STABILITY OF PLANE POISEUILLE FLOW WITH TEMPERATURE-DEPENDENT VISCOSITY

Classical linear stability theory is extended to include the effect of temperature dependent viscosity. This effect is studied asymptotically by using a Taylor series expansion of viscosity with respect to temperature. In its general form the asymptotic solution holds for all Newtonian fluids for which the temperature dependence of viscosity is the dominating variable property effect. A shooting technique with Gram-Schmidt orthonormalization for the zero-order equation (classical Orr-Sommerfeld problem) and a multiple shooting method for all other equations are applied to solve the stiff differential equations.