Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet

Present model is devoted for the stagnation point flow of nanofluid with magneto-hydrodynamics (MHD) and thermal radiation effects passed over a stretching sheet. Moreover, we have considered the combined effects of velocity and thermal slip. Condition of zero normal flux of nanoparticles at the wall for the stretched flow phenomena is yet to be explored in the literature. Convinced partial differential equations of the model are transformed into the system of coupled nonlinear differential equations and then solved numerically. Graphical results are plotted for velocity, temperature and nanoparticle concentration for various values of emerging parameters. Variation of stream lines, skin friction coefficient, local Nusselt and Sherwood number are displayed along with the effective parameters. Final conclusion has been drawn on the basis of both numerical and graphs results.     

滑移流区内微环缝槽道中的层流流动与换热

本文针对微环缝槽道采用速度滑移和温度跳跃边界条件求解了不可压缩气体的Ｎ－Ｓ方程和能量方程,理论分析了微环缝槽道在单侧或双侧不同热流密度加热条件下的流动与层流换热特性,讨论了Ｋｎ数、内外径比对流动阻力及换热特性的影响。结果表明：滑移流区微环继通道内的流阻和Ｎｕｓｓｅｌｔ数明显低于连续流区;且随着Ｋｎ数的增加,流阻和Ｎｕｓｓｅｌｔ数均减小;但其随内外径比ｒ＊的变化趋势与连续流区相似。     

Binary scattering and breakup in the three-nucleon system

We present the further development of the three-particle formalism for differential Faddeev equations. The asymptotic boundary conditions in the hyperspherical adiabatic representation have been constructed. We prove that these conditions are asymptotically equivalent to the standard Merkuriev boundary conditions. With these boundary conditions we have formulated the boundary-value problem for Faddeev equations which has the property that the binary channel and the breakup channel are explicitly orthogonal. The effective numerical scheme for solving the formulated boundary-value problem is given.     

Heat transfer for boundary layers with cross flow

An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equations are transformed into a set of three self-similar ordinary differential equations by similarity transformations. These equations are solved numerically using the very efficient shooting method. This study reveals that the dual solutions of the transformed similarity equations for velocity and temperature distributions exist for certain values of the moving parameter, Prandtl number, and Eckert numbers. The reverse heat flux is observed for larger Eckert numbers; that is, heat absorption at the wall occurs.     

The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation

We consider the flow of a gas in a channel whose walls are kept at fixed (different) temperatures. There is a constant external force parallel to the boundaries which may themselves also be moving. The system is described by the stationary Boltzmann equation to which are added Maxwellian boundary conditions with unit accommodation coefficient. We prove that when the temperature gap, the relative velocity of the planes, and the force are all sufficiently small, there is a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of the corresponding compressible Navier-Stokes equations with no-slip voundary conditions. Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder.     

一种求解可压缩Navier-Stokes方程的隐式迭代时间推进方法

针对有壁面边界的可压缩流动问题,提出与基于非等距网格的高精度紧致型差分格式相结合的简化隐式迭代时间推进法,建立求解可压缩Navier-Stokes方程的直接数值模拟方法,提高了计算效率.应用该方法,直接数值模拟两种有壁面边界的二维可压缩流动问题,即可压缩平板边界层流动和可压缩槽道流动.     

激光通道传输热特性对远场光束质量的影响

 通过仿真计算分析了激光在光束控制系统通道内传输所产生的热效应及其对远场光束质量的影响。激光传播由近轴波方程描述，用快速傅里叶变换技术求解；激光热效应引起的流场密度变化采用完全Navier-Stokes方程计算。计算给出了不同波长、不同吸收系数条件下的远场光斑情况。计算结果表明，在典型的工作条件和状态下，较高能量激光在光束控制系统通道内产生的热效应影响不容忽视，它会明显降低远场目标处的能量集中度，增大光斑的发散。     

Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium

In the present work, thermal buckling of single-layered graphene sheets lying on an elastic medium is analyzed. For this purpose, the sinusoidal shear deformation plate theory in tandem with the nonlocal continuum theory, which takes the small scale effects into account, is employed. The non-linear stability equations, which contain the reaction of Winkler–Pasternak elastic substrate medium, are derived and then solved analytically for a plate with various boundary conditions and based on various plate theories. Closed form solutions are formulated for three types of thermal loadings as uniform, linear and nonlinear temperature rise through the thickness of the plate. A number of examples are presented to illustrate the numerical results concerned with the buckling temperature response of nanoplates resting on two-parameter elastic foundations. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, nonlocal parameter, and elastic foundation parameters are all investigated.     

Numerical Simulation of MHD Peristaltic Flow with Variable Electrical Conductivity and Joule Dissipation Using Generalized Differential Quadrature Method

In this paper, the MHD peristaltic flow inside wavy walls of an asymmetric channel is investigated, where the walls of the channel are moving with peristaltic wave velocity along the channel length. During this investigation,the electrical conductivity both in Lorentz force and Joule heating is taken to be temperature dependent. Also, the long wavelength and low Reynolds number assumptions are utilized to reduce the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. The new set of obtained equations is then numerically solved using the generalized differential quadrature method(GDQM). This is the first attempt to solve the nonlinear equations arising in the peristaltic flows using this method in combination with the Newton-Raphson technique. Moreover, in order to check the accuracy of the proposed numerical method, our results are compared with the results of built-in Mathematica command NDSolve. Taking Joule heating and viscous dissipation into account, the effects of various parameters appearing in the problem are used to discuss the fluid flow characteristics and heat transfer in the electrically conducting fluids graphically. In presence of variable electrical conductivity, velocity and temperature profiles are highly decreasing in nature when the intensity of the electrical conductivity parameter is strengthened.     

