Nonstationary poiseuille-type solutions for the second-grade fluid flow

We study solutions to the nonstationary equations describing the motion of the second-grade fluid in a twodimensional infinite channel and in a three-dimensional rotationally symmetric pipe. We prove the existence of a unique Poiseuille-type solution having a given flow rate (flux) and investigate the behavior of this solution as t → ∞.     

Inverse solutions for a second-grade fluid for porous medium channel and Hall current effects

Assuming certain forms of the stream function inverse solutions of an incompressible viscoelastic fluid for a porous medium channel in the presence of Hall currents are obtained. Expressions for streamlines, velocity components and pressure fields are described in each case and are compared with the known viscous and second-grade cases.     

Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equations

We present a very simple proof of the global existence of a C^∞ Lagrangian flow map for the 2D Euler and second-grade fluid equations (on a compact Riemannian manifold with boundary) which has C^∞ dependence on initial data u₀ in the class of H^s divergence-free vector fields for s > 2.     

Existence of global strong solution to the micropolar fluid system in a bounded domain

In this paper we are concerned with the initial boundary value problem of the micropolar fluid system in a three dimensional bounded domain. We study the resolvent problem of the linearized equations and prove the generation of analytic semigroup and its time decay estimates. In particular, L^p–L^q type estimates are obtained. By use of the L^p–L^q estimates for the semigroup, we prove the existence theorem of global in time solution to the original nonlinear problem for small initial data. Furthermore, we study the magneto‐micropolar fluid system in the final section. Copyright © 2005 John Wiley & Sons, Ltd.     

A note on the unsteady flow of a generalized second-grade fluid through a circular cylinder subject to a time dependent shear stress

The unsteady flow of a generalized second-grade fluid through an infinite straight circular cylinder is considered. The flow of the fluid is due to the longitudinal time dependent shear stress that is prescribed on the boundary of the cylinder. The fractional calculus approach in the governing equation corresponding to a second-grade fluid is introduced. The velocity field and the resulting shear stress are obtained by means of the finite Hankel and Laplace transforms. In order to avoid lengthy calculations of residues and contour integrals, the discrete inverse Laplace transform method is used. The corresponding solutions for ordinary second-grade and Newtonian fluids, performing the same motion, are obtained as limiting cases of our general solutions. Finally, the influence of the material constants and of the fractional parameter on the velocity and shear stress variations is underlined by graphical illustrations.     

Series solution for MHD channel flow of a Jeffery fluid

This paper is concerned with the magnetohydrodynamic (MHD) flow of a Jeffery fluid in a porous channel. Series solution to the nonlinear problem is constructed by a powerful analytic approach namely the homotopy analysis method (HAM). Convergence of the series solution is established. The obtained solutions are analyzed by plotting graphs.     

Experimental analysis of convergence of the numerical solution to a generalized solution in fluid dynamics

Convergence of the approximate solution of fluid dynamics problems obtained using Godunov’s scheme to the discontinuous solution is investigated.     

Analytical solution of stagnation-point flow of a viscoelastic fluid towards a stretching surface

In this paper the problem of stagnation-point flow of a viscoelastic fluid towards a stretching surface [T.R. Mahapatra, A.S. Gupta, Stagnation-point flow of a viscoelastic fluid towards a stretching surface, Int. J. Non-Linear Mech. 39 (2004) 811] is solved analytically by using the homotopy analysis method (HAM). The results for velocity and temperature profiles are obtained. It is noted that the behavior of the HAM solution for velocity and temperature profiles is in good agreement with the numerical solution given in reference [T.R. Mahapatra, A.S. Gupta, Stagnation-point flow of a viscoelastic fluid towards a stretching surface, Int. J. Non-Linear Mech. 39 (2004) 811].     

