共查询到20条相似文献,搜索用时 656 毫秒
1.
江福汝 《应用数学和力学(英文版)》1989,10(4):289-296
In this paper, some misunderstandings concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has been offered.Projects Supported by the Science Fund of the Chinese Academy of Sciences. 相似文献
2.
Emad M. Abo-Eldahab 《Heat and Mass Transfer》2005,41(8):734-743
A general analysis has been developed to study the combined effect of the free convective heat and mass transfer on the steady three-dimensional laminar boundary layer flow over a stretching surface. The flow is subject to a transverse magnetic field normal to the plate. The governing three-dimensional partial differential equations for the present case are transformed into ordinary differential equation using three-dimensional similarity variables. The resulting equations, are solved numerically by applying a fifth order Runge-Kutta-Fehlberg scheme with the shooting technique. The effects of the Magnetic field Parameter M, buoyancy parameter N, Prandtl number Pr and Schmidt number Sc are examined on the velocity, temperature and concentration distributions. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various parametric conditions. The results are compared with known from the literature. 相似文献
3.
This study is concerned with the magnetohydrodynamic (MHD) rotating boundary layer flow of a viscous fluid caused by the shrinking
surface. Homotopy analysis method (HAM) is employed for the analytic solution. The similarity transformations have been used
for reducing the partial differential equations into a system of two coupled ordinary differential equations. The series solution
of the obtained system is developed and convergence of the results are explicitly given. The effects of the parameters M, s and λ on the velocity fields are presented graphically and discussed. It is worth mentioning here that for the shrinking
surface the stable and convergent solutions are possible only for MHD flows. 相似文献
4.
Summary The nonsimilar boundary-layer flow and heat transfer over a stationary permeable surface in a rotating fluid in the presence
of magnetic field, mass transfer and free stream velocity are studied. The parabolic partial differential equations governing
the flow have been solved numerically by using a difference–differential method. For small streamwise distance, these partial
differential equations are also solved by a perturbation technique with Shanks transformation. For uniform mass transfer,
analytical solutions are obtained. The surface skin friction coefficients and the Nusselt number increase with the magnetic
field, suction and streamwise distance from the leading edge of the plate except the skin friction coefficient in the y-direction which decreases with the increasing magnetic field.
Received 4 December 2001; accepted for publication 24 September 2002 相似文献
5.
The non-Darcy flow characteristics of power-law non-Newtonian fluids past a wedge embedded in a porous medium have been studied. The governing equations are converted to a system of first-order ordinary differential equations by means of a local similarity transformation and have been solved numerically, for a number of parameter combinations of wedge angle parameter m, power-law index of the non-Newtonian fluids n, first-order resistance A and second-order resistance B, using a fourth-order Runge–Kutta integration scheme with the Newton–Raphson shooting method. Velocity and shear stress at the body surface are presented for a range of the above parameters. These results are also compared with the corresponding flow problems for a Newtonian fluid. Numerical results show that for the case of the constant wedge angle and material parameter A, the local skin friction coefficient is lower for a dilatant fluid as compared with the pseudo-plastic or Newtonian fluids. 相似文献
6.
P. C. Jain 《Applied Scientific Research》1959,8(1):219-227
Summary Homogeneous and isotropic turbulence has been discussed in the present paper. An attempt has been made to find the simplifying hypothesis for connecting the higher order correlation tensor with the lower ones. Starting from the Navier-Stokes equations of motion for an incompressible fluid and following the usual method of taking the averages, a differential equation in Q and X, the defining scalar of the second order correlation tensor Q
x
and the defining scalar of a third order isotropic tensor X
ijk
, has been derived. The tensor X
ijk
stands for a tensorial expression containing the derivatives of the third and the fourth order tensors. Then the hypothesis is used that X=F(Q), where F is an unknown function. To find the forms of F, Kolmogoroff's similarity principles have been used, and thus two forms for F(Q) corresponding to two regions of the validity of these principles have been deduced. 相似文献
7.
