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Generalized Deformation Rates In Secondary Flows Of Viscoelastic Fluids Between Rotating Spheres
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Book Synopsis Generalized Deformation-rates in Secondary Flows of Viscoelastic Fluids Between Rotating Spheres by : Ronald Norman Knoshaug
Download or read book Generalized Deformation-rates in Secondary Flows of Viscoelastic Fluids Between Rotating Spheres written by Ronald Norman Knoshaug and published by . This book was released on 1969 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: By various experiments, it has been found that the response of real materials to external forces is, in general, nonlinear in character. In classical continuum mechanics, the use of ordinary measures of strain have forced the constitutive equations to take complex forms and since the orders of these measures are not fixed, many unknown response coefficients have to be introduced into the constitutive equations. In general, there is no basis of choosing these coefficients. Seth attempted to resolve this difficulty by introducing generalized measures in continuum mechanics and Narasimhan and Sra extended these measures in such a way as to adequately explain some rheological behavior of materials. The constitutive equation of Narasimhan and Sra essentially contains two terms and four rheological constants and, unlike some previous theories, it does not contain any unknown functions of the invariants of kinematic matrices while at the same time explains many viscoelastic phenomena. In the present investigation, a theorem has been proved establishing certain criteria for fixing the orders of generalized measures suitably so as to predict different types of viscoelastic phenomena, such as dilatancy. We have found during the course of this investigation that the constitutive equation of Narasimhan and Sra does not adequately explain such physical phenomena as pseudoplasticity. However, in order to construct a constitutive equation so that it does explain such phenomena, we have found it necessary to construct combinations of sets of generalized measures. The resulting constitutive equation is found to be quite general and is able to explain a vast range of physical behavior of fluids. To illustrate the use of this constitutive equation based upon combined generalized measures, we have investigated the important problem of secondary flows for fluids in the presence of moving boundaries. This problem is very important, since the investigation of secondary flows allows us to obtain a clearer picture of the actual motion of the fluid. For the problem of flow of a fluid in the annulus of two rotating spheres, we have obtained the solution for the velocity and pressure fields. In order to investigate the secondary flow pattern more thoroughly, we have obtained the streamline function of the flow. The streamlines in meridian planes containing the axis of rotation are found to be closed loops and the nature of the closed loops is found to be strongly dependent upon the viscoelastic parameter S. For S less than critical value, the flow is found to be very much like that of a Newtonian fluid, with the fluid advancing toward the inner sphere along the pole and outward along the equation. At the critical value the flow region is found to split into two subregions, each containing closed loops of streamlines. As S is increased further, another critical value is reached whereby the streamlines again become one set of closed loops, with the sense of rotation reversed from that of Newtonian fluid.
Book Synopsis Generalized Measures of Deformation-rates in Torsional Flows of Viscoelastic Fluids Between Two Infinite Parallel Planes by : Moon Up Park
Download or read book Generalized Measures of Deformation-rates in Torsional Flows of Viscoelastic Fluids Between Two Infinite Parallel Planes written by Moon Up Park and published by . This book was released on 1971 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the generalized measures of deformation- rates involving not only velocity gradients but also acceleration gradients is given and constitutive equations using these measures have been discussed. These new constitutive equations are then used to study torsional flows of viscoelastic fluids between two infinite parallel planes. In order to assess the advantage of this theory over the existing theories, a brief review of the existing nonlinear theories of continuous media has been made. In this review, it has been pointed out that the existing theories involve a number of terms in powers and products of the ordinary measures of strain or strain-rate and several unknown response functions of invariants of kinematic matrices. This is owing to the fact that the order of the measures of strain and strain-rates have not been fixed and their generalized measures have not been used in the formulation of constitutive equations. In the present investigation we have, by fixing a priori the orders of the measures of the deformation-rates mentioned above, developed the concept of the generalized measures and been able to obtain a suitable constitutive equation for viscoelastic fluids. The orders of the measures are so chosen that the resulting constitutive equation describes pseudoplastic fluids, for which the apparent coefficient of viscosity decreases with the increase in rate of shear. These new constitutive equations have been found to contain only four terms in the deformation-rate tensors and four rheological constants, and no unknown functions of the invariants. The constitutive equation obtained thus is applied to torsional flows of a viscoelastic fluid between two infinite parallel planes. The velocity components and pressure have been expanded in power series of a small parameter, and first- and second-order approximations to the velocity components have been obtained. The normal stress differences, velocity profiles, apparent coefficient of viscosity and their behavior depending on the rheological constants nave been investigated. The phenomena of reversed flows have also been discussed. Besides the freedom to choose the order of the measures, the rheological parameter entering the constitutive equations can also be suitably varied so as to correlate the theory with experiments. It is found that the behavior of a viscoelastic fluid depends on the sign as well as the magnitude of the rheological constants. Thus, the constitutive equations based on the concept of combined generalized measures predict adequately qualitative as well as quantitative information on the behavior of viscoelastic fluids and eliminate the need for assuming unknown response coefficients.
