Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t=0) steady and then at t>0 it becomes unsteady. The semi-similar solution of the unsteady Navier–Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier–Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier–Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time.     

Flows induced by a plate moving normal to stagnation-point flow

The flow generated by an infinite flat plate advancing toward or receding from a normal stagnation-point flow is obtained as an exact reduction of the Navier?CStokes equations for the case when the plate moves at constant velocity V. Both Hiemenz (planar) and Homann (axisymmetric) stagnation flows are considered. In each case, the problem is governed by a Reynolds number R proportional to V. Small and large R behaviors of the shear stress parameters are found for both advancing and receding plates. Numerical solutions determined over an intermediate range of R accurately match onto the small and large R asymptotic behaviors. As a side note, we report an interesting exact solution for plates advancing toward or receding from an exact rotational stagnation-point flow discovered by Agrawal (1957).     

MHD stagnation-point flow of an electrically conducting fluid on the surface of another quiescent fluid

An analysis is made of the orthogonal stagnation-point flow of an incompressible viscous electrically conducting fluid on the surface of another incompressible viscous electrically conducting quiescent fluid in the presence of a uniform magnetic field normal to the interface between the fluids. It is found that for small magnetic Reynolds number, the velocity at a point in the upper fluid increases and that at a point in the lower fluid decreases with increase in the magnetic field. It is also observed from the temperature distributions in the two given fluids that the interface temperature increases with increase in the magnetic field.     

Transition of boundary layer flow past a stretching sheet due to a step change in applied constant mass flux

The problem of transition of boundary layer flow from the initial unsteady flow to the final steady flow past a permeable stretching sheet is considered in this paper. Two cases are considered: (1) Case-I deals with the transition of the unsteady flow due to a sudden application of constant suction/injection at the surface of the stretching sheet, from the initially prevailing steady flow; (2) Case-II deals with unsteady flow transition due to a sudden removal of constant suction/injection at the surface of the stretching sheet, from the initially prevailing steady flow. Numerical results are obtained using the implicit finite difference method of Crank-Nicholson type. The velocity and local skin friction for different values of injection/suction parameter are graphically presented and discussed. It is found that for the same magnitude of applied mass flux in Case-I and mass flux removal in Case-II, the time to reach steady-state flow is different.     

Analysis of transient flow of MHD nanofluid past a non-linear stretching sheet considering Navier’s slip boundary condition

Induced boundary layer flow in the nanofluid caused by impulsively started nonlinear stretching sheet is analyzed in the presence of thermal radiation and magnetic field considering Navier’s velocity sip boundary condition. The similarity solution is achieved numerically using Galerkin finite element technique. The variation of flow characteristics viz. nanofluid velocity, temperature and nanoparticle concentration is examined corresponding to different flow parameters considered in the problem. The findings of the investigation reveal that nonlinearity in the stretching sheet leads to a deceleration in the nanofluid velocity, temperature and nanoparticle concentration while the unsteadiness in the stretching tends to decelerate the velocity whereas temperature and nanoparticle concentration are found to be increasing with increase in unsteadiness. The problem investigated in this article is basically an extension for unsteady case of the previously done works on nanofluid flow over a sheet stretching with a power-law velocity.     

Unsteady free convection flow over a continuous moving vertical surface

Summary The problem of heat transfer in the unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid has been investigated. Both constant surface temperature and constant surface heat flux conditions have been considered. The nonlinear coupled partial differential equations governing the flow have been solved numerically using the Keller box method and the Nakamura method which both give closely similar solutions. The results indicate that the cooling rate of the sheet can be enhanced by increasing the buoancy parameter or the velocity of the sheet. It is found that a better cooling performance could be achieved by using a liquid as a cooling medium rather than a gas. The overshoot in the velocity occurs near the surface when the buoyancy parameter exceeds a certain critical value.     

