Mechanical heating in lineal tube flow of non-Newtonian fluids

The effect of mechanical heating on the heat transfer characteristics of a heated non-Newtonian fluid in lineal flow through a circular tube is examined. Marked enhancement in the local rate of heat transferred to the tube wall is found.

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Zusammenfassung Die Wirkung der mechanischen Wärmeerzeugung auf die Wärmeübertragung einer erwärmten nicht-Newtonschen Flüssigkeit, in geradliniger Strömung in einem kreisrunden Rohr, wird untersucht. Es wird eine merkbare Vergrößerung des lokalen Wärmeüberganges an die Rohrwand gefunden.

     

Simultaneously developing flow and heat transfer of non-Newtonian fluids in equilateral triangular duct

A numerical investigation based on the Galerkin finite element method was carried out to solve the full three-dimensional governing equations for simultaneously developing steady laminar flow and heat transfer to a purely viscous non-Newtonian fluid described by a power law model flowing in equilateral triangular ducts. Two commonly used thermal boundary conditions, constant wall temperature (T boundary condition) and constant wall heat flux both axially and peripherally (H2 boundary condition) were examined. It is shown that the Nusselt number distribution along the walls is affected appreciably by the variation of the power law index. Results are presented and discussed for a wide range of power law indices and Prandtl numbers for T and H2 boundary conditions.     

Steady flow of non-Newtonian fluids — monotonicity methods in generalized Orlicz spaces

Our purpose is to show the existence of weak solutions to steady flow of non-Newtonian incompressible fluids with nonstandard growth conditions of the Cauchy stress tensor. We are motivated by the fluids of strongly inhomogeneous behavior and characterized by rapid shear thickening. Since L^p framework is not sufficient to capture the described model, we describe the growth conditions with the help of a general x-dependent convex function and formulate our problem in generalized Orlicz spaces.     

The convergence of non-Newtonian fluids to Navier-Stokes equations

In this paper, the convergence of solutions for incompressible dipolar viscous non-Newtonian fluids is investigated. We obtain the conclusion that the solutions of non-Newtonian fluids converge to the solutions of Navier-Stokes equations in the sense of L²-norm (resp. H¹-norm), as the viscosities tend to zero and the initial data belong to H¹(Ω) (resp. H²(Ω)). Moreover, we obtain L^∞-norm convergence of solutions if the initial data belong to H²(Ω).     

On the falling of objects in non-Newtonian fluids

The falling of a lamina in between two parallel plates containing a fluid of second grade is studied. The velocity of the lamina and the fluid are determined by solving the mixed initial—boundary value problem using Laplace transform. Explicit exact solutions are obtained for the velocity of the lamina and the fluid. Next, the falling of a cylinder in a tube containing a fluid of second grade is analyzed using Laplace transform, and once again exact solutions are found.

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Sunto Si studia la caduta di una lamina fra due piastre parallele contenenti un fluido di secondo grado. La velocità della lamina e del fluido sono determinate risolvendo un problema misto al contorno—a valori iniziali per mezzo della trasformata di Laplace—.Si studia poi la caduta di un cilindro in un tubo contenente un fluido di secondo grado utilizzando ancora la trasformata di Laplace e anche in questo caso si determina la soluzione esatta.

     

Variational models for quasi-static non-Newtonian fluids

This note is devoted to some recent results concerning regularity problems in non-Newtonian fluid mechanics. Bibliography: 7 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 233, 1966, pp. 55–62.     

Stagnation point flows of non-Newtonian power law fluids

Zusammenfassung Zur Berechnung der exakten Lösungen der nichtlinearen Differentialgleichungen, welche die Grenzschichtströmungen der nicht-Newtonschen Flüssigkeiten mit Potenzgesetz in der Gegend des zweidimensionalen oder axialsymmetrischen Staupunktes beschreiben, wird ein numerisches Verfahren entwickelt. Diese Berechnungen zeigen, dass die Methode von Pohlhausen in den angeführten Fällen zu widerspruchsvollen Resultaten führen kann.     

Distributed control for a class of non-Newtonian fluids

We consider control problems with a general cost functional where the state equations are the stationary, incompressible Navier-Stokes equations with shear-dependent viscosity. The equations are quasi-linear. The control function is given as the inhomogeneity of the momentum equation. In this paper, we study a general class of viscosity functions which correspond to shear-thinning or shear-thickening behavior. The basic results concerning existence, uniqueness, boundedness, and regularity of the solutions of the state equations are reviewed. The main topic of the paper is the proof of Gâteaux differentiability, which extends known results. It is shown that the derivative is the unique solution to a linearized equation. Moreover, necessary first-order optimality conditions are stated, and the existence of a solution of a class of control problems is shown.     

