Viscous fluid flow near the line of intersection of curved surfaces

Viscous fluid flow near the line of intersection of curved surfaces at large Re numbers is a topic of considerable interest. The intersection of two fixed planes has been the subject of many experimental and theoretical studies. This case is characterized by very small transverse velocities and by the fact that the corner does not affect the remoter parts of the flow [1–4]. The flows near intersecting curved surfaces have received very little attention, except for the particular case of the intersection of a concave cylindrical surface and a plane in an incompressible fluid flow. With reference to this example it has been shown that the curvature qualitatively affects the flow pattern not only near the line of intersection but also at a distance from it [5]. The present article is concerned with viscous fluid flow at Re1 near the line of intersection of arbitrary, relatively smooth surfaces in the presence of external body forces and, moreover, in the noninertial coordinate system moving with the exposed surfaces (for example, rotating surfaces). On the basis of an analysis of the Navier-Stokes equations and the energy equation as Re sufficient conditions are obtained for the development of intense transverse flows near the line of intersection, which also lead to a qualitative change in the flow pattern; it is shown that depending on the external forces and the geometric parameters of the surfaces various types of flow are possible; the relations determining the occurrence of a particular type of flow and the equations and necessary boundary conditions describing some of these flows are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 16–21, May–June, 1985.     

On fluid flow between rotating surfaces

Viscous fluid flow in the space between a spherical and an ellipsoidal surfaces rotating with different angular velocities was studied. The conditions of the occurrence and features of radial fluid flows are discussed. The results can be used to study a number of geophysical phenomena related to the dynamics of the flow of fluid.     

Fluctuating flow of a second-order fluid near a stagnation point

Summary The boundary layer equations for axisymmetric flow of an incompressible second-order fluid have been deduced. The flow of such a fluid near a stagnation point when the main stream outside the boundary layer fluctuates in magnitude but not in direction has been discussed. The velocity distribution is found for various values of the steady mean in two limiting cases of small and large values of the frequency of the oscillation of the main stream. The frequency for which two approximate solutions overlap has been calculated in each case.     

Axisymmetric magnetohydrodynamic flow of micropolar fluid between unsteady stretching surfaces

This investigation examines the time dependent magnetohydrodynamic (MHD) flow problem of a micropolar fluid between two radially stretching sheets. Both strong and weak concentrations of microelements are taken into account. Suitable transformations are employed for the conversion of partial differential equations into ordinary differential equations. Solutions to the resulting problems are developed with a homotopy analysis method (HAM). The angular velocity, skin friction coefficient, and wall couple stress coefficient are illustrated for various parameters.     

CENTRIFUGAL INERTIA EFFECTS OF THE FLUID FLOW BETWEEN STEPPED SPHERICAL SURFACES

ＣＥＮＴＲＩＦＵＧＡＬＩＮＥＲＴＩＡＥＦＦＥＣＴＳＯＦＴＨＥＦＬＵＩＤＦＬＯＷＢＥＴＷＥＥＮＳＴＥＰＰＥＤＳＰＨＥＲＩＣＡＬＳＵＲＦＡＣＥＳＬｉｕＺｈｉｅｎ－ｂｅｉ（刘震北）（ＨａｒｈｉｎＩｎｓｔｉｔｕｔｅｏｆｔｅｃｈｎｏｌｏｇｙ．Ｈａｒｂｉｎ）（Ｒ...     

Steady viscous fluid flow near a cylinder subject to longitudinal deformation

Within the framework of the class of exact solutions of the hydrodynamic equations, characterized by the linear dependence of some of the velocity components on the axial coordinate, the axisymmetric and rotationally symmetric regimes are considered for viscous fluid flow in the gap between two cylinders one of which is being longitudinally deformed while the other is rigid. In the investigated region of the Reynolds number spectrum a point at which a rotationally symmetric solution branches off from the solution without swirl is found and the intervals of multiple values of this parameter, within which each fixed Re corresponds to more than one solution of the rotationally symmetric or axisymmetric type, are distinguished.     

