Stability of the flow of an elastico-viscous fluid

Summary The eigenvalues of the generalized Orr-Sommerfeld equation for an elasticoviscous fluid are found for a constant velocity profile. The result shows that the effect of elasticity is to stabilize the flow.It is also shown that the second-order equation of state is not a suitable model for a fluid when the stability of that fluid is to be analysed.

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Zusammenfassung Die Eigenwerte der allgemeinen Orr-Sommerfeld-Gleichung für eine elastisch-viskose Flüssigkeit werden für ein Profil mit konstanter Geschwindigkeit angegeben. Das Ergebnis beweist, daß der Einfluß der Elastizität eine Stabilisierung der Strömung bewirkt.Es wird auch gezeigt, daß die Zustandsgleichung zweiter Ordnung kein geeignetes Modell für eine Flüssigkeit ist, deren Stabilität analysiert werden soll.

     

Fully developed flow and heat transfer of water at 4° C confined between two parallel vertical walls with linearly varying wall temperatures

The title problem has been considered for detailed analysis in view of its physical application taking account of the QDT-variation in the buoyancy term. The governing equations of the problem have been reduced to two coupled non-linear ordinary differential equations, which have been solved by the linearization technique (iteration scheme) used by Ostrach. Several qualitatively interesting behaviours of the flow — and heat transfer—characteristics have been pointed out after making a comparative study of the QDT-results with the LDT-counterparts.     

Laminar swirling flow in an annulus with porous walls

Flow of an incompressible viscous fluid under constant pressure gradient in a porous annulus is considered, with surface mass transfer, both in the radial and circumferential directions. Expressions for the fully developed velocities are then obtained. With these fully developed velocities on a section of the annulus, on which the origin of co-ordinates lies, the downstream decay of the swirl velocity is analysed, subject to the condition that the velocities on the boundaries are now purely radial. The perturbations in the axial and radial velocities, caused by the decaying swirl, are also determined. It is observed that the decay of the swirl velocity is faster for suction at the inner boundary and injection at the outer andvice versa.     

Laminar flow through parallel and uniformly porous walls of different permeability

Résumé Le problème de l'écoulement constant d'un liquide visqueux laminaire incompressible à travers un conduit à deux dimensions, le liquide étant aspiré ou injecté à travers ses parois uniformément poreuses, est généralisé dans le cas où les vitesses le long des parois sont différentes. L'écoulement qui s'ensuit satisfait une équation différentielle non linéaire ordinaire d'un nombre Reynolds d'absorbtion, et cette équation est résolue par la technique de perturbation. Cette équation différentielle est également résolue par le calcul, et l'on vérifie l'exactitude de la solution de série. Des expressions générales pour les distributions de vitesse, les coefficients de pression et la friction de surfaces sont données au moyen du nombre Reynolds. Le graphique de friction des surfaces indique que l'écoulement à travers un conduit ayant des parois poreuses de perméabilité inégale est régulier et stable comme dans le cas d'un écoulement symétrique.     

Unsteady flow of an elastico-viscous fluid past a circular cylinder

Résumé Une solution numérique est obtenue pour l'écoulement initial d'un fluid élastique et visqueux autour d'un cylindre circulaire, à nombres de Reynolds 40 et 100. On emploi la méthode d'integration numérique de l'équation de tourbillon.     

Steady flow and heat transfer in a visco-elastic fluid between two coaxial rotating disks

Flow and heat transfer of an elastico-viscous liquid between two parallel uniformly porous disks rotating about a common axis, are studied by perturbation technique. It is seen that for such a fluid, drag increases with suction and decreases with injection, while the rate of heat transfer increases in the presence of either suction or injection.     

Computational treatment of free convection effect on flow of elastico-viscous fluid past an accelerated plate with constant heat flux

Effect of free convection on the visco-elastic fluid (Walter - B’ type) flow past an infinite vertical plate accelerating in its own plane with constant heat flux is examined analytically. It is found that for given values of Grashof number, Prandtl number and Newtonian parameter; flow velocity at any point increases with the increase in time and non-Newtonian parameter, however, it decreases with both, the heating and cooling of the plate.     

Generalized couette flow of a dipolar fluid between two parallel plates

Résumé Dans ce travail, on présente une solution du problème de l'écoulement d'un fluide dipolaire entre deux plaques parallèles, dont l'une est en mouvement et l'autre fixe, en présence d'un gradient de pression. On trouve qu'il n'y a pas d'effet dipolaire sur l'écoulement si le gradient de pression n'est pas appliqué, et que pour un fluide dipolaire avec =0, étant le rapport entre l'espace des deux plaques et la constante dipolaire du fluide, le profil de vitesse n'est pas affecté par le gradient de pression.     

Laminar flow heat transfer from a flat plate with variable thermal conductivity

Zusammenfassung Es wird der Einfluss einer mit der Temperatur linear veränderlichen Leitfähigkeit auf die Wärmeübertragung an einer ebenen Platte untersucht.     

