Buoyant plumes due to mass diffusion

This paper presents the results of a numerical study of laminar axisymmetric plumes that emanate from a point source of mass diffusion. Various flow configurations that arise in mass diffusion plumes are identified. In the ambient, the cases of constant concentration and stable density stratification are considered. The governing conservation equations of mass, momentum, and species diffusion are cast in finite-difference form using an explicit scheme. Boundary layer and Boussinesq approximations are incorporated. Upwind-differencing is employed for convective terms. Velocity and concentration fields are obtained for various values of Schmidt number, and concentration stratification levels in the ambient. The results are explained in terms of the basic physical mechanisms that govern these flows. The complex interactions between the buoyancy and the Schmidt number, and the stratification parameter are discussed.     

Soret and Dufour effects on heat and mass transfer by mixed convection over a vertical surface saturated porous medium with temperature dependent viscosity

The diffusion‐thermo and thermal‐diffusion effects on heat and mass transfer by mixed convection boundary layer flow over a vertical isothermal permeable surface embedded in a porous medium were studied numerically in the presence of chemical reaction with temperature‐dependent viscosity. The governing nonlinear partial differential equations are transformed into a set of coupled ordinary differential equations, which are solved numerically by using Runge–Kutta method with shooting technique. Numerical results are obtained for the velocity, temperature and concentration distributions, and the local skin friction coefficient, local Nusselt number and local Sherwood number for several values of the parameters, namely, the variable viscosity parameter, suction/injection parameter, Darcy number, chemical reaction parameter, and Dufour and Soret numbers. The obtained results are presented graphically and in tabulated form, and the physical aspects of the problem are discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

High-temperature discrete dislocation plasticity

A framework for solving problems of dislocation-mediated plasticity coupled with point-defect diffusion is presented. The dislocations are modeled as line singularities embedded in a linear elastic medium while the point defects are represented by a concentration field as in continuum diffusion theory. Plastic flow arises due to the collective motion of a large number of dislocations. Both conservative (glide) and nonconservative (diffusion-mediated climb) motions are accounted for. Time scale separation is contingent upon the existence of quasi-equilibrium dislocation configurations. A variational principle is used to derive the coupled governing equations for point-defect diffusion and dislocation climb. Superposition is used to obtain the mechanical fields in terms of the infinite-medium discrete dislocation fields and an image field that enforces the boundary conditions while the point-defect concentration is obtained by solving the stress-dependent diffusion equations on the same finite-element grid. Core-level boundary conditions for the concentration field are avoided by invoking an approximate, yet robust kinetic law. Aspects of the formulation are general but its implementation in a simple plane strain model enables the modeling of high-temperature phenomena such as creep, recovery and relaxation in crystalline materials. With emphasis laid on lattice vacancies, the creep response of planar single crystals in simple tension emerges as a natural outcome in the simulations. A large number of boundary-value problem solutions are obtained which depict transitions from diffusional to power-law creep, in keeping with long-standing phenomenological theories of creep. In addition, some unique experimental aspects of creep in small scale specimens are also reproduced in the simulations.     

Diffusiophoresis of an aerosol particle in a binary gas mixture

The diffusion force and rate are calculated for the diffusiophoresis of a spherical particle in a binary gas mixture by solving the gas–kinetic equations. Two schemes of diffusiophoresis are considered: constant–pressure diffusion and diffusion of one mixture component through the other fixed component. The problem is solved by the integral–momentum method at arbitrary Knudsen numbers. Diffuse scattering of the gas molecules on the particle surface is assumed. The Lorentzian and Rayleigh models of a binary gas mixture are considered. The dependences of the force and rate of diffusiophoresis on the Knudsen number and the other determining parameters are analyzed. The results obtained are compared with well–known experimental data.     

Separation of species of a binary fluid mixture confined between two concentric rotating circular cylinders in presence of a strong radial magnetic field

The effect of a radial magnetic field on separation of a binary mixture of incompressible viscous thermally and electrically conducting fluids confined between two concentric rotating circular cylinders with different angular velocity is examined. The equations governing the motion, temperature and concentration in cylindrical polar coordinate are solved analytically. The solution obtained in closed form for concentration distribution is plotted against the radial distances from the surface of the inner circular cylinder for various values of non-dimensional parameters. It is found that the non-dimensional parameters viz. the Hartmann number, thermal diffusion number, baro diffusion number, rotational Reynolds number, the product of Prandtl number and Eckert number, magnetic Prandtl number and the ratio of the angular velocities of inner and outer cylinders affects the species separation of rarer and lighter component significantly. The problem discussed here derives its application in the basic fluid dynamics separation processes to separate the rarer component of the different isotopes of heavier molecules where electromagnetic method of separation does not work.     

