Effect of thermophoretic particle deposition in non-Newtonian free convection flow over a vertical plate with magnetic field effect

The present contribution deals with the effects of thermophoretic particle deposition on the free convective flow over a vertical flat plate embedded in a non-Newtonian fluid-saturated porous medium in the presence of a magnetic field. The governing partial differential equations are transformed into ordinary differential equations by using special transformations. The resulting similarity equations are solved numerically by an efficient implicit finite-difference method. For various values of the problem parameters, graphs of the profile concentration in the boundary layer and of thermophoretic deposition velocity are presented.     

Thermophoresis in laminar flow over cold inclined plates with variable properties

This paper deals with the analysis of two dimensional laminar thermophoretic flow over inclined plates. Cold wall conditions are assumed and the governing equations are solved by a finite difference marching technique. Results for the hydrodynamic, thermal and particle concentration boundary layers are obtained over a wide range of parameters. Special emphasis is placed on the external aerosol particle deposition process.     

Conduction-radiation effect on transient natural convection with thermophoresis

This paper discusses the effect of thermophoretic particle deposition on the transient natural convection laminar flow along a vertical flat surface,which is immersed in an optically dense gray fluid in the presence of thermal radiation.In the analysis,the radiative heat flux term is expressed by adopting the Rosseland diffusion approximation.The governing equations are reduced to a set of parabolic partial differential equations.Then,these equations are solved numerically with a finite-difference scheme in the entire time regime.The asymptotic solutions are also obtained for sufficiently small and large time.The obtained asymptotic solutions are then compared with the numerical solutions,and they are found in excellent agreement.Moreover,the effects of different physical parameters,i.e.,the thermal radiation parameter,the surface temperature parameter,and the thermophoretic parameter,on the transient surface shear stress,the rate of surface heat transfer,and the rate of species concentration,as well as the transient velocity,temperature,and concentration profiles are shown graphically for a fluid(i.e.,air) with the Prandtl number of 0.7 at 20 C and 1.013 × 10 5 Pa.     

Effects of thermophoresis particle deposition and of the thermal conductivity in a porous plate with dissipative heat and mass transfer

Network simulation method(NSM) is used to solve the laminar heat and mass transfer of an electricallyconducting,heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule heating problem. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations,in a single independent variable,η. The resulting coupled,nonlinear equations are solved under appropriate transformed boundary conditions. Computations are performed for a wide range of the governing flow parameters,viz Prandtl number,thermophoretic coeffcient(a function of Knudsen number),thermal conductivity parameter,wall transpiration parameter and Schmidt number. The numerical details are discussed with relevant applications. The present problem finds applications in optical fiber fabrication,aerosol filter precipitators,particle deposition on hydronautical blades,semiconductor wafer design,thermo-electronics and problems including nuclear reactor safety.     

Quadratic convective flow of radiated nano-Jeffrey liquid subject to multiple convective conditions and Cattaneo-Christov double diffusion

A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic (MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg (RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.     

Thermophoretic augmentation of particle deposition in natural convection flow through a parallel plate channel

Present paper deals with temperature driven mass deposition rate of particles known as thermophoretic wall flux when a hot flue gas in natural convection flow through a cooled isothermal vertical parallel plate channel. Present study finds application in particle filters used to trap soot particles from post combustion gases issuing out of small furnaces with low technical implications. Governing equations are solved using finite difference marching technique with channel inlet values as initial values. Channel heights required to regain hydrostatic pressure at the exit are estimated for various entry velocities. Effect of temperature ratio between wall and gas on thermophoretic wall flux is analysed and wall flux found to increase with decrease in temperature ratio. Results are compared with published works wherever possible and can be used to predict particle deposition rate as well as the conditions favourable for maximum particle deposition rate.     

Combined radiation and natural convection effects on graetz problem in horizontal isothermal circular tubes

A numerical analysis is performed on the combined thermal radiation and mixed convection for a gray fluid flow in a horizontal isothermally-heated circular tube. The governing equations of vorticity-velocity form are employed and solved by DuFort-Frankel method. The contribution of radiation is formulated by integral expression and solved by finite element nodal approximation. The effects of radiation and convection on local Nusselt number and the developing of bulk temperature are presented. The result shows that the heat transfer can be significantly enhanced by the effects of radiation and secondary flow induced by buoyancy. Besides, the fluctuation in local Nusselt number curve which is caused by the existence of secondary flow is reduced by the effect of thermal radiation.     

Slip effect on the magnetohydrodynamics channel flow in the presence of the across mass transfer phenomenon

This paper deals with the slip effect on the across mass transfer (AMT) phenomenon in a three-dimensional flow of a hydromagnetic viscous fluid in a channel with a stretching lower wall. Both walls of the channel are considered to be porous so that the AMT phenomenon can be established. The governing equations are solved analytically. The accuracy of the series solution is proved by comparing the results with a numerical solution. The slip condition is observed to be helpful in reducing the viscous drag on the stretching sheet.     

