Two half-space problems based on a synthetic-kernel model of the linearized Boltzmann equation

An analytical discrete-ordinates method is used to solve two basic half-space problems based on a new synthetic-kernel model of the linearized Boltzmann equation. In particular, Kramers’ problem and the half-space problem of thermal creep, both basic to the general area of rarefied-gas dynamics, are defined by model equations that are solved (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented to yield numerical results for the slip coefficients and the velocity and heat-flow profiles that compare well with solutions derived from much more computationally intensive techniques.     

Poiseuille and Thermal-Creep Flow in a Cylindrical Tube

A version of the discrete-ordinates method is used to solve, for the case of flow in a cylindrical tube, the classical Poiseuille and thermal-creep problems based on the Bhatnagar, Gross, and Krook model in the theory of rarefied-gas dynamics. In addition to the development of a discrete-ordinates solution that is valid for a wide range of the Knudsen number, the solution is evaluated numerically for selected cases to yield results, thought to be correct to many significant figures, for the slip velocities, the macroscopic velocity profiles, and the flow rates.     

Generalized boundary conditions for the S-model kinetic equations basic to flow in a plane channel

An analytical version of the discrete-ordinates method is used to solve the classical problems of Poiseuille flow and thermal-creep flow in a plane channel. The kinetic theory for the rarefied-gas flow is based on the S model (a generalization of the BGK model), and in addition to the use of the diffuse-specular reflection model (based on a single accommodation coefficient) for describing particle scattering from the channel walls, the Cercignani-Lampis model defined in terms of normal and tangential accommodation coefficients is implemented. The established solution is tested numerically, and results for the velocity and heat-flow profiles, the particle-flow rate and the heat-flow rate thought to be correct to many significant figures are reported for various values of the channel width.     

Liquid flows and vibration characteristics of straight-tube cylindrical shells

The influence of a moving fluid confined by a solid circular cylindrical shell on the propagation of acoustic waves generated by sources located on the circular cylindrical shell is examined. An expression for the acoustic pressure in a moving fluid is derived including azimuthal asymmetry effects in the general case, where the fluid velocity points along the cylindrical shell axis and can be written as an infinite power series expansion in the radial co-ordinate. Secondly, continuity of pressure and normal velocity at the liquid-shell interface is imposed to (a) derive a set of coupled differential equations governing the possible vibrational modes of the shell and (b) determine dispersion relations, i.e., mode propagation constants β as a function of frequency as well as changes in β values accomodated by flow. In the remaining part of the paper, phase speed changes with flow and transit-time differentials of circular cylindrical shell vibrations are discussed with special emphasis to flow measurement properties.     

Near Continuum Velocity and Temperature Coupled Compressible Boundary Layer Flow over a Flat Plate

The problem of a compressible gas flows over a flat plate with the velocity-slip and temperature-jump boundary conditions are being studied. The standard single- shooting method is applied to obtain the exact solutions for velocity and temperature profiles when the momentum and energy equations are weakly coupled. A double-shooting method is applied if these two equations are closely coupled. If the temperature affects the velocity directly, more significant velocity slip happens at locations closer to the plate’s leading edge, and inflections on the velocity profiles appear, indicating flows may become unstable. As a consequence, the temperature-jump and velocity-slip boundary conditions may trigger earlier flow transitions from a laminar to a turbulent flow state.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Velocity Profiles of Slow Blood Flow in a Narrow Tube

A fractal model is introduced into the slow blood motion. When blood flows slowly in a narrow tube, red cell aggregation results in the formation of an approximately cylindrical core of red cells. By introducing the fractal model and using the power law relation between area fraction φ and distance from tube axis ρ, rigorous velocity profiles of the fluid ia and outside the aggregated core and of the core itself are obtained analytically for different fractal dimensions. It shows a blunted velocity distribution for a relatively large fractal dimension (D～2), which can be observed in normal blood; a pathological velocity profile for moderate dimension (D = 1), which is similar to the Segre-Silberberg effect; and a parabolic profile for negligible red cell concentration (D = 0), which likes in the Poiseuille flow.     

