The role of variable viscosity in the stability of channel flow

Abstract

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.