趋旋性微生物在幂律流体饱和水平多孔层中的热-生物对流稳定性分析

基于趋旋性微生物和幂律流体模型,研究了在含有非Newton流体饱和多孔介质中生物对流的线性稳定性问题.利用Galerkin数值方法求解了该系统的控制方程,得到生物Rayleigh数的数值解,讨论了非Newton流体的幂律指数对生物对流稳定性在假塑性流体和膨胀性流体间的变化规律.研究结果表明,随着幂律流体的速度增大,幂律指数对生物对流稳定性的影响会发生变化,并且这种变化会受到热Rayleigh数和生物Lewis数的影响.另外,微生物趋旋性特征越明显,生物对流系统就越不稳定,而适当增大非Newton流体的幂律指数则有利于系统的稳定性.     

一类具衰减位势的Schrdinger-Poisson方程变号基态解的存在性

本文研究一类具有衰减位势的Schrdinger-Poisson方程变号基态解的存在性,应用Nehari流形和变分方法,我们得到了该类方程存在一个变号基态解.进一步,如果该问题具有对称性时,我们证明了无穷多个非平凡解的存在性.在本文的结论中非线性项只要求是连续的.     

退化Sobolev-Galpern 方程有界解的保持性

在这篇文章中, 我们考虑了一类退化Sobolev-Galpern 方程有界解的保持性. 我们先研究了线性Sobolev-Galpern 方程的解的存在性、唯一性, 并由其解定义出了一簇发展算子. 在此基础上, 我们研究了发展算子的指数二分性、非齐次线性方程有界解的Fredholm 更替. 最后, 我们将此结果用以研究退化Sobolev-Galpern 方程在非自治扰动下有界解的保持性, 并给出了保持的条件.     

具有非Lipschitz系数的多值随机发展方程

本文在发展三元组的框架下,研究了一种具有极大单调算子和非Lipschitz系数的多值随机发展方程.在一定条件下,我们证明了这种方程的解的存在唯一性.     

退化Sobolev-Galpern方程有界解的保持性 谨以此文致《中国科学》创刊六十周年

在这篇文章中,我们考虑了一类退化Sobolev-Galpern方程有界解的保持性.我们先研究了线性Sobolev-Galpern方程的解的存在性、唯一性,并由其解定义出了一簇发展算子.在此基础上,我们研究了发展算子的指数二分性、非齐次线性方程有界解的Fredholm更替.最后,我们将此结果用以研究退化Sobolev-Galpern方程在非自治扰动下有界解的保持性,并给出了保持的条件.     

非齐次光纤介质中孤子解和奇异波的特性研究

以非齐次光纤介质中的非线性薛定谔方程为研究对象,采用相似变换将变系数非线性薛定谔方程转化为标准非线性薛定谔方程,然后利用待定系数法求出方程的孤子解和奇异波解.基于该解表达式,选取不同类型函数和相应参数进行数值模拟,分析其动力学特性,所得结果对研究孤子在非齐次光纤介质中的传播具有重要意义.     

一类一阶中立型泛函微分方程的三个非负周期解的存在性

本文研究了一类一阶中立型泛函微分方程周期解的存在性问题.采用合适的算子并应用Leggett-Williams不动点定理,获得了该方程具有三个非负ω-周期解的充分条件     

具非自治微小扰动的脉冲方程三个古典解的存在性

在半直线无穷区间上,我们研究具有微小非自治扰动项的脉冲方程边值问题的古典解,应用变分方法和相应的临界点理论得到了三个古典解的存在性.     

具变系数时滞微分方程解的振动性

研究了时滞微分方程解的振动性，其中P（t）、τ（t）非负连续．我们证明了：如果对充分大的，且，则方程（*）每一解振动．该结论改进和推广了许多已知结果．     

正倒向随机微分方程的适应解及其比较定理(英文)

研究了一类正倒向随机微分方程的适应解 ,其中正向方程不需要满足非退化条件 .我们证明了在某些单调条件下 ,正倒向随机微分方程存在唯一的适应解 ,并给出了该正倒向随机微分方程的比较定理 .     

A finite element method for heat transfer of power‐law flow in channels with a transverse magnetic field

Heat transfer of a power‐law non‐Newtonian incompressible fluid in channels with porous walls has not been carefully studied using a proper numerical method despite a few constructions of approximate analytic solutions through the similarity transformation and perturbation method for Newtonian fluids (i.e. power‐law index being one). In this paper, we propose a finite element method for the thermal incompressible flow equations. The incompressible condition is treated by a penalty formulation. Numerical solutions are validated by comparing them with an approximate analytic solution of the Navier–Stokes equation in the Newtonian fluid case. Then, the method is used to simulate the heat transfer of various power‐law fluids. Additionally, unlike previous studies, we allow the thermal diffusivity to be a function of temperature gradient. The effect of different values of the parameters on the temperature and velocity is also discussed in this paper. Copyright © 2013 John Wiley & Sons, Ltd.     