Physiological Flow of Jeffrey Six Constant Fluid Model due to Ciliary Motion

The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ciliated tips in the presence of heat and mass transfer. The effects of viscous dissipation are also considered. The flow equations of non-Newtonian fluid for the two-dimensional tube in cylindrical coordinates are simplified using the low Reynolds number and long wave-length approximations. The main equations for Jeffrey six constant fluid are considered in cylindrical coordinates system. The resulting nonlinear problem is solved using the regular perturbation technique in terms of a variant of small dimensionless parameter α. The results of the solutions for velocity, temperature and concentration field are presented graphically. B_k is Brinkman number, ST is soret number, and SH is the Schmidth number. Outcome for the longitudinal velocity, pressure rise, pressure gradient and stream lines are represented through graphs. In the history, the viscous-dissipation effect is usually represented by the Brinkman number.     

Magnetohydrodynamic free convection and mass transfer flow in micropolar fluid with constant suction

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid bounded by a vertical infinite surface under the action of a transverse magnetic field. Approximate solutions of the coupled nonlinear governing equations are obtained for different values of the microrotation- and the magnetic-parameters. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, angular velocity, temperature and concentration profiles are shown graphically. The numerical values of the skin friction, the wall couple stress, the rate of heat transfer and the concentration gradient at the wall are entered in tables.     

Numerical investigation of a fast-axial-flow CW CO2 laser

This paper presents the results of the calculation of the parameters of the active medium of a fast-axial-flow CO₂ laser using numerical methods in the framework of a one-dimensional approximation of the set of continuity equations, Bernoulli equation, equation of gas state, energy equation and multi-temperature rate equations with regard to diffusion for the gas flow in the cylindrical discharge tube. The spatial distribution of the small-signal gain and gas temperature along the gas flow direction have been calculated for a given set of initial conditions, namely, gas flow velocity, gas pressure and the tube diameter. In addition, the dependence of small-signal gain, the asymmetric stretch vibrational temperature of CO₂ (T₃) and the gas temperature on the discharge current were studied.     

圆管内自由固体相变材料定热流接触熔化

针对水平圆管内自由固体相变材料储能时的吸热熔化,运用接触熔化理论建立定热流圆管热源接触熔化模型.运用Nusselt液膜理论,建立熔化控制方程,并求解得到无量纲熔化方程组.分析讨论不同工况下熔化速度、液膜层厚度和压力分布等熔化参数的变化规律,探讨各影响因素对熔化的影响,并与温差熔化结果进行比较,研究第二类热边界条件下的接触熔化规律.发现,熔化过程中随着固体高度的减小,接触熔化液膜厚度逐渐增大,使熔化速度降低;热流密度较小时,其变化对熔化影响显著.     

MHD Stagnation Point Flow of Williamson Fluid over a Stretching Cylinder with Variable Thermal Conductivity and Homogeneous/Heterogeneous Reaction

The present study reveals the effect of homogeneous/hetereogeneous reaction on stagnation point flow of Williamson fluid in the presence of magnetohydrodynamics and heat generation/absorption coefficient over a stretching cylinder. Further the effects of variable thermal conductivity and thermal stratification are also considered. The governing partial differential equations are converted to ordinary differential equations with the help of similarity transformation.The system of coupled non-linear ordinary differential equations is then solved by shooting technique. MATLAB shooting code is validated by comparison with the previously published work in limiting case. Results are further strengthened when the present results are compared with MATLAB built-in function bvp4c. Effects of prominent parameters are deliberated graphically for the velocity, temperature and concentration profiles. Skin-friction coefficient and Nusselt number for the different parameters are investigated with the help of tables.     

基于混合发展的超声速段射流式COIL的数值优化

应用CFD技术,发展三维多组分化学反应流计算程序,对采用超声速段射流方式的氧碘化学激光进行数值模拟,考察分解率与增益等参考变量的详细三维分布.计算结果说明,超声速区域的高速流动以及混合效率降低使COIL无法在有限空间内完成整个运转流程;提高碘含量以加快反应速度的手段导致主流无法提供足够的载能介质,无法形成合理增益.在不改变喷管长度的前提下,提出主流无载气方式的探索,结果证明了超声速段射流方式采用无载气主流配置的可行性与优势,通过减小气流速度保证混合与化学反应在光腔上游完成,在合理的流量配比下光腔位置处可得到1.3%cm^-1的增益峰值.     