The boundary layer flow of a Reiner-Rivlin fluid near a spinning cone

Summary The steady motion of an incompressible inelastic Reiner-Rivlin fluid near a spinning cone has been studied and a similarity solution has been presented. It has been shown that the flow patterns can be obtained from Srivastava-Jain's work. But the pressure distribution is not the same and we have given the numerical values of the pressure in two tables and have also shown their variation in two figures.Sponsored by the Mathematics Research Center, United States Army, Madison Wisconsin under Contract No.: DA-11-022-ORD-2059.     

Heat transfer from non-isothermal surfaces in the stagnation-point flow of a micropolar fluid

Summary This paper contains a numerical study of the development of the thermal boundary layer on an impermeable flat surface, following a step change in surface temperature, for stagnation-point flow of a micropolar fluid. A study is made of the relative effects of the individual parameters in the equations, and a comparison of certain integral parameters, representative of the flow, is used to assess the accuracy of the results.

---

Zusammenfassung Diese Arbeit enthält eine numerische Untersuchung der Entwicklung der thermischen Grenzschicht auf einer undurchlässigen ebenen Oberfläche nach stufenförmigem Sprung in der Oberflächentemperatur für die Staupunktsströmung einer mikropolaren Flüssigkeit. Die relativen Auswirkungen der einzelnen Parameter in den Gleichungen werden untersucht und ein Vergleich von gewissen, für die Strömung repräsentativen integralen Parametern wird durchgeführt, um die Genauigkeit der Ergebnisse abzuschätzen.

---

---

With 4 figures and 1 table     

Optical studies (LDA) of an electrorheological fluid in slit flow

Measurements via Laser-Doppler-Anemometry (LDA) were performed with the electrorheological fluid P 1723 (laboratory sample supplied by Robert Bosch GmbH, Stuttgart) inside a flat channel with electrically conducting walls. The results show i) marked quantitative differences to data obtained viscometrically and ii) large velocity fluctuations in the bulk regions of the channel. Formation of — possibly transient — structures would be consistent with this result.     

Soret and Dufour effects on magnetohydrodynamic （MHD） flow of Casson fluid

This article studies the Soret and Dufour effects on the magnetohydrodynamic (MHD) flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined.     

Averaged fluid velocities near a cylinder in turbulent flow in an open channel: Experiment

The results of experiments in which a circular cylinder located near the bottom of a rectangular channel was exposed to transverse statistically stationary turbulent subcritical flow with free surface are presented. The particle image velocimetry (PIV) was used to obtain data on the averaged velocity field near the cylinder. The gradients of the longitudinal velocity component were used to determine the shear stresses on the bottom of the channel. It is shown that the presence of the cylinder in the flow causes considerable averaged vertical velocities and a significant change in the shear stresses on the bottom of the channel.     

Dynamics of mutually coupled quantum dot spin-VCSELs subject to key parameters

A symmetric model based on optically pumped quantum dot (QD) spin-polarized vertical cavity surface emitting lasers (spin-VCSELs) subject to mutual coupling is proposed. Compared with the conventional solitary model, more plentiful dynamical regimes associated with different dynamical regions are displayed visually by numerous bifurcation maps, and the detailed direct numerical simulations accurately reveal the dependence of dynamical behavior on external and internal parameters through introducing mutual coupling scheme. We then find that the roles played by the mutual coupling strength and delay time are remarkably significant in intensifying the regime of complex dynamical oscillation. Beyond that, the crucial effects of capture rate, gain parameter, linewidth enhancement factor and frequency detuning on determining the evolvement of dynamical behavior in the mutually coupled QD spin-VCSELs model are shown evidently in the plane of the optical pump intensity and polarization. Through a comprehensive investigation of the dynamical behavior dependent on key parameters, the dynamical mechanism expressed in the current model can be adjusted and even controlled well. Therefore, the involved efforts are enlightening and foresighted to promote a deeply research in the field of QD lasers-based expansion.

