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2017 | Buch

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Viscous Flows

Stretching and Shrinking of Surfaces

verfasst von: Ahmer Mehmood

Verlag: Springer International Publishing

Buchreihe : Mathematical Engineering

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

This authored monograph provides a detailed discussion of the boundary layer flow due to a moving plate. The topical focus lies on the 2- and 3-dimensional case, considering axially symmetric and unsteady flows. The author derives a criterion for the self-similar and non-similar flow, and the turbulent flow due to a stretching or shrinking sheet is also discussed. The target audience primarily comprises research experts in the field of boundary layer flow, but the book will also be beneficial for graduate students.

Inhaltsverzeichnis

Frontmatter

Essential Fundamental Material

Frontmatter

Chapter 1. Viscous Flow Due to Moving Continuous Surfaces

Abstract

Boundary layer flow due to moving continuous surfaces is the subject of this book. Since the very first studies on the boundary layer flows, the viscous flows past the surfaces of finite length had been the subject of interest in the majority of the studies. Moreover, most of the books concerning the boundary layer flows do also prefer to consider the boundary layer flow past the surfaces of finite length. Under these circumstances, it seems quite important to embark in a bit detail on the boundary layer character of the viscous flow caused by the moving continuous surfaces involving no leading edge. In this chapter, the boundary layer flow due to uniformly translating surface and stretching or shrinking surfaces have been introduced.

Ahmer Mehmood

Chapter 2. Governing Equations

Abstract

In this chapter, the boundary layer character of the flow due to moving continuous surfaces has been confirmed. The differential and integral boundary layer equations corresponding to the planar and axisymmetric cases have also been presented.

Ahmer Mehmood

Chapter 3. The Concept of Self-similarity

Abstract

One of the important classes of boundary-layer flows comprises the self-similar flows. The concept of self-similarity is equally important in mathematical as well as physical point of views. In this chapter, the concept of self-similarity has been explained in a bit detail. The general procedure for determining the similarity transformations has also been explained by considering suitable examples.

Ahmer Mehmood

Chapter 4. Solution Techniques

Abstract

In this chapter, some suitable solution techniques have been mentioned for the solution of boundary layer equations arising in this book.

Ahmer Mehmood

Self-similar Flows

Frontmatter

Chapter 5. The Criterion of Self-similarity for Wall Velocities

Abstract

In this chapter, the criterion of self-similarity for the two- and three-dimensional flows and the axially symmetric flows has been derived completely. The construction of similarity variables for these flows has been done in full detail.

Ahmer Mehmood

Chapter 6. Viscous Flow Due to Accelerated/Decelerated Stretching Surfaces

Abstract

Boundary layer flows due to different stretching surfaces have been considered in this chapter. The designation of the wall velocities as accelerated or decelerated has also been highlighted as it plays an important role in the understanding of shrinking sheet flows, in particular. Equivalence of the two-dimensional and the disk cases has been proved and it is shown that the disk case can easily be recovered from the two-dimensional case.

Ahmer Mehmood

Chapter 7. Viscous Flow Due to the Shrinking Surfaces

Abstract

In this chapter, the viscous flow due to shrinking continuous surfaces has been considered. It has been proved that the general perceptions, regarding the nonexistence and the multiplicity of the solution, about the shrinking surface flows are wrong. It has been shown that in the existing literature the shrinking surface flow has never been studied in accordance with the correct physics. It is also shown that the correct analysis of this flow does not exhibit far more different behavior than the stretching surface flows.

Ahmer Mehmood

Chapter 8. Unsteady Flow Due to the Stretching/Shrinking Surfaces

Abstract

The preceding three chapters have strictly been restricted to the cases of steady viscous flows due to the motion of continuous surfaces. The similarity criterion has been established for such flows regarding the rectangular and axisymmetric flow geometries. So far, attention has not been given to the unsteady flows of this category regarding the existence of self-similarity, in this book. This chapter is particular to the unsteady flows regarding the determination of similarity criterion in the planar and axisymmetric flow situations.

Ahmer Mehmood

Non-similar Flows

Frontmatter

Chapter 9. Two-Dimensional Non-similar Flows

Abstract

In the previous part, it has been seen that the wall velocities either follow the power law or the exponential forms in order to ensure the self-similar solution. Particular to the two-dimensional case, all other forms of the wall velocities result in the nonsimilar flows. In this chapter, the nonsimilar formulation for the planar two-dimensional case has been presented. As an examplary case, the accelerated and decelerated wall velocities of Howarth's type has been investigated in detail.

Ahmer Mehmood

Chapter 10. Axially Symmetric Non-similar Flows

Abstract

In the continuation of the previous chapter, the nonsimilar flow in the axially symmetric case is the subject under consideration here. The nonsimilar formulations for the cylinder and the disk cases have been presented and some particularly chosen flows have also been discussed in this chapter.

Ahmer Mehmood

Chapter 11. Time-Dependent Non-similarity

Abstract

In the previous part, it has already been seen that the concept of similarity is not particular to the space variables only but is also equally applicable to the time variable. Ultimately, the happening of nonsimilar flows due to the time variable can never be ignored. In this chapter, the temporal nonsimilarity has been modeled and some particular time-dependent nonsimilar flows have also been investigated.

Ahmer Mehmood

Turbulent Flows

Frontmatter

Chapter 12. Turbulent Flow Due to Moving Continuous Surfaces

Abstract

The turbulent flow due to moving continuous surfaces is another aspect of the viscous boundary-layers in addition to the laminar flows presented in the previous two parts.

Ahmer Mehmood

Titel: Viscous Flows
verfasst von: Ahmer Mehmood
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-55432-7
Print ISBN: 978-3-319-55431-0
DOI: https://doi.org/10.1007/978-3-319-55432-7

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