Book Synopsis Recent Advances in Engineering Science by : Society of Engineering Science
Download or read book Recent Advances in Engineering Science written by Society of Engineering Science and published by . This book was released on 1977 with total page 1408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings ... Annual Meeting of the Society of Engineering Science,inc by : Society of Engineering Science
Download or read book Proceedings ... Annual Meeting of the Society of Engineering Science,inc written by Society of Engineering Science and published by . This book was released on 1977 with total page 1400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Translation of Two Contacting Spheres in a Viscoelastic Fluid by : Mohammad Amin Jefri
Download or read book Translation of Two Contacting Spheres in a Viscoelastic Fluid written by Mohammad Amin Jefri and published by . This book was released on 1983 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Experiments on the Flow of Viscoelastic Fluids Between Eccentric Rotating Cylinders by : Steven Roy Burdette
Download or read book Experiments on the Flow of Viscoelastic Fluids Between Eccentric Rotating Cylinders written by Steven Roy Burdette and published by . This book was released on 1987 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Viscoelastic Fluid Flow in the Disk and Cylinder System by : Christopher Thomas Hill
Download or read book Viscoelastic Fluid Flow in the Disk and Cylinder System written by Christopher Thomas Hill and published by . This book was released on 1969 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1969 with total page 1090 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Experimental and Theoretical Study of the Flow about Spheres and Discs Rotating Slowly in Viscoelastic Fluids by : Eugene Kenneth Cairncross
Download or read book An Experimental and Theoretical Study of the Flow about Spheres and Discs Rotating Slowly in Viscoelastic Fluids written by Eugene Kenneth Cairncross and published by . This book was released on 1974* with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Study of Sphere Migration and Interactions in a Viscoelastic Fluid Undergoing Oscillatory Couette Flow by : Bradley Michael Lormand
Download or read book The Study of Sphere Migration and Interactions in a Viscoelastic Fluid Undergoing Oscillatory Couette Flow written by Bradley Michael Lormand and published by . This book was released on 2002 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elements of Stability of Viscoelastic Fluids by : J. Dunwoody
Download or read book Elements of Stability of Viscoelastic Fluids written by J. Dunwoody and published by Longman. This book was released on 1989 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analytical Study of Viscoelastic Fluid Flow in the Disc and Cylinder System by : John Michael Kramer
Download or read book Analytical Study of Viscoelastic Fluid Flow in the Disc and Cylinder System written by John Michael Kramer and published by . This book was released on 1969 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1970 with total page 1338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamics of Polymeric Liquids, Volume 1 by : R. Byron Bird
Download or read book Dynamics of Polymeric Liquids, Volume 1 written by R. Byron Bird and published by Wiley-Interscience. This book was released on 1987-05-27 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revision of an introductory text examines Newtonian liquids and polymer fluid mechanics. It begins with a review of the main ideas of fluid dynamics as well as key points of Newtonian fluids.
Book Synopsis Observation of Elastic Effects in Confined Flow of Viscoelastic Fluids by : Jason R. Stokes
Download or read book Observation of Elastic Effects in Confined Flow of Viscoelastic Fluids written by Jason R. Stokes and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The effect of elasticity on the secondary motion of viscoelastic fluids due to swirl was analysed using flow visualisation. A closed cylinder containing a rotating base was used to induce the swirling motion of a flexible polymer Boger fluid. The secondary motion is observed to flow in the opposite direction to that for Newtonian fluids at low rotation rates. As the rotation rate is increased an instability is observed where the vortex core is seen to spiral with the primary motion of the fluid and an asymmetrical ting vortex appears on the centre of the rotating base.
Book Synopsis Experiments in the Stability of Rotating Flows for Viscoelastic Fluids by : Bakul Ratilal Kamani
Download or read book Experiments in the Stability of Rotating Flows for Viscoelastic Fluids written by Bakul Ratilal Kamani and published by . This book was released on 1971 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rotating Flow written by Peter Childs and published by Elsevier. This book was released on 2010-10-29 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rotating flow is critically important across a wide range of scientific, engineering and product applications, providing design and modeling capability for diverse products such as jet engines, pumps and vacuum cleaners, as well as geophysical flows.Developed over the course of 20 years’ research into rotating fluids and associated heat transfer at the University of Sussex Thermo-Fluid Mechanics Research Centre (TFMRC), Rotating Flow is an indispensable reference and resource for all those working within the gas turbine and rotating machinery industries.Traditional fluid and flow dynamics titles offer the essential background but generally include very sparse coverage of rotating flows—which is where this book comes in. Beginning with an accessible introduction to rotating flow, recognized expert Peter Childs takes you through fundamental equations, vorticity and vortices, rotating disc flow, flow around rotating cylinders and flow in rotating cavities, with an introduction to atmospheric and oceanic circulations included to help deepen understanding.Whilst competing resources are weighed down with complex mathematics, this book focuses on the essential equations and provides full workings to take readers step-by-step through the theory so they can concentrate on the practical applications. A detailed yet accessible introduction to rotating flows, illustrating the differences between flows where rotation is significant and highlighting the non-intuitive nature of rotating flow fields Written by world-leading authority on rotating flow, Peter Childs, making this a unique and authoritative work Covers the essential theory behind engineering applications such as rotating discs, cylinders, and cavities, with natural phenomena such as atmospheric and oceanic flows used to explain underlying principles Provides a rigorous, fully worked mathematical account of rotating flows whilst also including numerous practical examples in daily life to highlight the relevance and prevalence of different flow types Concise summaries of the results of important research and lists of references included to direct readers to significant further resources