��Note on ��Flows induced by a plate moving normal to stagnation-point flow�� by P. D. Weidman and M. A. Sprague (Acta Mech. 219, 219�C229, 2011)��

In a recent paper of Weidman and Sprague (Acta Mech., 2011), the unsteady flows generated by an impermeable infinite flat plate advancing with constant velocity V toward, or receding from an orthogonal (plane or axisymmetric) stagnation-point flow, have been investigated by an exact similarity reduction of the Navier?CStokes equations. It has been shown that in the co-moving reference frame of the plate, the induced flow appears as a steady flow, with an additional term R f??? in the governing equation of the similar stream function f (??). The Reynolds number R involved in this additional term is proportional to the plate velocity V. The present paper shows, however, that with the aid of a simple transformation, the additional term R f??? can be removed from the governing equation, its effect being transferred in the boundary condition for f (??). As a consequence, the unsteady flow problems of Weidman and Sprague reduce to the classical steady stagnation-point flow problems for permeable surfaces with a uniform lateral suction or injection of the fluid, so that the transpiration parameter f (0) coincides with R for the plane and with R/2 for the axisymmetric flow, respectively. The main benefit of this approach is that all the results of the latter well-investigated problems can simply be transcribed for the problems formulated by Weidman and Sprague (Acta Mech, 2011).     

电镀锌板摩擦系数的影响因素分析

采用销盘摩擦试验研究了正压力和速度对电镀锌板摩擦系数的影响规律,运用正交试验及方差分析的方法研究了正压力、速度、镀锌层对摩擦系数的影响水平.结果表明:当速度在5654.86～9424.78 mm/min,正压力在0.3～5 N的范围内,随着正压力的增大,镀锌板的摩擦系数逐渐降低,随着速度的增大,摩擦系数也逐渐增大,镀锌层对镀锌板摩擦系数影响最大.     

A note on the flow over a stretching sheet

Summary This study deals with the viscous incompressible flow over a stretching sheet. The velocity of the sheet is a quadratic polynomial of the distance from the slit and the sheet is subjected to a linear mass flux. A closed form solution is obtained under some restrictions on the linear mass flux. Stream line patterns are plotted and the effect of mass flux on the flow is also studied.     

Effect of stretching on interfacial stability

Summary. The effect of stretching on the stability of a horizontal interface between two fluids with different viscosities and densities is discussed. A local elongational flow acts to reduce the amplitude of perturbations and increase the wavelength of periodic waves, and thereby alter the instantaneous growth rate of disturbances. Linear stability analysis for Stokes flow reveals that, in the case of a horizontal interface between two semi-infinite fluids subjected to orthogonal stagnation-point flow, interfacial stretching is not able to suppress the Rayleigh-Taylor instability of unstably stratified fluids. In contrast, stretching is able to suppress the growth of periodic waves on the surface of a flat film resting on a horizontal surface. Numerical simulations based on the boundary-integral method for Stokes flow confirm that localized perturbations on the film surface are suppressed when the elongational flow is sufficiently strong.     

The flow of an elastico-viscous fluid past a stretching sheet with partial slip

Summary An analysis is carried out to study the flow characteristics in an elastico-viscous fluid (Walters' liquid-B model) over a stretching sheet with partial slip. The flow is generated due to linear stretching of the sheet. Using suitable similarity transformations on the highly non-linear partial differential equations we derive exact analytical solution with appropriate boundary conditions. The important finding in this communication is the effect of partial slip on the velocity and skin friction coefficient.     

A uniformly valid asymptotic solution for a transverse jet and its linear stability analysis

An expansion in terms of the ratio lambda of the characteristic crossflow velocity U infinity to jet velocity Uj, where lambda=U infinity/Uj<1, is used to obtain a representation of the basic three-dimensional steady flow in the nearfield of a transverse jet at large Reynolds numbers and to study its dominant instability. The inviscid vortex sheet analysis of Coelho and Hunt is extended so as to include asymptotic analysis of the viscous shear layers forming along the boundaries of the jet. These not only allow for continuity of the velocity components but also create vorticity whose advection induces an O(lambda) axial flow in the direction of the jet. A uniformly valid solution is then constructed for use in a stability analysis that concentrates on the effect of crossflow upon the dominant mode of the free jet. Both the characteristic frequency and growth rate of this mode are found to increase with lambda, in qualitative agreement with recent experimental observations.     

Viscous flow due to an exponentially shrinking permeable sheet in nanofluid in presence of slip

Classical problem of steady boundary layer flow of nanofluid over an exponentially permeable shrinking sheet in presence of slip is investigated. The model used for nanofluid includes Brownian motion and thermophoresis effects. The governing equations for momentum, energy, and nanofluid solid volume fraction are transformed to ordinary differential equations with the help of similarity transformations and then solved numerically using fourth order Runge–Kutta method with shooting technique. It is found that the governing parameters, viz. the suction/blowing parameter, velocity slip, thermal and mass slip parameters, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number significantly affect the flow field, heat, and mass transfer. The results obtained indicate that the dual solutions exist for certain values of the mass suction parameter. Velocity increases whereas the temperature and nanoparticle volume fraction decrease due to suction through the porous sheet. It is noted that with the increase in velocity slip fluid velocity increases whereas temperature and concentration decrease. Due to increase in thermal slip and mass slip both temperature and concentration decrease.     

