The role of variable viscosity in the stability of channel flow

Pinarbasi A. , Liakopoulos A.

International Communications in Heat and Mass Transfer, vol.22, no.6, pp.837-847, 1995 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 6
  • Publication Date: 1995
  • Doi Number: 10.1016/0735-1933(95)00072-0
  • Title of Journal : International Communications in Heat and Mass Transfer
  • Page Numbers: pp.837-847


The stability of plane Poiseuille flow is studied for liquids exhibiting exponential viscosity-temperature dependence. In contrast to previously published studies, viscosity and temperature fluctuations are included in the formulation. Equations describing the evolution of small, two-dimensional disturbances are derived and the stability problem is formulated as an eigenvalue problem for a set of two ordinary differential equations. A Chebyshev collocation discretization method leads to a generalized matrix eigenvalue problem which is solved by the QZ algorithm. It is found that an imposed wall temperature difference, Δ T -, is always destabilizing. The instability region in the wavenumber-Reynolds number plane grows considerably as Δ T - increases. The influence of Prandtl number, temperature fluctuations and viscosity fluctuations on the flow stability/instability is small. However, their influence on the margin of stability for small wavenumbers is appreciable. © 1995.