Transition in inclined internally heated fluid layers

Sotos C. Generalis, Friedrich Busse

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.
Original languageEnglish
Title of host publicationProceedings 5th European Thermal-Sciences Conference
EditorsG.G.M. Stoffels, T.H. van der Meer, A.A. van Steenhoven
Place of PublicationEindhoven (NL)
PublisherEindhoven University of Technology
PagesFCV_10
ISBN (Print)9789038612744
Publication statusPublished - May 2008

Fingerprint

Grashof number
fluids
steady flow
Prandtl number
pressure gradients
inclination
disturbances
cross sections

Bibliographical note

5th European Thermal-Sciences Conference, 18-21 May 2008, Eindhoven (NL).

Keywords

  • non-linear solutions
  • homogeneously heated fluid layer
  • constant pressure gradient
  • critical Grashof number
  • linear stability analysis
  • bifurcating longitudinal rolls
  • secondary
  • solutions
  • streamwise x-coordinate
  • supercritical Grashof number
  • Prandtl numbers
  • angles of inclination
  • Hopf bifurcation

Cite this

Generalis, S. C., & Busse, F. (2008). Transition in inclined internally heated fluid layers. In G. G. M. Stoffels, T. H. van der Meer, & A. A. van Steenhoven (Eds.), Proceedings 5th European Thermal-Sciences Conference (pp. FCV_10). Eindhoven (NL): Eindhoven University of Technology.
Generalis, Sotos C. ; Busse, Friedrich. / Transition in inclined internally heated fluid layers. Proceedings 5th European Thermal-Sciences Conference. editor / G.G.M. Stoffels ; T.H. van der Meer ; A.A. van Steenhoven. Eindhoven (NL) : Eindhoven University of Technology, 2008. pp. FCV_10
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Generalis, SC & Busse, F 2008, Transition in inclined internally heated fluid layers. in GGM Stoffels, TH van der Meer & AA van Steenhoven (eds), Proceedings 5th European Thermal-Sciences Conference. Eindhoven University of Technology, Eindhoven (NL), pp. FCV_10.

Transition in inclined internally heated fluid layers. / Generalis, Sotos C.; Busse, Friedrich.

Proceedings 5th European Thermal-Sciences Conference. ed. / G.G.M. Stoffels; T.H. van der Meer; A.A. van Steenhoven. Eindhoven (NL) : Eindhoven University of Technology, 2008. p. FCV_10.

Research output: Chapter in Book/Report/Conference proceedingChapter

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PY - 2008/5

Y1 - 2008/5

N2 - Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.

AB - Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.

KW - non-linear solutions

KW - homogeneously heated fluid layer

KW - constant pressure gradient

KW - critical Grashof number

KW - linear stability analysis

KW - bifurcating longitudinal rolls

KW - secondary

KW - solutions

KW - streamwise x-coordinate

KW - supercritical Grashof number

KW - Prandtl numbers

KW - angles of inclination

KW - Hopf bifurcation

M3 - Chapter

SN - 9789038612744

SP - FCV_10

BT - Proceedings 5th European Thermal-Sciences Conference

A2 - Stoffels, G.G.M.

A2 - van der Meer, T.H.

A2 - van Steenhoven, A.A.

PB - Eindhoven University of Technology

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Generalis SC, Busse F. Transition in inclined internally heated fluid layers. In Stoffels GGM, van der Meer TH, van Steenhoven AA, editors, Proceedings 5th European Thermal-Sciences Conference. Eindhoven (NL): Eindhoven University of Technology. 2008. p. FCV_10