Boundary Layer Flow over a Continuously Moving Thin Needle in a Parallel Free Stream

We investigate the boundary-layer flow on a moving isothermal thin needle parallel to a moving stream. The governing equations are solved numerically by a finite-difference method. Dual solutions are found to exist when the needle and the free stream move in the opposite directions.     

A Numerical Tackling on Sakiadis Flow with Thermal Radiation

Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.     

On the analytical solution of viscous fluid flow past a flat plate

In this Letter, we propose a simple approach using HAM to obtain accurate totally analytical solution of viscous fluid flow over a flat plate. First, we show that the solution obtained using HPM is not a reliable one; moreover, we show that HPM is only a special case of HAM and its basic assumptions are restrictive rather than useful. We set ?=−1 for the case of comparison of our results to those obtained using HPM. Afterwards, we introduce an extra auxiliary parameter and a straightforward approach to find best values of this auxiliary parameter which plays a prominent role in the frame of our solution and makes it more convergent in comparison to previous works.     

MHD stagnation point flow towards a stretching sheet

The steady two-dimensional MHD stagnation point flow towards a stretching sheet with variable surface temperature is investigated. The governing system of partial differential equations are transformed into ordinary differential equations, which are then solved numerically using a finite-difference scheme known as the Keller-box method. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases with the magnetic parameter when the free stream velocity exceeds the stretching velocity, i.e. ε>1, and the opposite is observed when ε<1.     

The influence of slip on the peristaltic motion of a third order fluid in an asymmetric channel

In this investigation, the peristaltic flow of a third order fluid in an asymmetric channel is considered in the presence of a slip condition. The series solution of the stream function and longitudinal pressure gradient is given under long wave length and low Reynolds number approximations. Pressure rise and frictional forces per wave length are analyzed through numerical integration. Pumping and trapping phenomena are examined and the obtained results are compared with those of no-slip condition. Comparison is made with the results of no-slip and viscous fluid cases.     

MHD mixed convection flow near the stagnation-point on a vertical permeable surface

The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the stagnation-point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.     

Wavelet Cross-Spectrum Analysis of Multi-Scale Disturbance Instability and Transition on Sharp Cone Hypersonic Boundary Layer

Experimental measurement of hypersonic boundary layer stability and transition on a sharp cone with a half angle of 5° is carried out at free-coming stream Mach number 6 in a hypersonic wind tunnel. Mean andfluctuation surface-thermal-flux characteristics of the hypersonic boundary layer flow are measured by Pt-thin-film thermocouple temperature sensors installed at 28 stations on the cone surface along longitudinal direction. At hypersonic speeds, the dominant flow instabilities demonstrate that the growth rate of the second mode tends to exceed that of the low-frequency mode. Wavelet-based cross-spectrum technique is introduced to obtain the multi-scale cross-spectral characteristics of the fluctuating signals in thefrequency range of the second mode. Nonlinear interactions both of the second mode disturbance and the first mode disturbance are demonstrated to be dominant instabilities in the initial stage of laminar-turbulence transition for hypersonic shear flow.     

Vortex fields and the Lamb-Stokes dissipation relation of fluid dynamics

Energy dissipation in Newtonian fluids containing a unified vortex field is shown to depend on , where η, ? and ζ=u×? are viscosity, vorticity and swirl. This term augments viscous dissipation where stream tube geometry is curved, e.g., in turbulent or helical flows.     

Standing and travelling waves in the shallow-water circular hydraulic jump

A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the flow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the flow in the vicinity of the jump, for which experimental support has been given.     

Hydrodynamic screening and axisymmetric turbulence in the transient sedimentation of a dilute suspension at small Reynolds number

A theory of settling of a dilute suspension of identical spherical particles in a viscous incompressible fluid is developed on the basis of the equations of transient Stokesian dynamics. The equations describe hydrodynamic interactions between particles moving under the influence of a constant force, starting to act at a particular instant of time. For a dilute suspension, a monopole approximation can be used. It is argued that the growth of velocity fluctuations is bounded by a combination of two effects, destructive interference of the flow patterns of individual particles, and a rearrangement of particle positions leading to a time-dependent microstructure of the suspension. After a long time, the microstructure tends to a steady state. The corresponding structure factor is described phenomenologically. The corresponding pair correlation function and the velocity correlation functions describing axisymmetric turbulence on the length scale of the mean distance between particles are evaluated.     

On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame

Analytic solution for unsteady magnetohydrodynamic (MHD) flow is constructed in a rotating non-Newtonian fluid through a porous medium. Constitutive equations for a Maxwell fluid have been taken into consideration. The hydromagnetic flow in the uniformly rotating fluid is generated by a suddenly moved infinite plate in its own plane. Analytic solution of the governing flow problem is obtained by means of the Fourier sine transform. It is shown that the obtained solution satisfies both the associate partial differential equation and the initial and boundary conditions. The solution for a Navier-Stokes fluid is recovered if λ→0. The steady state solution is also obtained for t→∞.     

MHD Flow Towards a Permeable Surface with Prescribed Wall Heat Flux

The steady magnetohydrodynamic （MHD） mixed convection flow towards a vertical permeable surface with prescribed heat flux is investigated. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides the solutions usually reported in the literature for the opposing flow.     

Stability of inertialess liquid film flowing down a heated inclined plane

This paper investigates the stability of inertialess falling film down an uniformly heated inclined plane. Normal mode analysis is performed to study the linear stability of the falling film.     