The non-linear differential equations of motion, and boundary conditions, for Euler-Bernoulli beams able to experience flexure along two principal directions (and, thus, flexure in any direction in space), torsion and extension are formulated. The beam's material is assumed to be Hookean but its properties may vary along its span. The nonlinearities present in the differential equations include contributions from the curvature expression and from inertia terms. A set of differential equations with polynomial nonlinearities to cubic order, suitable for a perturbation analysis of the motion, is also developed and the validity of the inextensional approximation is assessed. The equations developed here reduce to those for an inextensional beam. In Part II of this paper, a specific example of application is analyzed and the results obtained are compared with those available in the literature where several non-linear terms have been neglected a priori. 相似文献
8.
Ahmet Kahraman 《Nonlinear dynamics》1992,3(3):183-198
The dynamic behavior of a harmonically excited, preloaded mechanical oscillator with dead-zone nonlinearity is described quantiatively. The governing strongly nonlinear differential equation is solved numerically. Damping coefficient-force ratio maps for two different values of the excitation frequency have been formed and the boundaries of the regions of different motion types are determined. The results have been compared with the results of the forced Duffing's equation available in the literature in order to identify the differences between cubic and dead-zone nonlinearities. Period-doubling bifurcations, which take place with a change of any of the system parameters, have been found to be the most common route to chaos. Such bifurcations follow the scaling rule of Feigenbaum.
b half length of the clearance. 相似文献
9.
In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation ∇2
u+u+ɛu
3 =b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual
reciprocity method(DRM)in solving nonlinear differential equations. 相似文献
10.
Loss of flow transients with reference to L.O.F. accidents in nuclear reactor cores have been systematically studied employing freon 12 as coolant. Two pressures (with reference to BWR and PWR characteristic liquid to vapour densities ratios), three periods of the coast-down flow transients during the simulated pump trips, and different specific mass flow rates have been investigated. The uniformly heated channel (L = 200 cm, D = 0.75 cm), instrumented with wall thermocouples and inlet to outlet differential pressure enabled recording of the following transients, inlet specific mass flowrate, inlet pressure, inlet to outlet Δp, inlet fluid temperature, outlet wall temperature, outlet bulk temperature.Through the wall temperature being close to the outlet it is possible to detect the onset of DNB and hence the time to DNB from the beginning of the flow transient. All the experimental runs (105) have been systematically compared with the G.E. (PEPE) code with the introduction of a CNEN DNB freon correlation. The results enable a series of conclusions which are extensively shown in the paper. 相似文献
11.
In this note, the essence and some supplements for the unified definition of divergence, rotation and gradient advanced by
Tai have been presented based on the method of exterior differential form with an expression of vectors of tensors. The main
purpose of this note is to introduce the useful expressions and their applications, and to simplify the proofs of many theorems
in various field theories, and they are also important because of their utility for establishing a wide class of principles. 相似文献
12.
In this paper, the flow of a visco-elastic liquid between two parallel plates has been studied when one plate is stationary and the other plate suddenly starts oscillating. Both finite Fourier sine transform and Laplace transform technique have been employed to solve the basic differential equations. The flow phenomenon has been characterized by the parameters, and and the effects of these on the flow characteristics have been studied through several graphs.Late professor of the department, who died in an accident on 7th July 1978. 相似文献
13.
A three-parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time-averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T ′2. Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl. The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results. 相似文献
14.
Eleftherios Papoutsakis Doraiswami Ramkrishna Henry C. Lim 《Applied Scientific Research》1980,36(1):13-34
The extension of the Graetz problem to include axial conduction has been of interest in view of its application to a number
of low Peclet number heat or mass transfer situations. Past efforts in dealing with this problem have been plagued with uncertainties
arising from expansion in terms of “eigenfunctions” and “eigenvalues” belonging to a nonselfadjoint operator. The uncertainties
spring from a lack of basis for the assumptions that no complex eigenvalues exist and that the calculated eigenvectors originate
from a complete set. Other methods have been entirely numerical.
The present work produces an entirelyanalytical solution to the Graetz problem for the Dirichlet boundary condition based on a selfadjoint formalism resulting from a decomposition
of the convective diffusion equation into a pair of first order partial differential equations. Physically, the decomposition
views the convective diffusion process as a pair of stipulations on how the temperature (or concentration) and theaxial energy (or mass) flow through a partial tube cross-section vary with radial and axial distances. The solution obtained is
simple, and readily computed.
To whom correspondence may be addressed 相似文献
15.
Recently a third-order existence theorem has been proven to establish the sufficient conditions of periodicity for the most general third-order ordinary differential equation
x+f(t,x,x′,x″)=0