UNSTEADY FLUID AND HEAT FLOW INDUCED BY A STRETCHING SHEET WITH MASS TRANSFER AND CHEMICAL REACTION

The effect of chemical reaction on the flow, heat, and mass transfer within a viscous fluid on an unsteady stretching sheet is examined. The stretching rate, temperature and concentration of the sheet, and the chemical reaction rate are assumed to vary with time. The time-dependent boundary layer equations governing the flow are reduced through a convenient similarity transformation to a set of ordinary differential equations, which are numerically solved by applying the fourth-order Runge-Kutta-Fehlberg scheme with the shooting technique. Results for the velocity, temperature, and concentration distributions as well as the wall temperature and concentration gradients are presented graphically for various values of the unsteadiness parameter A, Prandtl number Pr, Schmidt number Sc, and chemical reaction parameter γ.     

UNSTEADY MIXED CONVECTION WITH SORET AND DUFOUR EFFECTS PAST A POROUS PLATE MOVING THROUGH A BINARY MIXTURE OF CHEMICALLY REACTING FLUID

This study investigates the unsteady mixed convection flow past a vertical porous flat plate moving through a binary mixture in the presence of radiative heat transfer and nth-order Arrhenius type of irreversible chemical reaction by taking into account the diffusion-thermal (Dufour) and thermo-diffusion (Soret) effects. Assuming an optically thin radiating fluid and using a local similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth-order Runge-Kutta integration scheme. Graphical results for the dimensionless velocity, temperature, and concentration distributions are shown for various values of the thermophysical parameters controlling the flow regime. Finally, numerical values of physical quantities, such as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented in tabular form.     

On the unsteady forces during the motion of a sedimenting particle

We consider the unsteady motion of a sedimenting rigid spherical particle in order to examine the relative strength of the hydrodynamical forces acting on particles in fluid flows. The relative strength of the forces on all stages of the particle motion is a major concern for closing constitutive equations describing the more complex motion of particulate flows such as fluidised beds. The formulation results in a first order nonlinear integro-differential equation in terms of the instantaneous velocity of the sphere. This equation is made dimensionless and the particle Reynolds number and the fluid-particle density ratio are identified as the relevant physical parameters describing the particle motion. We obtain analytical solutions for the limits of small density ratios and small Reynolds number. In addition, a numerical solution is used for arbitrary values of the density ratio. The results show that the motion of spherical particles is significantly affected by the unsteady drag dominated by the memory Basset force on the early stages of the motion and on the approach to the steady state (terminal velocity). The present calculations indicate that the unsteady hydrodynamic drags might become of the same order of magnitude of the dominant viscous drag for flows with moderate particle-fluid density ratio. Therefore, unsteady drags should be taken into account on modelling multiphase particulate flows with moderate density ratio.     

UNSTEADY HEAT AND MASS TRANSFER BY MHD MIXED CONVECTION FLOW OVER AN IMPULSIVELY STRETCHED VERTICAL SURFACE WITH CHEMICAL REACTION AND SORET AND DUFOUR EFFECTS

This work considers unsteady, laminar, and coupled heat and mass transfer by MHD mixed convective boundary-layer flow of an electrically conducting fluid over an impulsively stretched vertical surface in an unbounded quiescent fluid with aiding external flow in the presence of a transverse magnetic field, homogeneous chemical reaction, and Soret and Dufour effects. The stretching velocity and surface temperature and concentration are assumed to vary linearly with the distance along the surface. The flow is impulsively set into motion and both the temperature and concentration at the surface are also suddenly changed from those of the ambient fluid. The governing partial differential equations are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. A parametric study illustrating the influence of various physical parameters is performed. Numerical results for the steady-state velocity, temperature, and concentration profiles as well as the time histories of the skin-friction coefficient, local Nusselt number, and local Sherwood number are presented graphically and discussed.     

T型反应器内非稳态吞噬流机理

运用激光诱导荧光（PLIF）技术和大涡模拟方法对T型反应器内的流动特性进行了研究。发现随着Reynolds数（Re）的增大,T型反应器中依次出现分离流（Re<120）、稳定吞噬流（120≤Re<190）、非稳态吞噬流（190≤Re≤300）、非稳态对称流（Re>300）四种流动模式。通过大涡模拟重点考察了非稳态吞噬流的振荡特性。结果表明,在非稳态吞噬流型下,T型反应器内撞击面上会周期性地出现旋涡合并现象,合并的涡向下传递,产生自持振荡。此时撞击区的压力、速度和涡量也发生周期性变化,且变化周期与旋涡合并周期相同,这种振荡是由速度和压力的周期性转换引起的。     

Unsteady flow and heat transfer on an accelerating surface with blowing or suction in the absence and presence of a heat source or sink

The problem of unsteady flow and heat transfer in the laminar boundary layer on a linearly accelerating surface with suction or blowing in the absence and presence of a heat source or sink is considered. The governing partial differential equations for this investigation are transformed into the non-dimensional equations by using pseudo-similarity time and pseudo-similarity coordinate. The resulting two points boundary-value problem is solved numerically by the central finite difference method associated with Newton's iteration from the initial stage (ξ=0) to a steady state (ξ=1) completely. A parametric study is performed to illustrate the effects of Prandtl number, power-law surface temperature (PLST) or power-law heat flux (PLHF), heat sink or heat source, and suction or blowing parameter on the dynamic velocity and temperature fields as well as the transient development of the skin-friction coefficients and the Nusselt number. These results are depicted graphically to display special aspects of unsteady flow and heat transfer characteristics in all time.     

A numerical study of the Dufour and Soret effects on unsteady natural convection flow past an isothermal vertical cylinder

The Dufour and Soret effects on the unsteady laminar free convective flow with mass transfer flow past a semi-infinite isothermal vertical cylinder were studied numerically. The governing partial differential equations were converted into a non-dimensional form and solved numerically by applying a Crank-Nicolson type of implicit finite-difference method with a tri-diagonal matrix manipulation and an iterative procedure. For the hydrogen-air mixture, which is a non-chemical reacting fluid, the profiles of the unsteady dimensionless velocity, temperature and concentration are shown graphically for the different values of thermal and mass Grashof numbers, thermal diffusion parameters (Soret numbers) and diffusion-thermo parameters (Dufour numbers). Finally, the simulated values of the average skin-friction coefficient, the average Nusselt number and the average Sherwood number are presented. The numerical results reveal that for an increasing Soret number or decreasing Dufour number, the time to reach the temporal maximum and the steady-state decreases for the flow variables. As the Soret number increases or the Dufour number decreases, both the skin friction and the Sherwood number increase, whereas the Nusselt number decreases.     

双热源作用下轮胎非稳态温度场的研究

同时考虑轮胎胶料滞后热源和摩擦热源的作用对轮胎非稳态温度场进行模拟,并以165/70R10轮胎为例对轮胎从启动到稳态行驶阶段的温度场进行分析.结果发现,在轮胎启动初始阶段摩擦热源对温升的影响不能忽略,但当轮胎进入稳态行驶阶段后,滞后热源成为影响轮胎温升的主要因素,而摩擦热源可以忽略不计.     

THE TRANSIENT MOTION OF A SPHERICAL FLUID DROPLET

A numerical method is developed for investigation of the unsteady motion of a spherical fluid droplet under the influence of gravity. This study extends previous work valid for creeping flow to moderate Reynolds number. The unsteady flow fields inside and outside of the fluid sphere are described by the two-dimensional, axisymmetric Navier-Stokes equations in the form of vorticity and stream function, along with the equation of motion of the droplet. The governing equations are approximated by a central difference and a second-order upwind difference, and are solved iteratively using the Gauss-Siedel and secant methods. Numerical results of the time-dependent vorticity, stream function and drop velocity are presented for a water droplet moving through air and for an air bubble rising in water. The steady state drop velocity and the drag coefficient at various Reynolds numbers are examined, and they are shown to agree very well with previous results.     

ON THE EFFECTIVNESS OF ION SLIP AND UNIFORM SUCTION OR INJECTION ON STEADY MHD FLOW DUE TO A ROTATING DISK WITH HEAT TRANSFER AND OHMIC HEATING

The steady flow and heat transfer of a conducting fluid due to the rotation of an infinite nonconducting porous disk in the presence of an axial uniform steady magnetic field are studied considering ion slip and ohmic heating. A uniform injection or suction is applied through the surface of the disk. The relevant equations are solved numerically using finite differences, and the solution shows that the inclusion of ion slip and the injection or suction through the surface of the disk gives some interesting results. It is found that the influence of the Hall and ion slip parameters on the velocity components is more pronounced in the injection than in the suction case. Also, ohmic heating has a marked effect on the heat transfer rate and it is of interest to see the reversal of the sign of the heat transfer rate for some values of the ion slip and suction parameters.     

ON THE EFFECTIVNESS OF ION SLIP AND UNIFORM SUCTION OR INJECTION ON STEADY MHD FLOW DUE TO A ROTATING DISK WITH HEAT TRANSFER AND OHMIC HEATING

The steady flow and heat transfer of a conducting fluid due to the rotation of an infinite nonconducting porous disk in the presence of an axial uniform steady magnetic field are studied considering ion slip and ohmic heating. A uniform injection or suction is applied through the surface of the disk. The relevant equations are solved numerically using finite differences, and the solution shows that the inclusion of ion slip and the injection or suction through the surface of the disk gives some interesting results. It is found that the influence of the Hall and ion slip parameters on the velocity components is more pronounced in the injection than in the suction case. Also, ohmic heating has a marked effect on the heat transfer rate and it is of interest to see the reversal of the sign of the heat transfer rate for some values of the ion slip and suction parameters.     

Consideration of maldistribution in heat exchangers using the hyperbolic dispersion model

Axial temperature profiles in a shell and tube heat exchanger are numerically calculated for given maldistributions on the tube side. For comparison the same maldistributions are handled with the parabolic and hyperbolic dispersion model with fitted values for the axial dispersion coefficient and third sound wave velocity. The analytical results clearly demonstrate that the hyperbolic model is better suited to describe the steady state axial temperature profiles.     

On stability of a bubble column

The goal of this contribution is to formulate the simplest possible model for the bubble column hydrodynamics and analyse it for steady states, stability, and unsteady behaviour. The governing equations are based on the mass balance of the gas phase. Two closures for the gas velocity are used and reflect two typical operational regimes, homogeneous (HoR) and heterogeneous (HeR). The model has five parameters: column height H, terminal bubble speed u₀, hindrance exponent n, enhance exponent m, gas flow rate q. Three branches of steady solutions were found for HoR, one stable, one unstable, one neutrally stable. The first two are physically relevant, are of the node-type, and merge in the turning point bifurcation at large enough gas input. Two branches of steady solutions were found for HeR, one stable and one neutrally stable. The first one is physically relevant, is of the node-type, and persists for all plausible parameter values. In both regimes, the neutrally stable solution was classified as unphysical. The transition regime (TrR) was obtained by matching the stable solutions of HoR and HeR, with help of a sigmoidal bridging function. The system stability was related to the model topology. The linear approximation of the bubble column dynamics was studied and the relaxation time estimated. The full nonlinear dynamics was demonstrated too. Both the steady and unsteady behaviour of the bubble column was compared with available experimental data.     

Transient three-dimensional heat transfer from rotating spheres with surface blowing

Transient heat transfer and thermal patterns around a rotating spherical particle with surface blowing are studied numerically for Reynolds numbers in the range 10?Re?300 and non-dimensional angular velocities up to Ω=1. This range of Reynolds number includes three distinct wake regimes: steady and axisymmetrical, steady but non-symmetrical, and unsteady with vortex shedding. The Navier-Stokes and energy equations for an incompressible viscous flow are solved numerically by a finite-volume method in a three-dimensional and time-accurate manner. The transient aspects of the thermal wakes associated with the aforementioned wake regimes have been explored. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that an unsteady three-dimensional flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects, and thus, the temperature distributions around the particle are significantly affected. Despite the fact that particle rotation brings about major changes locally, the surface-averaged heat transfer rates are not influenced appreciably even at high rotational speeds; consequently, it is shown that the total heat transfer rates associated with rotating spheres with surface blowing can be calculated from heat transfer correlations developed for flow over evaporating droplets.     

Transition from periodic to chaotic AC electroosmotic flows near electric double layer

Electroosmotic flows (EOFs) on insulated interfacial surface commonly exists as interfacial flows. Previously theoretical studies indicate that EOFs of Newtonian fluids on the insulated interfacial surface are steady in microchannels with symmetric zeta potentials (Suresh and Homsy, Physics of Fluids, 2004, 16, 2,349). Restricted by flow diagnostic methods in microfluidics, few velocity measurements of instantaneous EOFs have been reported, and the existence of unsteady EOFs on the insulated surface remains unclear. In this investigation, the velocity fluctuations of EOFs generated under AC electric field (named as ACFEOF) overlapped on a steady pressure-driven flow are measured by laser induced fluorescence photobleaching anemometer, at the diffuse electric double layer (EDL) on the bottom wall far from electrodes. Chaotic velocity fluctuations according to unsteady ACFEOF has been, for the first time, observed. Stokes number (St ) and electrical Reynolds number (Re_E ) related to oscillation and electro-inertial effect are suggested to control chaotic ACFEOF.     

HALL EFFECTS ON UNSTEADY FLOW DUE TO NON-COAXIALLY ROTATING DISK AND A FLUID AT INFINITY

An investigation is made on the unsteady magnetohydrodynamic (MHD) flow caused by the non-coaxial rotation of a disk and a fluid at infinity being permeated by a transverse magnetic field. The disk is porous and nonconducting and executes oscillations in its own plane. The Laplace transform method is used to obtain the exact solution of the velocity field. The structure of the steady and unsteady flow fields is investigated. It is shown that the ultimate steady-state blowing solution is established in the presence of Hall current also for resonant frequency, which was not possible in the hydrodynamic case. The combined effects of Hall current, rotation, and suction or blowing are examined. The physical significance of mathematical results is given with various limiting cases.     

A study of the evaporation of water on a wet mobile plane surface in a hot draft

The authors study the case of the evaporation of water from a wet plane surface moving with a constant velocity in the same direction as a laminar hot draft. They numerically solve the unsteady transfer equations formulated with vorticity, stream function and constant physical properties, using a finite-difference scheme with an implicit alternating directions method. They determine the space–time distributions of temperatures, humidities and velocity components as well as the local values of their gradients according to the system parameters. In this study, the main results can be summarized as follows: The emission of vapor does not significantly disturb air flow. The velocity of the wall does not affect the hydrodynamic entrance length, that is correctly given by the Schlichting formula, but it increases the mean temperature in a section of the tunnel and the temperature and humidity wall gradients in proportion to the Lewis number. A privileged point exists in a section of the tunnel, at which the longitudinal velocity component is independent of the mobile plane velocity. Finally, the authors study the influence of inner drying with the help of the Luikov model.     

HALL EFFECTS ON UNSTEADY FLOW DUE TO NON-COAXIALLY ROTATING DISK AND A FLUID AT INFINITY

An investigation is made on the unsteady magnetohydrodynamic (MHD) flow caused by the non-coaxial rotation of a disk and a fluid at infinity being permeated by a transverse magnetic field. The disk is porous and nonconducting and executes oscillations in its own plane. The Laplace transform method is used to obtain the exact solution of the velocity field. The structure of the steady and unsteady flow fields is investigated. It is shown that the ultimate steady-state blowing solution is established in the presence of Hall current also for resonant frequency, which was not possible in the hydrodynamic case. The combined effects of Hall current, rotation, and suction or blowing are examined. The physical significance of mathematical results is given with various limiting cases.     

A Model for the Relative Velocity of a Particle in an Impingement Dryer: Application to Heat Transfer

A simplified mathematical model for the relative gas-particle motion in a confined jet impingement dryer is developed. Model predictions based on an unsteady momentum balance are in good agreement with the observed cycling motion of a spherical particle. The model is applied to coriander seeds submerged in a flow field of superheated steam. It is found that relative motion occurs in unsteady turbulent regime, and that steady settling velocity of particles is never achieved. Model results are applied to correlate experimental heat transfer data of an impingement dryer. Experimental Nu numbers compare fairly well with correlations for fluidized systems.     

UNSTEADY FLOW DUE TO NON-COAXIAL ROTATION OF A POROUS DISK AND A FLUID AT INFINITY THROUGH POROUS MEDIUM

An exact solution of the unsteady hydrodynamic flow in a porous medium due to non-coaxial rotations of a porous disk and a fluid at infinity has been obtained. An analytical solution of the problem is obtained at small and large times by the Laplace transform method. It is found that the primary velocity decreases while the secondary velocity increases with the increase in porosity parameter σ. It is also found that the porosity takes more time to reach the steady state than that in the case of no porosity.