Stability of heated laminar boundary layers in water with nonuniform surface temperature

Abstract

As part of a continuing study of the stability of heated laminar boundary layers in water, an experiment has been performed for the case of nonuniform surface temperature where disturbances are introduced by a vibrating ribbon and the response measured using temperature compensated hot-film anemometry. Two types of nonuniform wall temperature distributions have been studied. These are: (a) power law distributions of the form ΔT= (Tw−T∞) =Axn, and (b) step changes in wall temperature. Measured mean velocity and temperature profiles agree with solutions of the mean boundary layer equations. Measured stability characteristics for power law temperature distributions indicate that, at a fixed Reynolds number and local ΔT, both the disturbance growth rate and the band of frequencies receiving amplification are reduced relative to the uniform wall temperature case when n<0 and increase relative to the uniform wall temperature case when n≳0. The maximum growth rate for ΔT =2.78°C (5°F) and n=−0.5 is negative indicating damped disturbances at all frequencies. Disturbance growth rates for step changes in wall temperature at first decrease and then increase relative to those for uniform wall temperature as the step change location is moved downstream.