配置点谱方法-人工压缩法(SCM-ACM)求解同心圆筒内流体流动

发展了配置点谱方法SCM(Spectral collocation method)和人工压缩法ACM(Artificial compressibility method)相结合的SCM-ACM数值方法,计算了柱坐标系下稳态不可压缩流动N-S方程组。选取典型的同心圆筒间旋转流动Taylor-Couette流作为测试对象,首先,采用人工压缩法获得人工压缩格式的非稳态可压缩流动控制方程;再将控制方程中的空间偏微分项用配置点谱方法进行离散,得到矩阵形式的代数方程;编写了SCM-ACM求解不可压缩流动问题的程序;最后,通过与公开发表的Taylor-Couette流的计算结果对比,验证了求解程序的有效性。结果证明,本文发展的SCM-ACM数值方法能够用于求解圆筒内不可压缩流体流动问题,该方法既保留了谱方法指数收敛的特性,也具有ACM形式简单和易于实施的特点。本文发展的SCM-ACM数值方法为求解柱坐标下不可压缩流体流动问题提供了一种新的选择。     

A perturbation solution for non-linear vibration of uniformly curved pipes conveying fluid

The first-order non-linear interactions between the pipe structure and the flowing fluid are considered to formulate the governing equations of motion for the in-plane vibration of a circular-arc pipe containing flowing fluid. The forces and moments induced in a pipe element by the flowing fluid are analyzed as functions of the instantaneous local curvature of the pipe. The flow field is assumed to be one-dimensional, incompressible and of uniform flow, and to remain independent of pipe motion. For a fixed-end circular-arc pipe with arbitrary arc angle, the non-linear governing equations are solved by the method of multiple scales in conjunction with the Bubnov-Galerkin method. The non-linear solutions indicate that the vibrational behavior of the system can differ substantially from that predicted by a linear analysis.     

Conduction-radiation effect on natural convection flow in fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls

The combined effect of conduction-convection-radiation on natural convection flow of an optically thick Newtonian fluid with gray radiant properties, confined in a porous media square cavity with Darcy-Brinkman-Forchheimer drag is studied numerically. For a gray fluid, Rosseland diffusion approximation is considered. It is assumed that (i) the temperature of the left vertical wall varies linearly with height, (ii) the right vertical and top walls are at a lower temperature, and (iii) the bottom wall is uniformly-heated. The governing equations are solved using the alternate direct implicit method together with the successive over relaxation technique. The investigation of the effect of governing parameters, namely, the Forschheimer resistance (Γ), the temperature difference (Δ), and the Plank number (Rd), on the flow pattern and heat transfer characteristics is carried out. It can be seen that the reduction of flow and heat transfer occur as the Forschheimer resistance is increased. On the other hand, both the flow strength and heat transfer increase as the temperature ratio Δ is increased.     

Numerische Berechnung des Partikeltransportes zu einer laminar angeströmten Kreisscheibe

Increasingly process steps become important, in which particles as product particles or contaminants are deposited on substrates out of the gas phase. In this paper the particles transport processes are investigated close to the surface of a circular plate surrounded by a laminar flow. The analogy between the governing equations of momentum, energy and mass is applied to the extended diffusion equation. In the nondimensional form the results of the numerical calculations give informations about velocity, temperature and particle concentration boundary layer thickness as well as their distributions. Especially the impact of external forces on particle concentration boundary layer thickness and profile is discussed. The transport of submicron particles to the surface due to convection, diffusion, gravity and thermophoretic forces acting independently is investigated. In the used normalized form the different forces are acting as one resulting force independently of their origin. Their resulting effect in comparison to the effect due to convective diffusive transport is important for particle deposition.     

Flow of an oldroyd fluid in a circular pipe with time dependent pressure gradient

The problem of pulsating flow superimposed on the steady laminar flow in a circular tube is investigated for the fluid characterized by the Oldroyd's constitutive equations. The governing equations are solved in an exact manner and the solution is obtained in terms of two non-dimensional fluid parameters. Several interesting illustrations are provided comparing the behaviour of Newtonian fluid and Oldroyd fluids regarding the velocity field, sectional mean velocity, surface friction and balance of force. The flow for small and large frequencies of vibration are obtained as special cases. For Oldroyd fluids also the flow is basically parabolic for small frequencies while it possesses a boundary layer character at large frequencies. The solution for second order fluids and Maxwell fluids can be obtained by appropriately choosing the two fluid parameters.     