Unsteady flow of viscoelastic fluid with the fractional K-BKZ model between two parallel plates

In the present paper, we investigate the unsteady flow of a viscoelastic fluid between two parallel plates which is generated by the impulsively accelerated motion of the bottom plate. Based on the result of (Jaishankar and McKinley, 2014), the fractional K-BKZ constitutive equation is obtained from the fractional Maxwell model. Using respectively the fractional Maxwell model and fractional K-BKZ model, the unidirectional flows between two plates are simulated and compared. The velocity field and shear stress of the flows are calculated by developing efficient finite difference schemes. The results show that the fluid with the fractional Maxwell model gradually loses the viscoelasticity, but the fluid with the fractional K-BKZ model continues to preserve the viscoelasticity. The dependence of the flow velocity on various parameters of the fractional K-BKZ model is analyzed graphically.     

A boundary-layer in an elastico-viscous fluid

Zusammenfassung Die Prandtlsche Grenzschichttheorie wird verallgemeinert, so dass sie die Nollschen «einfachen Flüssigkeiten» erfasst. Es wird bewiesen, dass bei Flüssigkeiten mit geringem «Erinnerungsvermögen» die in der Grenzschicht vorhandenen Spannungen denjenigen ähnlich sind, welche bei einer einfachen Schubbeanspruchung vorkommen.     

On the steady flow of a Newtonian fluid between two parallel disk

Summary We show that the steady flow of a viscous fluid of moderate Reynolds number between two parallel disks has an exact solution which takes the form of a power series. Employing this exact solution the two-point boundary value problem for this class of flow is reduced to a nonlinear algebraic system which is then solved by a standard optimization method. Results are given for two particular cases, the continuous squeezing flow and the coaxial-disk flow.

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Zusammenfassung Wir zeigen, daß die ständige Strömung einer viskosen Flüssigkeit von mäßiger Reynoldszahl zwischen zwei parallelen Scheiben eine exakte Lösung hat, die die Form einer Potenzreihe annimmt. Wenn wir diese exakte Lösung anwenden, wird das Zwei-Punkte-Grenzwertproblem für diese Art von Strömung reduziert auf ein nichtlineares algebraisches System, das dann durch eine Optimierungsmethode gelöst werden kann. Angegeben werden Resultate für zwei Einzelfälle: die kontinuierliche Quetschströmung und die Strömung für Koaxialscheiben.

     

Natural convection flow of a generalized second grade fluid between two vertical walls

We study the flow due to natural convection of a non-Newtonian fluid, modeled as a generalized second grade fluid, between two vertical parallel walls. The flow results from the two walls being held at different temperatures. The viscosity of the fluid is taken to be a function of temperature according to Reynolds’ exponential law. We solve for the dimensionless velocity and temperature profiles and study their dependence upon certain material parameters.     

Steady plane-parallel flow of an anomalously viscous fluid between parallel plates

The authors consider the plane-parallel flow of an anomalously viscous fluid between two parallel plates, one of which is fixed while the other moves at constant velocity. An empirical power law is used as the rheological equation of state. It is shown that in the presence of a counterpressure exceeding a certain value, which is a function of the rheological properties of the polymer, the geometry and the flow regime, a counterflow develops near the bottom of the channel. The existence of a counterflow leads to the appearance of a minimum on the V_X(y) curve. This additional boundary condition makes it possible to obtain an approximate solution of the differential equations of motion and to describe the velocity distribution in the flow by means of two exponential equations. Integration of the velocity distribution thus obtained over the height of the channel gives an equation for the volume flow rate in plane-parallel flow in the presence of a counterpressure. It is shown that if the counterpressure gradient exceeds a critical value, the volume flow rate decreases much more sharply than for a Newtonian fluid.Mekhanika Polimerov, Vol. 1, No. 6, pp. 138–145, 1965     

Some exact solutions of an elastico-viscous fluid

The exact solutions for the unsteady flow of an elastico-viscous fluid caused by general periodic oscillations are obtained. Further, the plate is assumed to be rigid as well as porous executing periodic rotary oscillations. The velocity field and shear stress are established.     

Three-dimensional Couette flow of a dusty fluid with heat transfer

This work is focused on the mathematical modeling of three-dimensional Couette flow and heat transfer of a dusty fluid between two infinite horizontal parallel porous flat plates. The problem is formulated using a continuum two-phase model and the resulting equations are solved analytically. The lower plate is stationary while the upper plate is undergoing uniform motion in its plane. These plates are, respectively, subjected to transverse exponential injection and its corresponding removal by constant suction. Due to this type of injection velocity, the flow becomes three dimensional. The closed-form expressions for velocity and temperature fields of both the fluid and dust phases are obtained by solving the governing partial differential equations using the perturbation method. A selective set of graphical results is presented and discussed to show interesting features of the problem.     

Analysis of fluid flow and heat transfer over an unsteady stretching surface

This article considers two situations involving unsteady laminar boundary layer flow due to a stretching surface in a quiescent viscous incompressible fluid. In one configuration, the surface is impermeable with prescribed heat flux, in the other, the surface is permeable with prescribed temperature. The boundary value problems governing a similarity reduction for each of these situations are investigated and the existence of a solution is proved for all relevant values of physical parameters. The uniqueness of the solution is also proved for some (but not all) values of the parameters. Finally, a priori bounds are obtained for the skin friction coefficient and local Nusselt number.