Wave Instability of Mixed Convection Flow Along a Vertical Flat Plate

Abstract

An analysis is performed to investigate the linear wave instability of laminar mixed convection flow over an isothermal vertical flat plate, in which the buoyancy force arises solely from the temperature gradients in the fluid. In the stability analysis, the main flow and thermal fields are treated as nonparallel, and are obtained by the local nonsimilarity solution method The eigenvalue problem consisting of the linearized system of coupled differential equations for the velocity and temperature disturbances are solved by a direct Runge-Kutta numerical integration scheme along with a filtering technique to remove the “parasitic errors” inherent in the numerical integration of the disturbance equations. Neutral stability curves and critical Reynolds numbers are presented for a range of buoyancy parameters covering both assisting and opposing flow situations for two representative Prandtl numbers of 0.7 and 7. It is found that the flow becomes more stable as the buoyancy force increases for assisting flow and less stable as the buoyancy force increases for opposing flow. The curve of Grashof number versus Reynolds number that separates the unstable flow region from the stable one is also presented.