the datad=(A, b, c) of the linear program is changed. These bounds are all linear or polynomial functions of certain natural parameters associated
with the linear program, namely the condition number C(d), the distance to ill-posedness ρ(d), the norm of the data ‖d‖, and the dimensionsm andn. 相似文献
19.
E. Momoniat 《Journal of Mathematical Analysis and Applications》2006,322(1):41-50
A second-order non-linear partial differential equation modelling the gravity driven spreading of a thin viscous liquid film with time-dependent non-uniform surface tension Σ(t,r) is considered. The problem is specified in cylindrical polar coordinates where we assume the flow is axisymmetric. Similarity solutions describing the spreading of a thin drop and the flattening of a thin bubble are investigated. 相似文献
20.
Kallol Paul 《Mathematica Slovaca》2010,60(1):121-128
One of the couple of translatable radii of an operator in the direction of another operator introduced in earlier work [PAUL,
K.: Translatable radii of an operator in the direction of another operator, Scientae Mathematicae 2 (1999), 119–122] is studied in details. A necessary and sufficient condition for a unit vector f to be a stationary vector of the generalized eigenvalue problem Tf = λAf is obtained. Finally a theorem of Williams ([WILLIAMS, J. P.: Finite operators, Proc. Amer. Math. Soc. 26 (1970), 129–136]) is generalized to obtain a translatable radius of an operator in the direction of another operator. 相似文献