Multiple solutions and hysteresis in steady parallel viscous flows

Stephen H. Davis*, Gregory A. Kriegsmann, Robert L. Laurence, S. Rosenblat

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


A study is made of flows of viscous fluids when viscosity varies with temperature according to an Arrhenius law, and when viscous dissipation is taken into account. It is shown that for fluids with highly temperature-sensitive viscosity the graph of shear rate against shear stress is an S-shaped curve, with either one or three values of shear rate for given shear stress. In this situation hysteresis can occur if steady unidirectional flow is maintained. The velocity and temperature profiles are calculated, and the manner in which the temperature-sensitivity parameter affects the conclusions is discussed. The calculations serve as criteria for evaluating the importance of viscous-heating effects in applications.

Original languageEnglish (US)
Pages (from-to)1177-1182
Number of pages6
JournalPhysics of Fluids
Issue number5
StatePublished - 1983
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes
  • Computational Mechanics


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