Squeezing flow between parallel plates

Summary The flow between two parallel plates (rectangular or circular) approaching or receding from each other symmetrically is analysed. The Xavier-Stokes equations have been transformed into an ordinary differential equation using a similarity transformation and the resulting equations are solved numerically. Results for the velocity components, pressure distribution and shearing stress on the wall are presented. In the case of squeezing flow between two circular plates the load supporting capacity of the upper plate has been calculated.

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Quetschströmung zwischen parallelen Platten

Übersicht Untersucht wird die Strömung zwischen zwei parallelen Rechteck- bzw. Kreisplatten, die sich einander nähern oder entfernen. Die Navier-Stokes-Gleichungen werden durch eine Ähnlichkeitstransformation in eine gewöhnliche Differentialgleichung überführt. Die Lösung erfolgt numerisch. Ergebnisse für die Geschwindigkeitskomponenten, die Druckverteilung und die Wandschubspannung werden vorgestellt. Für die Quetschströmung zwischen zwei Kreisplatten wird die Tragkraft bestimmt.

     

Oscillating radial flow between parallel plates

An analysis is presented for laminar radial flow due to an oscillating source between parallel plates. The source strength varies according to Q=Q ₀ cos ωt, and the solution is in the form of an infinite series in terms of a reduced Reynolds number, R _a ^* =Q ₀/4πνa/(r/a)². (Q ₀ = amplitude of source strength, ω = frequency, a = half distance between plates, r = radial coordinate, t = time, and ν = kinematic viscosity.) The results are valid for small values of R _a ^* and all values of the frequency Reynolds number, α=ωa ²/ν. The effects of the parameters R _a ^* and α are discussed.     

On heat and mass transfer in the unsteady squeezing flow between parallel plates

This paper reports the heat and mass transfer characteristics in a viscous fluid which is squeezed between parallel plates. The governing partial differential equations for unsteady two-dimensional flow with heat and mass transfer of a viscous fluid are reduced to ordinary differential equations by similarity transformations. Homotopy analysis method (HAM) is employed to construct the series solution of the problem. Physical interpretation to various embedding parameters is assigned through graphs for temperature and concentration profiles and tables for skin friction coefficient, local Nusselt number and local Sherwood number.     

Viscous fluid flow between moving parallel plates

The problem of two-dimensional time-dependent viscous fluid flow in a clearance between transversely and longitudinally moving rigid planes is considered. Non-self-similar solutions of this problem are found within the framework of the Hiemenz class of exact solutions of hydrodynamic equations and the admissible laws of motion of a movable plane are described.     

Simultaneous convection and radiation in flow between two parallel plates

A numerical solution is described for simultaneous forced convection and radiation in flow between two parallel plates forming ahannel. The front plate is transparent to thermal radiation while the back one is thermally insulated. Analyses for both flow and heat are presented for the case of a non-emitting ‘blackened’ fluid. The governing equations of the stream function and the temperature together with their boundary conditions are presented in non-dimensional expressions. The solution is found to depend on eight dimensionless parameters, namely the ratio of the height of the channel to the distance between the plates, the initial dimensionless temperature, the optical thickness, the absorptivities of both plates, the Reynolds number, the Prandtl number and the heat transfer coefficient from the front plate to the surroundings. The numerical solution is obtained using a finite-difference technique. A study has been made of the effect of the initial temperature of the flow at the channel inlet, the dimensionless loss coefficient from the front plate, the absorptivity of the back plate and the optical thickness, on the temperature distribution in the channel, the heat collection efficiency and the average temperature rise in the channel. Results showed that increasing the optical thickness increases the temperature of the front plate and decreases the temperature of the back plate. Also, increasing the optical thickness increases the efficiency of heat collection, which reaches its maximum asymptotic value at an optical thickness of about 1.5. Moreover, the location of the maximum temperature is found to depend on both the optical thickness and the dimensionless heat loss coefficient from the front plate.     

Magnetohydrodynamic heat transfer in two-phase flow between parallel plates

This study dealt with two-phase magnetohydrodynamic (MHD) flow and heat transfer in a parallel-plate channel. Both phases were incompressible and the flow was assumed to be steady, one-dimensional and fully developed. The present study was expected to be useful in the understanding of the effect of the presence of slag layers on the heat transfer characteristics of a coal-fired MHD generator.The problem was investigated, in which one of the two fluids was assumed to be electrically non-conducting. The transport properties of the two fluids were taken to be constant, and the plates were assumed to be maintained at constant and equal temperatures. In this case, the governing differential equations were linear, and an exact solution was obtained. Results were presented for various height and viscosity ratios for the two fluids and for two values of the electric field loading parameter. The governing equations were also solved numerically in order to verify the exact solution.     