红外连续激光反射镜热畸变的有限元分析

 基于热传导方程和热弹方程，利用有限元分析方法，就光斑尺寸远大于或接近于基底材料热扩散长度的情况以及反射镜在固定或自由的边界条件下，分别计算了硅和石英两种基底材料多层膜红外连续激光反射镜的最大温升、最大形变及最大热应力，并探讨了它们随光斑尺寸的变化规律。结果表明：在自由边界条件下，反射镜表面的最大轴向位移与光斑半径之间近似为线性关系；而在固定边界条件下，反射镜的最大热应力与光斑半径之间近似为线性关系；反射镜的夹持状态对最大轴向位移及最大热应力的影响随着光斑尺寸的增加而增强；在相同的入射激光光源及相同的边界条件下，硅镜具有较低的温升值或较高的抗热损伤阈值，而石英镜具有较好的抗热畸变特性。     

行波管收集极的热分析

 随着行波管的大功率小型化,收集极的温度分布和采用的散热手段对行波管的正常工作有很大影响。利用ANSYS软件对行波管收集极的散热问题进行详细的模拟计算,分析比较了不同热流加载方式对收集极温度分布的影响。采用均匀热流加载定性地比较计算了自然冷却、风冷、单层水套和双层水套等不同散热条件下收集极的热耗散功率,计算结果与经验值一致,说明了所用模型和方法的正确性。模拟分析为行波管收集极的散热方案优化设计提供有效的参考依据和手段。     

Diffusion of a chemically active colloidal particle in composite channels

Diffusion of colloidal particles in microchannels has been extensively investigated, where the channel wall is either a no-slip or a slip-passive boundary. However, in the context of active fluids, driving boundary walls are ubiquitous and are expected to have a substantial effect on the particle dynamics. By mesoscale simulations, we study the diffusion of a chemically active colloidal particle in composite channels, which are constructed by alternately arranging the no-slip and diffusio-osmotic boundary walls. In this case, the chemical reaction catalyzed by the active colloidal particle creates a local chemical gradient along the channel wall, which drives a diffusio-osmotic flow parallel to the wall. We show that the diffusio-osmotic flow can significantly change the spatial distribution and diffusion dynamics of the colloidal particle in the composite channels. By modulating the surface properties of the channel wall, we can achieve different patterns of colloidal position distribution. The findings thus propose a novel possibility to manipulate colloidal diffusion in microfluidics, and highlight the importance of driving boundary walls in dynamics of colloidal particles in microchannels.     

Simulation of Incompressible Viscous Flows by Local DFD-Immersed Boundary Method

A local domain-free discretization-immersed boundary method (DFD-IBM) is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form. Like the conventional immersed boundary method (IBM), the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object. The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points. To be specific, the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity. As compared to the conventional IBM, the present approach accurately implements the non-slip boundary condition. As a result, there is no flow penetration, which is often appeared in the conventional IBM results. The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder. The obtained numerical results agree very well with the data in the literature.     

Global Well–Posedness of the 3<Emphasis Type="Italic">D</Emphasis> Primitive Equations with Partial Vertical Turbulence Mixing Heat Diffusion

The three–dimensional incompressible viscous Boussinesq equations, under the assumption of hydrostatic balance, govern the large scale dynamics of atmospheric and oceanic motion, and are commonly called the primitive equations. To overcome the turbulence mixing a partial vertical diffusion is usually added to the temperature advection (or density stratification) equation. In this paper we prove the global regularity of strong solutions to this model in a three-dimensional infinite horizontal channel, subject to periodic boundary conditions in the horizontal directions, and with no-penetration and stress-free boundary conditions on the solid, top and bottom boundaries. Specifically, we show that short time strong solutions to the above problem exist globally in time, and that they depend continuously on the initial data.     

Heat transfer in boundary layer stagnation-point flow towards a shrinking sheet with non-uniform heat flux

In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types: direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations (PDEs) are transformed into non linear self-similar ordinary differential equations (ODEs) by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.     

三维隔板方腔中流体流动的数值计算

本文对隔板方腔,应用堵塞系数技术和有限容积方法,数值求解完整的Navier-Stokes(N-S)方程。采用压力—速度修正算法(SIMPLE-C,Semi-Implic it Method for Pressure Linked Equation-Consistent)直接计算全部物理变量。应用堵塞系数技术模拟三维粘性流动,研究该方法的适用件,可行性与效率。 初步的结果表明,对于计算复杂边界域内的速度、压力和其它流动物理量,堵塞系数技术确实是一种简单方便的数值技术,它具有令人鼓舞的应用前景。     

Three-dimensional flow of Powell–Eyring nanofluid with heat and mass flux boundary conditions

This article investigates the three-dimensional flow of Powell–Eyring nanofluid with thermophoresis and Brownian motion effects. The energy equation is considered in the presence of thermal radiation. The heat and mass flux conditions are taken into account. Mathematical formulation is carried out through the boundary layer approach. The governing partial differential equations are transformed into the nonlinear ordinary differential equations through suitable variables. The resulting nonlinear ordinary differential equations have been solved for the series solutions. Effects of emerging physical parameters on the temperature and nanoparticles concentration are plotted and discussed. Numerical values of local Nusselt and Sherwood numbers are computed and examined.     

Analytic supernova models and black holes

Presented are new analytic solutions to Einstein's field equations with properties normally associated with supernovas. These are the first analytic supernova models with pressure, temperature, and luminosity. These solutions are used to compare a radiative nonzero model (for which the pressure is continuous accross the outer boundary of the star) with a radiative zero model [(standard model) for which the pressure within the star is zero at the outer boundary].