非自治阶段结构捕食系统的持续生存

研究了非自治阶段结构捕食幼年系统解的持久性，得到了该系统持续生存和全局吸引的条件。     

Asymptotic solution of a system of integro-differential equations

An asymptotic solution of a system of inegro-differential equations is constructed for the case where turning points are present. Vinnychenko Kirovograd Pedagogic Institute, Kirovograd. Translated from Ukrainskii Matematicheskii Zhurnal. Vol. 49, No. 12, pp. 1617–1623, December, 1997     

Analytical solution of magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface

A new kind of analytic technique, namely the homotopy analysis method (HAM), is employed to give an explicit analytical solution of the steady two-dimensional stagnation-point flow of an electrically conducting power-law fluid over a stretching surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. A uniform transverse magnetic field is applied normal to the surface. An explicit analytical solution is given by recursive formulae for the first-order power-law (Newtonian) fluid when the ratio of free stream velocity and stretching velocity is not equal to unity. For second and real order power-law fluids, an analytical approach is proposed for magnetic field parameter in a quite large range. All of our analytical results agree well with numerical results. The results obtained by HAM suggest that the solution of the problem under consideration converges.     

Recursive solution to a quorum queueing system

In this paper, a single-channel bulk service queueing system is considered. Given an accumulation level r, the server stops processing new customers whenever the queue falls below r and resumes service when the queue reaches level r. We have developed a recursive numerical procedure to find the steady-state system size probabilities. We assess accuracy and efficacy of the recursive procedure by comparing it to the exact solution procedure. Effectiveness and computation time of the recursive procedure are further assessed through comparison with other approximate solution procedures on a sample of 323 experimental problems.     

Periodic solution of a higher dimensional ecological system

The main purpose of this article is to study the periodicity of a Lotka-Volterra''s competition system with feedback controls. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions. Our method is base on combining matrix''s spectral theory and inequality $|x(t)|\leq x(t_{0})+\int_{0}^{\omega }|\dot{x}(t)|{\rm d}t$. Some examples and their simulations show the feasibility of our main result.     

Transient solution of a non-empty chemical queueing system

In this paper, we illustrate that a power series technique can be used to derive explicit expressions for the transient state distribution of a queueing problem having “chemical” rules with an arbitrary number of customers present initially in the system. Based on generating function and Laplace techniques Conolly et al. (in Math Sci 22:83–91, 1997) have obtained the distributions for a non-empty chemical queue. Their solution enables us only to recover the idle probability of the system in explicit form. Here, we extend not only the model of Conolly et al. but also get a new and simple solution for this model. The derived formula for the transient state is free of Bessel function or any integral forms. The transient solution of the standard M/M/1/∞ queue with λ = μ is a special case of our result. Furthermore, the probability density function of the virtual waiting time in a chemical queue is studied. Finally, the theory is underpinned by numerical results.      

On the homotopy solution for Poiseuille flow of a fourth grade fluid

This paper develops a mathematical model with an aim to compute the analytic solution for the flow of a fourth grade fluid between two fixed porous walls. The flow is induced under the application of a constant pressure gradient. The arising nonlinear problem is treated analytically yielding a series solution by homotopy analysis method (HAM). Results of velocity and shear stresses at the walls are obtained. The impacts of several flow parameters are examined on the velocity and shear stresses.     

MHD flow of a Newtonian fluid over a stretching sheet: an approximate solution

An approximate solution to the problem of steady laminar flow of a viscous incompressible electrically conducting fluid over a stretching sheet is presented. The approach is based on the idea of stretching the variables of the flow problem and then using least squares method to minimize the residual of a differential equation. The effects of the magnetic field on the flow characteristics are demonstrated through numerical computations with different values of the Hartman number.     

Analytic solution for MHD flow of a third order fluid in a porous channel

The present study investigates the channel flow of a third order fluid. The fluid is electrically conducting in the presence of a magnetic field applied transversely to the porous walls of a channel. Expression for velocity is developed by an analytic method, namely the homotopy analysis method (HAM). Convergence of the obtained solution is properly checked. The feature of the analytic solution as function of the physical parameters of the problem are discussed with the help of graphs. It is observed that unlike the flow of second grade fluid, the obtained solution for a third order fluid is non-similar. Also, the behavior of Hartmann number on the velocity is different to that of the Reynold's number.