SIMULATION OF THE FLOW OVER ELLIPTIC AIRFOILS OSCILLATING AT LARGE ANGLES OF ATTACK

The incompressible, viscous flow over two-dimensional elliptic airfoils oscillating in pitch at large angles of attack, such that flow separation occurs, has been simulated numerically for a Reynolds number of 3000. A vortex method is used to solve the two-dimensional Navier–Stokes equations in vorticity/stream-function form using a time-marching approach. Using an operator-splitting method the convection and diffusion equations are solved sequentially at each time step. The convection equation is solved using a vortex-in-cell method, and the diffusion equation using a second-order ADI finite-difference scheme. Elliptic profiles are obtained by mapping a circle in a computational domain into the physical domain using a Joukowski transformation. The effects of several parameters on the flow field are considered, such as: frequency of oscillation, mean angle of attack, location of pitch-axis and the thickness ratio of the ellipse. The results obtained are shown to compare favourably with available experimental results.     

Effects of chemical reaction on mixed convection flow of a polar fluid through a porous medium in the presence of internal heat generation

This paper reports a detailed numerical investigation on mixed convection flow of a polar fluid through a porous medium due to the combined effects of thermal and mass diffusion. The energy equation accounts for heat generation or absorption, while the nth order homogeneous chemical reaction between the fluid and the diffusing species is included in the mass diffusion equation. The governing equations of the linear momentum, angular momentum, energy and concentration are obtained in a non-similar form by introducing a suitable group of transformations. The final set of non-similar coupled non-linear partial differential equations is solved using an implicit finite-difference scheme in combination with quasi-linearization technique. The effects of various parameters on the velocity, angular velocity, temperature and concentration fields are investigated. Numerical results for the skin friction coefficient, wall stress of angular velocity, Nusselt number and Sherwood number are also presented.     

The theoretical study of the efficiency of diffusion deposition of nanoaerosols in the extended range of the Peclet numbers

The efficiencies of the diffusion deposition of nanoaerosols for a single fiber for the models of aerosol filter and wire mesh screen are studied numerically in the extended range of the Peclet number Pe. The rectangular periodic cell model for fluid flow and convective-diffusive transport of small aerosol particles is used. Most of the previous theoretical and experimental studies of single fiber diffusion deposition efficiency were for the case of Pe > 1. The array with uniform square or chess grid of fibers and of a row of circular cylindrical fibers are considered as the filter and wire mesh screen models. The flow and particles transport equations are solved numerically using the Boundary Element Method.The obtained numerical data are used to derive the approximate formulas for the deposition efficiency in the entire range of the Peclet number for the various porosities of the filter medium or distances between fibers in a wire mesh screen. The derived dependencies take into account nonlinearity of the deposition efficiency at the low Peclet numbers. The obtained analytical dependencies compare well with the numerical and experimental data.     

Uniqueness and stability of steady states of continuous chemical reactors

We examine the uniqueness and stability of the solutions to the problem of steady-state operation of a continuous chemical reactor in which longitudinal diffusion and heat conduction are taken into account. We investigate an adiabatic reactor in which the concentration and temperature distributions are similar (the thermal diffusivity and diffusion coeffecient are equal) and an isothermic reactor. These two cases are considered together because the mathematical formulations of the problem are equivalent.The question of the existence and number of steady states was analyzed in [1, 2], where references were made to earlier investigations. The results obtained in [1, 2] are now extended. The stability of the steady states is investigated by the small-perturbation method.     

Mass transfer of aerosols with axial diffusion in narrow rectangular channels

The problem of mass transfer of aerosols with axial, as well as radial, diffusion in laminar flow in a narrow rectangular channel is studied. Two cases are investigated. The first case is where all particles enter the channel inlet and none form within the channel; and the second, where no particles enter the channel, and “formation in flight” occurs within the channel. For each case, analyses are made for both slug and Poiseuille flows. The first twenty modes of the eigenvalues, the eigenfunctions, and the coefficients of series expansion are obtained for several diffusion Péclet numbers, Pe. The first twelve of them are presented for Pe=1, 5, 10, 100, and ∞. Asymptotic expressions for the eigenvalues and the eigenfunctions are also given. The effects of axial diffusion on the local particle concentration, the bulk concentration, the Sherwood number, and the fraction of aerosols arriving at any cross-section of the channel are studied for various diffusion Péclet numbers. It was found that, for diffusion with or without formation in flight, the effect of axial diffusion may be neglected at an axial distance from the channel inlet greater than one and a half times that of the channel height for 1<Pe<100.     