On some axial Couette flows of non-Newtonian fluids

The velocity fields corresponding to some flows of second grade and Maxwell fluids, induced by a circular cylinder subject to a constantly accelerating translation along its symmetry axis, are presented as Fourier-Bessel series in terms of the eigenfunctions of some suitable boundary value problems. These solutions satisfy both the associate partial differential equations and all imposed initial and boundary conditions. For α or λ → 0, they are going to those for a Newtonian fluid. Finally, for comparison, some diagrams corresponding to the solutions for the flow through a circular cylinder are presented for different values of t and of the material constants.     

On some axial Couette flows of non-Newtonian fluids

The velocity fields corresponding to some flows of second grade and Maxwell fluids, induced by a circular cylinder subject to a constantly accelerating translation along its symmetry axis, are presented as Fourier-Bessel series in terms of the eigenfunctions of some suitable boundary value problems. These solutions satisfy both the associate partial differential equations and all imposed initial and boundary conditions. For α or λ → 0, they are going to those for a Newtonian fluid. Finally, for comparison, some diagrams corresponding to the solutions for the flow through a circular cylinder are presented for different values of t and of the material constants. Received: March 18, 2004; revised: October 28, 2004     

On the use of lattice Boltzmann model for simulating dean flow of non-Newtonian fluids in curved square ducts

In the present work, the effect of a fluid’s shear-thinning and extension-hardening behavior is investigated on its flow characteristics in a typical curved square duct using a three-dimensional 27-velocities (D3Q27) incompressible lattice Boltzmann model. The main objective of the work is to examine how a fluid’s non-Newtonian viscous behavior affects the onset of Dean instability (i.e., the sudden shift from a two-cell to a four-cell vortex structure) in a curved square duct. The fluid of interest is assumed to obey Pinho’s rheological model in which shear-thinning and extension-hardening are both represented by a single power-law equation. It is found that shear-thinning has a stabilizing effect on the flow. On the other hand, extension-hardening is found to destabilize the flow.     

Flow and heat transfer of non-Newtonian fluids in enameling dies

The present work analyses computationally the flow inside wire enameling dies within the framework of the lubrication theory approximation. Non-Newtonian flow behavior and heat transfer are accounted for as well. It is shown that the developed approach most accurately predicts the momentum and heat fluxes along the wire. As such it is proven as a reliable and computationally efficient tool for the design of flow optimized die shapes. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variable speed coating with purely viscous non-Newtonian fluids

The flow between variable speed rollers is considered of purely viscous non-Newtonian fluids which obey the power law. The objective is to determine the dependence of the coating thickness on the upper roller,h ₁ , as a function of modified capillary number, ₁, of power indexn and speed ratioS=U ₁/U ₂ whereU ₁,U ₂ are the speeds of upper and lower rollers respectively. Analytical/numerical solutions are obtained forS close to unity;S=1+ where 1.

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Zusammenfassung Die Strömung zwischen zwei mit verschiedenen Geschwindigkeiten rotierenden Metallzylindern wird untersucht für rein viskose nicht-newtonische Flüssigkeiten, welche einem Potenzgesetz gehorchen. Das Ziel ist die Bestimmung der Abhängigkeit der Schichtdickeh ₁ am oberen Zylinder als Funktion der modifizierten Kapillaritätszahl ₁, des Geschwindigkeitsexponentenn und des VerhältnissesS=U ₁/U ₂, wobeiU ₁ undU ₂ die Geschwindigkeiten des oberen und unteren Zylinders sind. Analytische und numerische Lösungen liegen vor für den FallS nahe zu Eins.

     

Asymptotic stability for one-dimensional motion of non-Newtonian compressible fluids

Rarefaction wave solutions for a one-dimensional model system associated with nomNewtonian compressible fluid are investigated in terms of asymptotic stability. The rarefaction wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small. The proof is given by the elemental L2 energy method.     

Comparative study of some constitutive equations characterising non-Newtonian fluids

This paper compares, in a general way, the predictions of the constitutive equations given by Rivlin and Ericksen, Oldroyd, and Walters. Whether we consider the rotational problems in cylindrical co-ordinates or in spherical polar co-ordinates, the effect of the non-Newtonicity on the secondary flows is collected in a single parameterα which can be explicitly expressed in terms of the non-Newtonian parameters that occur in each of the above-mentioned constitutive equations. Thus, for a given value ofα, all the three fluids will have identical secondary flows. It is only through the study of appropriate normal stresses that a Rivlin-Ericksen fluid can be distinguished from the other two fluids which are indistinguishable as long as this non-Newtonian parameter has the same value.     

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions.     

Helical flow of non-Newtonian polymeric media

The helical flow problem is analyzed with reference to polypropylene. The methods and results of a series of helical flow experiments are described.Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 497–505, May–June, 1971.     

Model nonstationary systems in the theory of non-Newtonian fluids. III

One proves the generalized unique solvability “in the large” of the initialboundary value problem for the quasilinear system which describes the nonstationary flow of linear viscoelastic incompressible fluids having relaxation time λ and retardation time xν^?1.