TG合金空心阴极真空焊接熔池动态行为的数值模拟

建立了空心阴极真空电弧焊（Hollow Cathoda Vacuun Arc Welding,HCVAW)焊接TC4钛合金板（5mm)熔池中流体流动和传热过程动态行为的物理,数学模型,并对焊接过程进行了数值模拟计算和工艺试验,通过计算,找出了爆接速度和爆接电流等工艺参数对爆缝成型的影响规律,并计算出焊接过程中工作上的温度场分布和熔池中的流场分布,计算结果与实验结果基本相符。     

Base fluids with CNTs as nanoparticles through non-Darcy porous medium in convectively heated flow: A comparative study

Comparative analysis for flow of CNTs nanofluids is discoursed in the presence of non-Darcy porous medium. The consequences of homogeneous/heterogeneous process and heat transfer through convection are employed. The flow induced is due to non-linear stretching sheet of variable thickness. The bottom of the variable thickness sheet is heated by convective processes from a heated fluid. The velocity, temperature and concentration functions are formulated for the stretched flow problem. Convergence control variables and square residual errors for series solutions are obtained through OHAM (Optimal Homotopy Analysis Method). Biot number corresponds to larger temperature distribution in case of MWCNT than SWCNT. Comparison of nanoparicles SWCNT and MWCNT for the CNTs nanofluid fluids is highlighted. Water and engine oil CNTs fluids have higher magnitude of Nusselt number when compared with kerosene oil CNT fluid. The heat transfer rate in the presence of MWCNT is higher than SWCNT. Comparison of present study with previous published data is made. The outcomes are found in favorable agreement.     

Three-dimensional waves beneath an ice sheet due to a steadily moving pressure

Solutions of the nonlinear water wave equations under an ice sheet are computed using a boundary integral equation method. The ice sheet is modelled as a thin elastic plate and the fluid equations are nonlinear. Depending on the velocity of the moving disturbance generating the flow, different types of responses of the floating ice sheet are discussed.     

MHD boundary-layer flow due to a moving extensible surface

The flow due to a moving extensible sheet that obeys a more general stretching law is considered. The sheet occupies the negative x-axis and is moving continually in the positive x-direction, in an incompressible viscous and electrically conducting fluid. The sheet somehow disappears in a sink that is located at (x, y) = (0, 0). The governing system of partial differential equations is first transformed into a system of ordinary differential equations, and the transformed equations are solved numerically using a finite-difference scheme, namely the Keller-box method. The features of the flow and heat-transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the flow near x = 0, where the velocity profiles show a reversed flow.     

Quantitative simulation of gas-particle two phase plane mixing layer using discrete vortex method

The gas and particle phase in a two-phase plane mixing layer flow are numerically simulated using the discrete vortex method and a trajectory tracking method. It is shown that the number of vortex elements contained in two semi-infinite discrete vortex sheet and the method of generating control volumes for statistical calculation of the particle phase have important effects on the predicted results of particle phase, especially for quantitative prediction. By adopting different number of vortex elements for two semi-infinite discrete vortex sheet and overlapping the control volumes, predicted results including streamwise velocity, fluctuating velocity and Reynolds shear stress of both phases are obtained and agree well with experimental measurements quantitatively. It shows that the discrete vortex method can achieve the accurate quantitative simulation of two-phase flow.     

Boundary element simulation of inviscid flow around an oscillatory foil with vortex sheet

The dynamic performance of a rigid foil with harmonic vertical and rotational motions in fluid flow has been studied through velocity potential theory. A boundary element based time stepping scheme is introduced to simulate the flow around the foil and the vortex wake. The body surface condition is satisfied on the exact foil surface and the motion and deformation of the wake sheet shed at the trailing edge is tracked. Kelvin condition is satisfied and a Kutta condition for the unsteady motion is proposed to circumvent the singularity at the trailing edge. Point vortex, which is reduced from wake vortex dipole, is introduced to approximate the vorticity. The performance of foil NACA0012 with harmonic vertical and rotational motions are studied extensively; the propulsion/swimming mode, energy harvesting mode and the flying mode are analysed in detail.