Analysis of boundary layer control by heat transfer strips using an asymptotic approach to the PSE

Abstract

The effect of heating strips on the stability of boundary layer flow over a flat plate is investigated. Heating strips alter the flow stability through the temperature dependence of the fluid properties. A stability study is carried out using the parabolized stability equations (PSE) that calculates the effects of temperature dependent fluid properties in terms of asymptotic expansions based on the total heat input. The leading order influence is obtained as a general result and, for the particular Prandtl number taken, is independent of any special set of property laws. In a fluid for which the intrinsic viscosity increases with temperature and the density decreases with temperature (such as air) the results show that the optimal location for a heating strip to stabilise the flow is upstream of the neutral point. The optimal location moves further upstream as the total heat input level is increased. For a given heat input widening the heating strip further stabilises the flow. Finally, the potential of the asymptotic method as a tool for further analysis of the flow is discussed.