Transport coefficients of a dissociating gas

The calculation of the transport coefficients of a dissociating gas involves fundamental difficulties which arise when the internal degrees of freedom of the molecules are taken strictly into account. In practical calculations extensive use is made of the approximation proposed in [1], in the context of which the dependence of the diffusion velocity of the molecule on its internal state is totally neglected. In this case the expressions for the stress tensor and the diffusion velocities coincide with the corresponding expressions for a mixture of structureless particles; in the expression for the heat flux the diffusion transport of internal energy is taken only approximately into account. Here, analytic expressions for the diffusion velocities, heat flux and stress tensor are obtained without introducing simplifying assumptions. The calculation method is based on the results of [2], in which an approximate method of calculating the transport coefficients of a multicomponent mixture of structureless particles was proposed, and [3], in which the transport coefficients of a rotationally excited gas were calculated. The relations obtained are analyzed and compared with the existing results; their accuracy is estimated. A closed system of equations of gas dynamics is presented for a number of cases of practical importance.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 158–165, January–February, 1987.     

Diffusion of superintense pulsed magnetic fields

The phenomena accompanying the diffusion of superintense pulsed magnetic fields in metals are studied. Solutions are obtained for the diffusion of a constant superintense magnetic field into a half-space with a plane boundary and for the diffusion of an axial concentrated magnetic field. The limiting magnetic fields which can be obtained in various experimental devices are found. The results are compared with experiment.     

Motion of a flat piston in a gas at high Reynolds numbers taking account of chemical reactions

One-dimensional flows originating during motion of a heat-conducting piston in a gas at high values of the Reynolds number are studied. The influence of diffusion and chemical reactions is considered in the case of a binary gas mixture. A binomial external expansion taking account of the boundary-layer-displacement thickness formed ahead of the piston is found. A solution is obtained which describes the boundary layer, which includes accommodation effects. An analogous problem about plane shock reflection from a heat-conducting wall has been considered in [1–3], but without taking account of diffusion and chemical reactions. Accomodation effects were taken into account in later work, which improved the agreement between theoretical and experimental results for short times.     

Differential Diffusion Modelling in LES with RCCE-Reduced Chemistry

The present work shows results obtained from the incorporation of a soot model into a combined Large Eddy Simulation and Conditional Moment Closure approach to modelling turbulent non-premixed flames. Soot formation is determined via the solution of two transport equations for soot mass fraction and particle number density, where acetylene is employed as the incipient species responsible for soot nucleation. The concentrations of the gaseous species are calculated using a Rate-Controlled Constrain Equilibrium approach to reduce the number of species to solve from a detailed gas-phase kinetic scheme involving 63 species. The study focuses on the influence of differential diffusion of soot particles on soot volume fraction predictions. The results of calculations are compared with experimental data for atmospheric methane flames, Overall, the study demonstrates that the model, when used in conjunction with a representation of differential diffusion effects, is capable of predicting soot formation at a fundamental level in the turbulent non- premixed flames considered.     

Effects of Chemical Reaction,Heat, and Mass Transfer on Non-Newtonian Fluid Flow Through Porous Medium in a Vertical Peristaltic Tube

The effect of mass diffusion of chemical species with first-order reaction on peristaltic motion of an incompressible Jeffrey fluid has been investigated. The fluid flows through vertical porous media in the gap between concentric tubes with heat and mass transfer. The inner tube is uniform, while the outer one is a non-uniform tube has a sinusoidal wave traveling down its wall. A perturbation solution, under long-wavelength assumption, is obtained which satisfies the momentum, energy, and concentration equations for the case of small porosity parameter. Numerical results for the behaviors of pressure rise and frictional force per wavelength as well as for the skin friction, Nusselt number, and Sherwood number with other physical parameters are obtained. Several graphs for these results of physical interest are displayed and discussed in detail.     