非牛顿流体内流传热研究

在本文中,研究了注入轴对称模腔非牛顿流体非定常流动.本文的第二部份研究了上随体Maxwell流体管内热流动.对于注入模腔流动.其本构方程采用幂律流体模型方程.为了避免在表现粘度中温度关系引起的非线性.引进了一特征粘度的概念.描述本力学过程的基本方程是,本构方程、定常状态的运动方程、非定常能量方程及连续方程.该方程组在空间是二维问题,在数学上是三维问题.采用分裂差分格式求得本方程组的数值解答.分裂法曾成功应用于求解牛顿流体问题.在本文中,首次将分裂法成功地应用解决非牛顿流体流动问题.对于圆管内热流,给出了差分格式,使基本方程组化为一个三对角方程组.其结果,给出了不同时刻的模腔内二维温度分布.     

Analytic solution for MHD Transient rotating flow of a second grade fluid in a porous space

This article looks into the unsteady rotating magnetohydrodynamic (MHD) flow of an incompressible second grade fluid in a porous half space. The flow is induced by a suddenly moved plate in its own plane. Both the fluid and plate rotate in unison with the same angular velocity. Analytic solution of the governing flow problem is obtained by using Fourier sine transform. Based on the modified Darcy's law, expression for velocity is obtained. The influence of pertinent parameters on the flow is delineated and appropriate conclusions are drawn. Several existing solutions of Newtonian fluid have been also deduced as limiting cases.     

Simultaneously developing flow and heat transfer of non-Newtonian fluids in equilateral triangular duct

A numerical investigation based on the Galerkin finite element method was carried out to solve the full three-dimensional governing equations for simultaneously developing steady laminar flow and heat transfer to a purely viscous non-Newtonian fluid described by a power law model flowing in equilateral triangular ducts. Two commonly used thermal boundary conditions, constant wall temperature (T boundary condition) and constant wall heat flux both axially and peripherally (H2 boundary condition) were examined. It is shown that the Nusselt number distribution along the walls is affected appreciably by the variation of the power law index. Results are presented and discussed for a wide range of power law indices and Prandtl numbers for T and H2 boundary conditions.     

Heat transfer and Couette flow of a chemically reacting non‐linear fluid

In this paper we study the flow and heat transfer in a chemically reacting non‐linear fluid between two long horizontal parallel flat plates that are at different temperatures. The top plate is sheared, whereas the bottom plate is fixed. The fluid is modeled as a generalized power‐law fluid whose viscosity is also assumed to be a function of the concentration. The effects of radiation are neglected. The equations are made dimensionless and the boundary value problem is solved numerically; the velocity and temperature profiles are obtained for various dimensionless numbers. Published in 2009 by John Wiley & Sons, Ltd.     

Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels

Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel–Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to be non-linear. The objective of the study has been to examine the effect of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, wall shear stress, streamline pattern and trapping. It is observed that the numerical estimates for the aforesaid quantities in the case of peristaltic transport of blood in a channel are much different from those for flow in an axisymmetric vessel of circular cross-section. The study further shows that peristaltic pumping, flow velocity and wall shear stress are significantly altered due to the non-uniformity of the cross-sectional radius of blood vessels of the micro-circulatory system. Moreover, the magnitude of the amplitude ratio and the value of the fluid index are important parameters that affect the flow behaviour. Novel features of SSD wave propagation that affect the flow behaviour of blood have also been discussed.     

The study of Heat and Mass Transfer in a Visco elastic fluid due to a continuous stretching surface using Homotopy Analysis Method

In this paper, an approximate analytical solution is derived for the flow velocity and temperature due to the laminar, two-dimensional flow of non-Newtonian incompressible visco elastic fluid due to a continuous stretching surface. The surface is stretched with a velocity proportional to the distance $x$ along the surface. The surface is assumed to have either power-law heat flux or power-law temperature distribution. The presence of source/sink and the effect of uniform suction and injection on the flow are considered for analysis. An approximate analytical solution has been obtained using Homotopy Analysis Method(HAM) for various values of visco elastic parameter, suction and injection rates. Optimal values of the convergence control parameters are computed for the flow variables. It was found that the computational time required for averaged residual error calculation is very very small compared to the computation time of exact squared residual errors. The effect of mass transfer parameter, visco elastic parameter, source/sink parameter and the power law index on flow variables such as velocity, temperature profiles, shear stress, heat and mass transfer rates are discussed.     

非牛顿流体偏心环空螺旋流的解析解

石油和化工中许多问题需要求解非牛顿流体偏心环空螺旋流。本文全面地研究了幂律流体和宾汉流体在偏心环空中层流螺旋流的流动规律与流动状态的判别。在理论上,根据流体力学原理,运用数学方法,在作者同心环空螺旋流的理论基础上,通过对偏心环空螺旋流流场的无限细分法,给出了该流场的视粘度分布、速度分布、流量和压降方程,进而建立了判别流态的稳定性参数。     

On accelerated flows of an Oldroyd-B fluid in a porous medium

In this work, the problems dealing with unsteady unidirectional flows of an Oldroyd-B fluid in a porous medium are investigated. By using modified Darcy's law of an Oldroyd-B fluid, the equations governing the flow are modelled. Employing Fourier sine transform, the analytic solutions of the modelled equations are developed for the following two problems: (i) constant accelerated flow, (ii) variable accelerated flow. Explicit expressions for the velocity field and adequate tangential stress are obtained in each case. The solutions for Newtonian, second grade and Maxwell fluids in a porous medium appear as the limiting cases of the present analysis.     

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.