Aiding and Opposing Mixed Convection Flow in Melting From a Vertical Flat Plate Embedded in a Porous Medium

The problem of melting from a vertical flat plate embedded in a porous medium is studied. The main focus is to determine the effect of mixed convection flow in the liquid phase on the melting phenomenon. Both aiding and opposing flows are considered. The conservation equations that govern the problem are reduced to a system of nonlinear ordinary differential equations. The governing equations are solved numerically. Numerical results are obtained for the temperature and flow fields in the melting region. The melting phenomenon decreases the local Nusselt number at the solid–liquid interface.     

进动圆筒内液体流动不稳定的非线性特征

在建立进动充液圆筒内液体偏差流动方程的基础上，结合液体惯性波和轴向二次流动线性解，通过对定常二次流动的线性稳定性分析，提出了函数空间表达的流动不稳定性非线性分岔分析方程. 对非惯性坐标系下液体流动的Navier-Stokes方程进行了数值求解，并对惯性波发生破裂(实验提供的3种主模态下得出的共振破裂现象)时的压力时间序列进行分析，得出了液体流动不稳定的基本非线性特征.     

Lie group analysis for thermophoretic and radiative augmentation of heat and mass transfer in a Brinkman-Darcy flow over a flat surface with heat generation

A boundary layer analysis is presented to investigate numerically the effects of radiation,thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a flat surface in a porous medium.The boundary layer equations are transformed to non-linear ordinary differential equations using scaling group of transformations and they are solved numerically by using the fourth order Runge-Kutta method with shooting technique for some values of physical parameters.Comparisons with previously published work are performed and the results are found to be in very good agreement.Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity,temperature and concentration profiles as well as the local skin-friction coefficient,wall heat transfer,particle deposition rate and wall thermophoretic deposition velocity.The results show that the magnetic field induces acceleration of the flow,rather than deceleration(as in classical magnetohydrodynamics(MHD) boundary layer flow) but to reduce temperature and increase concentration of particles in boundary layer.Also,there is a strong dependency of the concentration in the boundary layer on both the Schmidt number and mass transfer parameter.     

Graphite dust deposition in the HTR-10 steam generator

Graphite dust has an important effect on the safe operation of a high-temperature gas-cooled reactor (HTR). The present study analyzes temperature and flow field distributions in the HTR-10 steam generator. The temperature and flow field distributions are then used to study thermophoretic deposition and turbulent deposition. The results show that as the dust diameter increases, the thermophoretic deposition decreases, while the turbulent deposition first decreases and then increases. The thermophoretic deposition is higher at higher reactor powers, with turbulent deposition growing more rapidly at higher reactor power. For small particles, the thermophoretic deposition effect is greater than the turbulent deposition effect, while for large particles, the turbulent deposition effect is dominant.     

等离子体氯化氧化法太白反应器流场的数值模拟

本文提出了等离子体氯化氧化法钛白反应器流程的物理化学流体动力学模型,用k-ε方程描述湍流运动,用Partankar-spalaing发展的SIMPLER方法对控制方程求解,就三种情况即a)有化学反应,壁面绝热,b)有化学反应,壁面温度T_w=450k,c)无化学反应,壁面绝热,给出了反应器中的速度场,温度场和浓度分布,对钛白生产的物理化学过程作了数值模拟,所得结果可作为有关工程设计的理论依据。     

Direct numerical simulation of particle–fluid systems by combining time-driven hard-sphere model and lattice Boltzmann method

A coupled numerical method for the direct numerical simulation of particle–fluid systems is formulated and implemented, resolving an order of magnitude smaller than particle size. The particle motion is described by the time-driven hard-sphere model, while the hydrodynamic equations governing fluid flow are solved by the lattice Boltzmann method (LBM). Particle–fluid coupling is realized by an immersed boundary method (IBM), which considers the effect of boundary on surrounding fluid as a restoring force added to the governing equations of the fluid. The proposed scheme is validated in the classical flow-around-cylinder simulations, and preliminary application of this scheme to fluidization is reported, demonstrating it to be a promising computational strategy for better understanding complex behavior in particle–fluid systems.     

Thin film flow of non‐Newtonian MHD fluid on a vertically moving belt

Thin film flow of an Oldroyd 6‐constant fluid on a vertical moving belt is investigated analytically and numerically. The governing equations for the flow field are derived for a steady one‐dimensional flow. The effect of constant applied magnetic field is included and its influence on the flow field is studied. The nonlinear governing equations are solved analytically and the exact solution is obtained in an elegant way. Numerical solutions are also obtained using higher‐order Chebyshev spectral methods. The influence of various non‐Newtonian parameters, gravitational force and applied magnetic field is investigated. The results showing the effect of gravity, magnetic field and material constants α₁ and α₂ are presented. Copyright © 2010 John Wiley & Sons, Ltd.