The stability and disturbance-amplification characteristics of vertical mixed convection flow

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Abstract
An experimental and theoretical investigation has been conducted to determine the stability and disturbance-amplification characteristics of the combined forced and free convection flow adjacent to a vertical uniform-heat-flux surface in a uniform free stream. Previous studies of the stability of mixed convection flows have been limited to linear stability analysis of the effect of weak buoyancy on the neutral stability of a stronger forced flow. Here we consider circumstances where forced-convection effects are small compared with buoyancy effects. The flow behaviour is analysed using linear stability theory. The analysis incorporates a new formulation which permits the calculation of amplification contours for a given flow circumstance. The governing equations have been solved numerically to generate stability planes including the neutral curve and constant amplification contours. Stability planes are presented for assisting and opposed flows at Prandtl numbers Pr of 0·733 and 6·7. In air (Pr = 0·733), the presence of a weak free stream is found to cause the disturbance-amplification rates and the filtered frequency to deviate strongly from those found in purely free-convection flow. In water (Pr = 6·7), the effect of a free stream is much weaker. In addition, hot-wire and thermocouple measurements of the filtered frequencies and the disturbance-amplitude distributions are presented for aiding mixed convection flow in air. The measurements are found to be in very good agreement with the calculated results of the stability analysis.