Measurements of rivulet flow between parallel vertical plates

The research presented considers laminar, fully-developed rivulet flow in the channel formed by two parallel vertical plates for flows intermediate between a lower limit of droplet flow and an upper limit where the rivulets meander. Although this regime is likely the most simple rivulet flow regime, it does not appear to have been previously investigated in detail. In an earlier paper, the authors derived relations to predict the terminal Reynolds number and non-dimensional width of the rivulet under the approximation that the width is large relative to the gap width of the plates (the spacing between the plates). The objective of the present study is to examine the limits of this simple treatment as the relative width becomes small, i.e., as the rivulets become narrow. Experiments were performed measuring rivulet widths and flow rates for gap widths ranging from 0.152 mm to 0.914 mm with water, light mineral oil, ethyl alcohol and water with a wetting agent. Predictions were found to agree well with the measurements for width-to-spacing ratios as low as unity and less. A numerical analysis shows that a plausible explanation of unexpected agreement for narrow rivulets is that the error in this one-dimensional assumption is approximately countered by the error in neglecting flow in the edge region. To account for curvature of the liquid–air interface at the edges, an additional geometric relationship was assumed; this approach also was found to be a good representation.     

Heat and mass transfer in laminar flow between parallel porous plates

Summary The problem of heat transfer in a two-dimensional porous channel has been discussed by Terrill [6] for small suction at the walls. In [6] the heat transfer problem of a discontinuous change in wall temperature was solved. In the present paper the solution of Terrill for small suction at the walls is revised and the whole problem is extended to the cases of large suction and large injection at the walls. It is found that, for all values of the Reynolds number R, the limiting Nusselt number Nu increases with increasing R.Nomenclature stream function - 2h channel width - x, y distances measured parallel and perpendicular to the channel walls respectively - U velocity of fluid at x=0 - V constant velocity of fluid at the wall - =y/h nondimensional distance perpendicular to the channel walls - f() function defined in equation (1) - coefficient of kinematic viscosity - R=Vh/ suction Reynolds number - density of fluid - C _p specific heat at constant pressure - K thermal conductivity - T temperature - x=x ₀ position where temperature of walls changes - T ₀, T ₁ temperature of walls for x<x ₀, x>x ₀ respectively - = (T – T ₁)/T ₀ – T ₁) nondimensional temperature - =x/h nondimensional distance along channel - R ^* = Uh/v channel Reynolds number - Pr = C _p/K Prandtl number - _n eigenvalues - B _n() eigenfunctions - B _n ⁽⁰⁾ , () eigenfunctions for R=0 - B ₀ ⁽ⁱ⁾ , B ₀ ⁽ⁱⁱ⁾ ... change in eigenfunctions when R0 and small - K _n constants given by equation (13) - h heat transfer coefficient - Nu Nusselt number - _m mean temperature - C _n constants given by equation (18) - perturbation parameter - B _0i () perturbation approximations to B ₀() - Q = B ₀/ ₀ derivative of eigenfunction with respect to eigenvalue - z nondimensional distance perpendicular to the channel walls - F(z) function defined by (54)     

Exact solution for entrance region flow between parallel plates

A method of obtaining an exact solution of the complete Navier-Stokes equations for incompressible flow has been developed to study the development of fluid flow between parallel plates. An analytical solution has been developed in the form of a convergent infinite series and a numerical solution obtained for Reynolds numbers of 10 and 500. These results have been compared with data available elsewhere. The method developed here is expected to have general application     

Viscoplastic flow around a cylinder kept between parallel plates

Numerical simulations have been undertaken for the creeping pressure-driven flow of a Bingham plastic past a cylinder kept between parallel plates. Different gap/cylinder diameter ratios have been studied ranging from 2:1 to 50:1. The Bingham constitutive equation is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both the yielded and practically unyielded regions. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coefficient for a wide range of Bingham numbers. The present results extend previous simulations for creeping flow of a cylinder in an infinite medium and provide calculations of the drag coefficient around a cylinder in the case of wall effects.     

A note on laminar radial flow between parallel plates

Various criticisms are given of the published work on the theoretical aspect of the title problem. Some suggestions are made for the improvement of the theory. The main contribution is concerned with inertial effects at moderately large radii.     

Transient free convection flow between two vertical parallel plates

Transient free convection flow between two infinite vertical parallel plates has been investigated and good agreement was found between the results for large values of time and the well known ones for the steady-state problem.     

Viscoplastic flow between two approaching or parallel circular plates

The problem of the flow of a viscoplastic medium between two parallel circular plates in translatory coaxial relative motion is solved. The Bingham model [1] of a viscoplastic medium is assumed. The problem is solved in the inertialess thin layer approximation [2] for arbitrary values of the viscosity coefficient and yield stress.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 9–17, January–February, 1996.     

Relations between structure functions of velocity and temperature in a turbulent jet

Experiments in Fluids - Measurements of the longitudinal velocity fluctuation and the temperature fluctuation on the centreline of a turbulent plane jet are used to obtain second and third order...