     

A diffuse-interface approach to two-phase isothermal flow of a Van der Waals fluid near the critical point

A novel numerical method for simulations of isothermal, compressible two-phase flows of one fluid component near the critical point is presented on the basis of a diffuse-interface model and a Van der Waals equation of state. Because of the non-convexity of the latter, the nature of the set of governing equations is mixed hyperbolic–elliptic. This prevents the application of standard numerical methods for compressible flow. Moreover, the Korteweg capillary stress tensor, characteristic for the diffuse-interface approach, introduces third-order spatial derivatives of mass density in the Navier–Stokes equation, resulting in a dispersive behavior of the solution. Our computational method relies on a transformation of the conserved variables, which controls dispersion, stabilizes the numerical simulation and enables the use of coarser grids. A one-dimensional simulation shows that this method provides better stability and accuracy than without transformation of variables. Two- and three-dimensional simulations for isothermal liquid–vapor flows, in particular the retraction of a liquid non-spherical drop in vapor and the binary droplet collision in vapor, show the applicability of the method. The surface tension calculated from the numerical results is in good agreement with its theoretical value if the computational grid is sufficiently fine.     

配置点谱方法-人工压缩法(SCM-ACM)求解不可压缩流体流动

开发了配置点谱方法SCM（spectral collocation method）与人工压缩法ACM（artificial compressibility method）相结合的方法SCM-ACM,用于求解不可压缩粘性流动问题。选取典型的方腔顶盖驱动流为研究测试对象,首先建立人工压缩格式的控制方程,其次采用SCM离散控制方程的空间偏微分项,推导出矩阵形式的代数方程,最后测试了SCM-ACM代码的有效性。结果显示,SCM-ACM能够有效求解不可压缩流动问题,并继承了谱方法的指数收敛特性,且具有ACM求解过程简单及易于实施的特点。     

Three‐dimensional flow of upper‐convected Maxwell (UCM) fluid

An analysis has been carried out for three‐dimensional fluid over a stretching surface. Similarity transformations are invoked for the conversion of nonlinear partial differential equations to the ordinary differential equations. Computations for the series solution are made by using homotopy analysis method. Graphical results are obtained. Attention has been particularly given to the influence of Deborah number. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental evidence of diffusion-induced bias in near-wall velocimetry using quantum dot measurements

Near-surface velocity measurements are carried out with quantum dot (QD) nanoparticles using evanescent wave illumination. Relying on the small size of QDs, their correspondingly small hydrodynamic radius and high Brownian diffusion coefficient, we consider the situation where the tracer diffusion length over the inter-frame time Δt is large compared to the size of the interrogation region next to the wall. While keeping all other experimental parameters fixed, we systematically increase Δt by as much as a factor of 25, resulting in an increase of the QD diffusion length by a factor of 5. Data indicate a significant overestimation of the “apparent” mean velocity measured experimentally. These results provide a direct confirmation of the phenomenon of diffusion-induced bias described by the simulations of Sadr et al. (2007).     

Magnetohydrodynamic (MHD) flow of a second grade fluid in a channel with porous wall

An analysis has been carried out to study the effect of magnetic field on an electrically conducting fluid of second grade in a parallel channel. The coolant fluid is injected into the porous channel through one side of the channel wall into the other heated impermeable wall. The combined effect of inertia, viscous, viscoelastic and magnetic forces are studied. The basic equations governing the flow and heat transfer are reduced to a set of ordinary differential equations by using appropriate transformations for velocity and temperature. Numerical solutions of these equations are obtained with the help of Runge-Kutta fourth order method in association with quasi-linear shooting technique. Numerical results for velocity field, temperature field, skin friction and Nusselt number are presented in terms of elastic parameter, Hartmann number, Prandtl number and Reynolds number. Special case of our results is in good agreement with earlier published work.