Landau damping in a bounded magnetized plasma column

The damping decrement of Landau damping and the effect of thermal velocity on the frequency spectrum of a propagating wave in a bounded plasma column are investigated.The magnetized plasma column partially filling a cylindrical metallic tube is considered to be collisionless and non-degenerate.The Landau damping is due to the thermal motion of charge carriers and appears whenever the phase velocity of the plasma waves exceeds the thermal velocity of carriers.The analysis is based on a self-consistent kinetic theory and the solutions of the wave equation in a cylindrical plasma waveguide are presented using Vlasov and Maxwell equations.The hybrid mode dispersion equation for the cylindrical plasma waveguide is obtained through the application of appropriate boundary conditions to the plasma-vacuum interface.The dependence of Landau damping on plasma parameters and the effects of the metallic tube boundary on the dispersion characteristics of plasma and waveguide modes are investigated in detail through numerical calculations.     

Heat and mass transfer analysis of time-dependent tangent hyperbolic nanofluid flow past a wedge

The candid intension of this article is to inspect the heat and mass transfer of a magnetohydrodynamic tangent hyperbolic nanofluid. The nanofluid flow has been assumed to be directed by a wedge on its way. In addition, the collective stimulus of the convective heating mode with thermal radiation is inspected. The governing set of PDEs is rendered into that of the coupled nonlinear ODEs. The resulting ordinary differential equations are then solved by the well known shooting technique for two different cases; the flow over a static wedge and flow over a stretching wedge. The impact of intricate physical parameters on the velocity, temperature and concentration profiles is analyzed graphically. It is noticed that the intensifying values of the generalized Biot number, Brownian motion parameter, thermophoresis parameter and Weissenberg number enhances the dimensionless temperature profile.     

Effect of couple stresses on transient MHD poiseuille flow

The unsteady laminar flow of an electrically conducting viscous fluid between parallel insulating plates subject to a transverse magnetic field is considered. The plates are fixed and flow is due to a constant pressure gradient. The induced field is taken into account. The fluid is incompressible and of couple stress type. The defining equations are coupled and numerical solutions for different values of couple stress parameter are obtained. The velocity and induced magnetic field profiles are sketched as functions of time, Hartmann number, and magnetic Prandtl number. The velocity decreases with increase in couple stress parameter.     

Input power flow in a submerged infinite cylindrical shell with doubly periodic supports

A submerged cylindrical shell reinforced by supports of rings and bulkheads is the primary structure of submarine, torpedo and all kinds of submerged aircrafts, so it is significant to study its characteristics of structure-borne sound. By means of periodic structure theory, the input power flow from a cosine harmonic line force into a submerged infinite cylindrical shell, reinforced by doubly periodic supports of rings and bulkheads, is studied analytically. The harmonic motion of the shell and the sound pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively. Since the fluid radical velocity and the shell radical velocity must be equal at the interface of the outer shell wall and the fluid, the motion equations of this coupled system are obtained. Both four kinds of forces (moments) between rings and shell and four kinds of forces (moments) between bulkheads and shell are considered. The solution is obtained in series form by expanding the system responses in terms of the space harmonics of the spacings of both stiffeners and bulkheads. The input vibrational power flow into the structure is obtained and the influences of different structural parameters on the results are analyzed. The analytic model is close to engineering practice, and it will give some guidelines for noise reduction of this kind of shell.     

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic(MHD) flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper(Cu), Silver(Ag), Alumina(Al2O3) and Titanium Oxide(TiO2). Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.     

Physiological Transportation of Casson Fluid in a Plumb Duct

This paper is devoted to a study of the peristaltic motion of a Casson fluid of a non-Newtonian fluid accompanied in a horizontai tube.To characterize the non-Newtonian fluid behavior,we have considered the Casson fluid model.Suitable similarity transformations are utilized to transform the governing partial differential momentum into the non-linear ordinary differential equations.Exact analytical solutions of these equations are obtained and are the properties of velocity,pressure and profiles are then studied graphically.     

Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet

An analysis is carried out to study the steady two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow to a melting stretching/shrinking sheet. The governing partial differential equations are converted into ordinary differential equations by similarity transformation, before being solved numerically using the Runge-Kutta-Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting parameter, stretching/shrinking parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique.