Flow and heat transfer in a moving fluid over a moving flat surface

In this paper, a numerical analysis of the momentum and heat transfer of an incompressible fluid past a parallel moving sheet based on composite reference velocity U is carried out. A single set of equations has been formulated for both momentum and thermal boundary layer problems containing the following parameters: r the ratio of the free stream velocity to the composite reference velocity, σ (Prandtl number) the ratio of the momentum diffusivity of the fluid to its thermal diffusivity, and E _c (E _ck ) (Eckert number). The present study has been carried out in the domain 0 ≤ r ≤ 1. It is found that the direction of the wall shear changes in such an interval and an increase of the parameter r yields an increase in temperature.      

Freeze-coating on a continuous moving sheet and on an axially moving cylinder

This paper considers one-dimensional heat transfer model for the freeze-coating of a polymeric substance on a continuously moving sheet and on an axially moving cylinder. Analytical expressions are obtained for the freeze-coat thickness; also presented the solutions for an upper bound on the thickness of the frozenlayer using thermodynamic equilibrium conditions. Effect of Stefan number on freeze-coat thickness is briefly discussed and also the application of the present results with an example.     

Mass transfer with a moving interface

Summary Two cases are considered for which mass transfer coefficients are calculated. The first case is a semi-infinite Couette flow bounded by a moving interface across which transfer takes place. In the second case the mass transfer coefficient is calculated for a liquid flow with a moving interface, along which a boundary layer develops.     

Kinetic cooling of a moving gas

A study is made of the effects that arise when a moving gas absorbs electromagnetic radiation whose frequency is in resonance with the frequency of the center of a spectral line of a vibrational-rotational transition of molecules of the mixture. It is shown that the variation of the gas-dynamic parameters depends on the relationships between the rates of the stimulated transitions, intramolecular V — V exchange, and V — T relaxation, and the maximal effects are attained in the neighborhood of the sonic point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 127–138, May–June, 1982.     

Instability of a moving plane-parallel layer

A study is made of infinitely small perturbations of a moving plane-parallel layer. It is shown that, in distinction from an isolated tangential discontinuity, a layer is unstable with any given values of the projection of the velocity of the layer on the wave vector of the perturbation. The instability of an isolated tangential discontinuity has been repeatedly investigated in detail (see, for example, [1–4]). The instability of a moving layer has remained almost unanalyzed. It is of importance to make such an analysis, the more so since the results for a layer differ qualitatively from the results for an isolated tangential discontinuity.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 11–14, May–June, 1972.     

Flows with a moving contact line

The problem of a two-dimensional viscous fluid drop which steadily moves along a horizontal rigid surface is considered. Such motion arises if the rigid surface wettability is nonuniform. A sequence of solutions for the velocity field and the free surface shape with the successively increasing applicability region near the moving contact lines is obtained for small capillary numbers Ca. The solution of the problem is found in the case when the distortion of the free surface of the drop during motion can be neglected. The problem is then reformulated using functions of a complex variable and expanded variables are introduced. In the new variables a more accurate solution of the same problem is found, with a much more narrow inapplicability region near the moving contact lines. In the solution obtained the free surface approaches the receding contact line at an angle of 180° and the advancing line at a zero angle. The solution is applicable up to the receding contact line and here approaches the known asymptotics. Near the advancing contact line the solution is applicable until the angle between the free surface and the rigid substrate becomes of the order of Ca^1/3.     

Corona discharge in a moving gas

Some aspects of the theory of corona discharges in a moving medium are considered. Two situations are analyzed: a corona discharge at a negative electrode under the condition that in the region of electrogasdynamic flow exterior and interior regions of the discharge can be distinguished, the motion of the gas being taken into account only in the exterior region, and corona discharge at a negative electrode under the condition that the effects of the motion of the gas are important in both the exterior and the interior regions of the discharge. For the first situation, a mathmatical generalization is proposed of the traditional model of the interior region, and dimensional and similarity methods are used to obtain functional relationships for the current—voltage characteristics of the discharge in the moving medium. The second situation is investigated for the example of a corona discharge between cylindrical electrodes through which gas is blown or sucked. In this case, the solution to the problem is found without dividing the flow region into exterior and interior regions of the discharge, a system of kinetic equations describing the flow in the complete interelectrode gap being used.     

Flow past a plate with a moving surface

On the basis of a numerical solution of the unsteady Navier-Stokes equations, the flow past a finite plate with an upstream-moving surface is investigated. For the Reynolds numbers Re =10²−10⁴, the flow past the plate is analyzed as a function of the relative plate surface velocity. On the basis of this analysis a limiting mathematical model of the flow as Re → ∞ is proposed.     

Entrainment of a liquid by a moving surface

There have been many studies of the capture of a liquid by a withdrawn surface [1–5]. All employ the method of solution developed in [1, 2], which is limited by the requirement that the thickness h₀ of the entrained film be small as compared with the Laplace capillary constant. In this paper a new approach is described and used as a basis for solving the problem of the entrainment of a second-order viscoelastic fluid by a wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 17–21, July–August, 1985.     

Free convection from a horizontal moving sheet

In this paper the free convection flow through a thin rigid hot sheet moving horizontally out of a slot is considered. It is found that there is a similarity formulation of the boundary-layer equations so that the problem reduces to solving a system of coupled ordinary differential equations with suitable boundary conditions. This system of equations is solved numerically for various values of the Prandtl number,Pr, namely 0.45≤Pr≤10000. It is found that for the flow under the sheet there is a reverse flow region near the sheet for small values ofPr, whilst in the case of the flow above the sheet there is no reverse flow region for any value ofPr we have investigated. For the flow under the sheet an asymptotic behaviour, which is valid near the minimum value of the Prandtl number for which it is possible to obtain a numerical solution, is proposed.     

Non-isothermal kinetics of a moving phase boundary

In this paper we derive an explicit formula for a kinetic relation governing the motion of a phase boundary in a bilinear thermoelastic material capable of undergoing solid-solid phase transitions. To obtain the relation, we study traveling wave solutions of a regularized problem that includes viscosity, heat conduction and convective heat exchange with an ambient medium. Both inertia and latent heat of transformation are taken into account. We investigate the effect of material parameters on the kinetic relation and show that in a certain range of parameters the driving force becomes a non-monotone function of the interface velocity. The model also predicts a nonzero resistance to phase boundary motion, part of which is caused by the thermal trapping. Received: November 15, 2001 / Published online September 4, 2002 RID="*" ID="*" e-mail: annav@math.pitt.edu Communicated by Lev Truskinovsky, Minneapolis     

Griffith crack moving in a piezoelectric strip

Summary  The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack in a piezoelectric strip. Received 14 August 2001; accepted for publication 24 September 2002 The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported by the National Natural Science Foundation of China under Grant 70272043.     

Longitudinal vibrations of a beam with a moving load

International Applied Mechanics -