J. Fluid zyxwvutsrqpon iMech. zyxwvutsrqp (1992), zyxwvutsrqp vol. zyxwvutsr 243, pp. 1-14 Printed in Greut Britain 1 Influence of variable properties on the stability of two-dimensional boundary layers By H. HERWIG AND P. SCHAFER Institut fur Thermo- und Fluiddynamik, Ruhr-Universitat, D-4630 Bochum, Germany (Received 5 August 1991 and in revised form 26 February 1992) zyx Classical linear stability theory is extended to include the effects of temperature- and pressure-dependent fluid properties. These effects are studied asymptotically by using Taylor series expansions for all the properties with respect to temperature and pressure. In this asymptotic approach all effects are well separated from each other, and only the Prandtl number remains as a parameter. In their general form the asymptotic solutions hold fqr all Newtonian fluids. A shooting technique with Gram-Schmidt orthonormalizatidn for the zero-order equation (classical Orr- Sommerfeld problem) and a multiple shooting method for all other equations is applied to solve the stiff differential equations. In particular the zero- and first-order equations are solved for a flat-plate boundary-layer flow with temperature-dependent viscosity. Physically, this corresponds to a fluid with a linear viscosity/temperature relation. The results show that decreasing the viscosity in the near-wall region of the boundary layer stabilizes the flow, whereas it would be destabilized for a uniformly decreased viscosity. 1. Introduction Among the studies that have investigated the stability of laminar boundary-layer flows, only a few have taken into account the effeot of variable properties, even though non-constant properties can have a strong ,effect on the critical Reynolds number. For example, Wazzan et al. (1972) invcstigatcd the boundary-layer stability of water under non-isothermal conditions. They found that the critical Reynolds number for a heated flat-plate boundary layer in water varies between 520 and nearly 16000. Other studies of forced-convection stability which take into account variable-property effects in a more or less systematic way are those by Hauptmann (1968), Lee, Chen zyxwvu & Armaly (1990) and Asfar, Masad & Nayfeh (1990). Natural- convection flows with variable property effects beyond that of the Boussinesq approximation were studied by Sabhapathy & Cheng (1986) and Chen & Pearlstein (1989), for example. The present study outlines a general method which includes the effect of small temperature and pressure variations on the physical properties. Results of this analysis will hold for all Newtonian fluids instead of just one particular fluid. The basic approach starts from a Taylor series expansion of the properties with respect to temperature and pressure. Next, a regular perturbation is applied to the basic equations of stability with the constant-property case representing leading-order behaviour . The basic stability equations which allow for the variation of all physical properties are given in $2. In $3, the regular perturbation procedure is described in