A simplified model for flows with eddies in symmetrically expanding channels

We derive a simplified model for two-dimensional (2D) channel flows with recirculated regions at moderate Reynolds numbers based on an extension of the boundary layer (BL) theory and averaging across the channel. The model reproduces symmetry-breaking bifurcations and resulting flow structures accurately. Analytical estimates for the decay rates toward the parabolic profile before and after a sudden change in the walls agree well with the full numerical simulations. A seemingly chaotic steady flow is also discovered in a channel with periodic expansions and contractions.     

Linear Stability of Taylor-Couette Flows with Axial Heat Buoyancy

The linear stability is studied of flows confined between two concentric cylinders, in which the radial temperature gradient and axial gravity are considered for an incompressible Newtonian fluid. Numerical method based on the Petrov-Galerkin scheme is developed to deal with the buoyancy term in momentum equations and an additional temperature perturbation equation. Computations of the neutral stability curves are performed for different rotation cases. It is found that the flow instability is influenced by both centrifugal and axial shear instabilities, and the two instability mechanisms interact with each other. The outer cylinder rotation plays dual roles of stabilizer and destabilizer under different rotating stages with the inner cylinder at rest. For the heat buoyancyinduced axial flow, spiral structures are found in the instability modes.     

Radiative Effects on Mixed Convection in a Uniformly Heated Vertical Convergent Channel with an Unheated Moving Plate

Fluids engineering is extremely important in a wide variety of materials processing systems, such as soldering, welding, extrusion of plastics and other polymeric materials, Chemical Vapor Deposition (CVD), composite materials manufacturing. In particular, mixed convection due to moving surfaces is very important in these applications. Mixed convection in a channel, as a result of buoyancy and motion of one of its walls has received little research attention and few guidelines are available for choosing the best performing channel configuration, particularly when radiative effects are significant. In this study a numerical investigation of the effect of radiation on mixed convection in air due to the interaction between a buoyancy flow and an unheated moving plate induced flow in a uniformly heated convergent vertical channel is carried out. The moving plate has a constant velocity and moves in the buoyancy force direction. The principal walls of the channel are heated at uniform heat flux. The numerical analysis is accomplished by means of the commercial code Fluent. The effects of the wall emissivity, the minimum channel spacing, the converging angle and the moving plate velocity are investigated and results in terms of air velocity and temperature fields inside the channel and wall temperature profiles, both of the moving and the heated plates, are given. Nusselt numbers, both accounting and not for the radiative contribution to heat removal, are also presented.     

New family of simple solutions of relativistic perfect fluid hydrodynamics

A new class of accelerating, exact and explicit solutions of relativistic hydrodynamics is found—more than 50 years after the previous similar result, the Landau–Khalatnikov solution. Surprisingly, the new solutions have a simple form, that generalizes the renowned, but accelerationless, Hwa–Bjorken solution. These new solutions take into account the work done by the fluid elements on each other, and work not only in one temporal and one spatial dimensions, but also in arbitrary number of spatial dimensions. They are applied here for an advanced estimation of initial energy density and life-time of the reaction in ultra-relativistic heavy ion collisions. New formulas are also conjectured, that yield further important increase of the initial energy density estimate and the measured life-time of the reaction if the value of the speed of sound is in the realistic range.     

A Zone Plate as a Tunable Terahertz Filter

A broadband tunable terahertz filter based on a zone plate is demonstrated in our terahertz time domain spec- trometer. The central bandpass frequency covers the whole spectral range of the terahertz wave emitted from a ZnTe emitter, from 0.5 THz to 2.5 THz, and can be tuned continuously by simply moving the zone plate along the terahertz beam path. The peak transmission is about 40% and the bandwidth varies from 0.16 THz to 0.25 THz at different bandpass frequencies when the aperture size is kept constant.     

Vibration analyses of an inclined flat plate subjected to moving loads

The object of this paper is to present a moving mass element so that one may easily perform the dynamic analysis of an inclined plate subjected to moving loads with the effects of inertia force, Coriolis force and centrifugal force considered. To this end, the mass, damping and stiffness matrices of the moving mass element, with respect to the local coordinate system, are derived first by using the principle of superposition and the definition of shape functions. Next, the last property matrices of the moving mass element are transformed into the global coordinate system and combined with the property matrices of the inclined plate itself to determine the effective overall property matrices and the instantaneous equations of motion of the entire vibrating system. Because the property matrices of the moving mass element have something to do with the instantaneous position of the moving load, both the property matrices of the moving mass element and the effective overall ones of the entire vibrating system are time-dependent. At any instant of time, solving the instantaneous equations of motion yields the instantaneous dynamic responses of the inclined plate. For validation, the presented technique is used to determine the dynamic responses of a horizontal pinned–pinned plate subjected to a moving load and a satisfactory agreement with the existing literature is achieved. Furthermore, extensive studies on the inclined plate subjected to moving loads reveal that the influences of moving-load speed, inclined angle of the plate and total number of the moving loads on the dynamic responses of the inclined plate are significant in most cases, and the effects of Coriolis force and centrifugal force are perceptible only in the case of higher moving-load speed.     

Slip effects on the peristaltic transport of MHD fluid with variable viscosity

This Letter concerns with the peristaltic analysis of MHD viscous fluid in a two-dimensional channel with variable viscosity under the effect of slip condition. A long wavelength and low Reynolds number assumption is used in the problem formulation. An exact solution is presented for the case of hydrodynamic fluid while for magnetohydrodynamic fluid a series solution is obtained in the small power of viscosity parameter. The salient features of pumping and trapping phenomena are discussed in detail through the numerical integration. It is noted that an increase in the slip parameter decreases the peristaltic pumping region. Moreover, the size of trapped bolus decreases by increasing the slip parameter.