Two problems of convective diffusion to the surfaces of poorly streamlined bodies

Problems of diffusion to particles of nonspherical shape at large Peclet numbers have been analyzed in many papers (see [1–7], for example). The solution of the problem of mass exchange of an ellipsoidal bubble at low Reynolds numbers was obtained in [1] while the solution at high Reynolds numbers was obtained in [2, 3]. In [4] an expression is given for the diffusional flux to the surface of a solid ellipsoidal particle over which a uniform Stokes stream flows. Generalization to the case of particles of arbitrary shape was done in [5, 6], while generalization to any number of critical lines on the surface of the body was done in [7, 8]. The two-dimensional problem of steady convective diffusion to the surface of a body of arbitrary shape is analyzed in the approximation of a diffusional boundary layer (ADBL). The simple analytical expressions obtained are more suitable for practical calculations than those in [5-8], since they allow one to determine at once, in the same coordinate system in which the field of flow over the particle was analyzed, the value of the diffusional flux to its surface (from the corresponding hydrodynamic characteristics). The plane problem of the diffusion to an elliptical cylinder in a uniform Stokes stream is solved. The problems of the diffusion to a plate of finite dimensions (in the plane case) and a disk (in the axisymmetric case) whose planes are normal to the direction of the incident stream are considered. It is shown that, in contrast to the results known earlier (see [4, 6-15], for example), where the total diffusional flux was proportional to the cube root of the Peclet number, here it is proportional to the one-fourth power.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 104–109, November–December, 1978.The authors thank Yu. P. Gupalo, Yu. S. Ryazantsev, and Yu. A. Sergeev for a useful discussion.     

Asymptotic solution of the equations of a laminar multicomponent boundary layer with intensive suction

An asymptotic solution is obtained for the equations of the laminar multicomponent boundary layer encountered in the plane-parallel and axially symmetrical flow of a gas with large values of the suction parameter. It is shown that the roots of the characteristic equation to which the solution of the diffusion equations reduce in the first approximation may be found in the form of radicals when the external gas flow contains chemical components capable of being combined into r5 groups as regards their diffusion properties. The number of components in the groups and the number of components in the boundary layer may be arbitrary. Asymptotic equations are obtained for the coefficient of friction, the temperature and concentration gradients, and the diffusion flows of the components on the surface of the body. By way of example, formulas are given for the thermal flux passing to a body during the flow of dissociated air or a dissociated mixture of N₂ and CO₂. A numerical solution is given for the equations of the boundary layer in the case of the flow of dissociated air. The asymptotic solution is compared with the numerical result, and the range of applicability of the asymptotic equations is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 66–74, November–December, 1970.The author wishes to thank G. A. Tirskii for discussion of this analysis.     

Efficient Approach to Description of Heat Transfer and Multicomponent Diffusion in Ionized Gases

The formulas for the heat fluxes of heavy components and electrons as well as the Stefan–Maxwell relations for the diffusion fluxes in amagnetic field are derived for amulticomponent two-temperature plasma with regard to the higher-order approximations in orthogonal expansions of the component distribution functions in Sonine polynomials. For the complex transport coefficients of heavy components and electrons exact formulas are obtained in the significantly simpler form as compared with the standard procedure of the Chapman–Enskog method with the minimum number of minimum-order matrix inversions.     

Transient mixed convection flow arising due to thermal and mass diffusion over porous sensor surface inside squeezing horizontal channel

The double diffusion effect on the mixed convection flow over a horizontal porous sensor surface placed inside a horizontal channel is analyzed.With the appropriate transformations,the unsteady equations governing the flow are reduced to non-similar boundary layer equations which are solved numerically for the time-dependent mixed convection parameter.The asymptotic solutions are obtained for small and large values of the time-dependent mixed convection parameter.The results are discussed in terms of the skin friction,the heat transfer coefficient,the mass transfer coefficient,and the velocity,temperature,and concentration profiles for different values of the Prandtl number,the Schmidt number,the squeezing index,and the mixed convection parameter.     

三维对流扩散方程的高精度全隐式多重网格方法

提出了数值求解三维非定常变系数对流扩散方程的一种高精度全隐紧致差分格式,该格式在空间上具有四阶精度,时间具有二阶精度。为了克服传统迭代法在每一个时间步上迭代求解隐格式时收敛速度慢的缺点,采用多重网格加速技术,建立了适用于本文高精度全隐紧致格式的多重网格算法,从而大大加快了迭代收敛速度。数值实验结果验证了本文方法的精确性、稳定性和对高网格雷诺数问题的强适应性。