THE ROLE OF VARIABLE VISCOSITY IN THE STABILITY OF CHANNEL FLOW

The stability of plane Poiseuille now is studied for liquids exhibitin g exponential viscosity-temperature dependence. Tn contrast to previou sly published studies, viscosity and temperature fluctuations are incl uded 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 differen tial equations. A Chebyshev collocation discretization method leads to a generalized matrix eigenvalue problem which is solved by the QZ alg orithm. It is found that an imposed wall temperature difference, Delta (T) over bar, is always destabilizing. The instability region in the wavenumber-Reynolds number plane grows considerably as Delta (T) over bar increases. The influence of Prandtl number, temperature fluctuatio ns and viscosity fluctuations on the flow stability/instability is sma ll. However, their influence on the margin of stability for small wave numbers is appreciable.