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8133 results in Fluid dynamics and solid mechanics

Page 44 of 407

Introductory Incompressible Fluid Mechanics
  • Frank H. Berkshire, Simon J. A. Malham, J. Trevor Stuart
  • Published online:
    05 January 2022
    Print publication:
    02 December 2021
  • This introduction to the mathematics of incompressible fluid mechanics and its applications keeps prerequisites to a minimum – only a background knowledge in multivariable calculus and differential equations is required. Part One covers inviscid fluid mechanics, guiding readers from the very basics of how to represent fluid flows through to the incompressible Euler equations and many real-world applications. Part Two covers viscous fluid mechanics, from the stress/rate of strain relation to deriving the incompressible Navier-Stokes equations, through to Beltrami flows, the Reynolds number, Stokes flows, lubrication theory and boundary layers. Also included is a self-contained guide on the global existence of solutions to the incompressible Navier-Stokes equations. Students can test their understanding on 100 progressively structured exercises and look beyond the scope of the text with carefully selected mini-projects. Based on the authors' extensive teaching experience, this is a valuable resource for undergraduate and graduate students across mathematics, science, and engineering.

Advanced Turbulent Combustion Physics and Applications
  • Edited by N. Swaminathan, X.-S. Bai, N. E. L. Haugen, C. Fureby, G. Brethouwer
  • Published online:
    09 December 2021
    Print publication:
    06 January 2022
  • Explore a thorough and up to date overview of the current knowledge, developments and outstanding challenges in turbulent combustion and application. The balance among various renewable and combustion technologies are surveyed, and numerical and experimental tools are discussed along with recent advances. Covers combustion of gaseous, liquid and solid fuels and subsonic and supersonic flows. This detailed insight into the turbulence-combustion coupling with turbulence and other physical aspects, shared by a number of the world leading experts in the field, makes this an excellent reference for graduate students, researchers and practitioners in the field.

  • ANZ VOLUME 63 ISSUE 4 COVER AND BACK MATTER

  • Journal:
    The ANZIAM Journal / Volume 63 / Issue 4 / October 2021
    Published online by Cambridge University Press:
    06 December 2021, pp. b1-b6
    • Article
      • You have access
    • PDF
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  • ANZ VOLUME 63 ISSUE 4 COVER AND FRONT MATTER

  • Journal:
    The ANZIAM Journal / Volume 63 / Issue 4 / October 2021
    Published online by Cambridge University Press:
    06 December 2021, pp. f1-f2
    • Article
      • You have access
    • PDF
    • Export citation

  • 4 - Navier–Stokes Flow

  • from Part II - Viscous Flow
  • Frank H. Berkshire, Imperial College of Science, Technology and Medicine, London, Simon J. A. Malham, Heriot-Watt University, Edinburgh, J. Trevor Stuart, Imperial College of Science, Technology and Medicine, London
  • Book:
    Introductory Incompressible Fluid Mechanics
    Published online:
    05 January 2022
    Print publication:
    02 December 2021, pp 143-181

  • Summary

    Recall our discussion on internal fluid forces in . Here and in the next two sections we consider the explicit form of the shear stresses and in particular the deviatoric stress matrix. This is necessary if we want to consider/model any real fluid, i.e. non-ideal fluid. We explain shear stresses as follows – see , p. 31).

  • 7 - Navier–Stokes Regularity

  • from Part II - Viscous Flow
  • Frank H. Berkshire, Imperial College of Science, Technology and Medicine, London, Simon J. A. Malham, Heriot-Watt University, Edinburgh, J. Trevor Stuart, Imperial College of Science, Technology and Medicine, London
  • Book:
    Introductory Incompressible Fluid Mechanics
    Published online:
    05 January 2022
    Print publication:
    02 December 2021, pp 253-296

  • Summary

    The well-posedness of smooth solutions to the three-dimensional incompressible Navier–Stokes equations globally in time is a major open mathematical problem. Our goal in this chapter is to provide a succinct though comprehensive introduction to the main well-posedness results that are known. In the three-dimensional case, we indicate how smooth solutions may develop singularities in finite time. At the same time we establish classical regularity assumptions/conditions that guarantee well-posedness globally in time, i.e. if we could prove three-dimensional incompressible Navier–Stokes solutions satisfied those assumptions/conditions, then we would establish global regularity.

  • 2 - Ideal Fluid Flow

  • from Part I - Inviscid Flow
  • Frank H. Berkshire, Imperial College of Science, Technology and Medicine, London, Simon J. A. Malham, Heriot-Watt University, Edinburgh, J. Trevor Stuart, Imperial College of Science, Technology and Medicine, London
  • Book:
    Introductory Incompressible Fluid Mechanics
    Published online:
    05 January 2022
    Print publication:
    02 December 2021, pp 27-99

  • Summary

    Let us consider the forces that act on a small parcel of fluid in a fluid flow. There are two types:

    1. 1. External or body forces, these may be due to gravity or external electromagnetic fields. They exert a force per unit volume on the continuum.

    2. 2. Surface or stress forces, these are forces, molecular in origin, that are applied by the neighbouring fluid across the surface of the fluid parcel.

    The surface or stress forces are normal stresses and tangential or shear stresses. In this chapter we only include the stress forces across the fluid parcels due to pressure differentials, representing a specific component of the normal stresses, and we entirely ignore the shear stresses. In other words, we leave out the stress components essentially resulting from molecular diffusion. This is what defines ideal fluid flow.

  • 6 - Boundary-Layer Theory

  • from Part II - Viscous Flow
  • Frank H. Berkshire, Imperial College of Science, Technology and Medicine, London, Simon J. A. Malham, Heriot-Watt University, Edinburgh, J. Trevor Stuart, Imperial College of Science, Technology and Medicine, London
  • Book:
    Introductory Incompressible Fluid Mechanics
    Published online:
    05 January 2022
    Print publication:
    02 December 2021, pp 223-252

  • Summary

    The Reynolds numbers associated with flows past aircraft or ships are typically large, indeed of the order of 108 of 109; recall Remark 4.36 and . For individual wings or fins, the Reynolds number may be an order of magnitude or two smaller. However, such Reynolds numbers are still large and the flow around a wing for example is well approximated by Euler flow. We can imagine the flow over the top of the wing of an aircraft has a high relative velocity tangential to the surface wing directed towards the rear edge of the wing.

Page 44 of 407