The effect of buoyancy on the stability mixed convection flow over a horizontal plate

Abstract

The effect of buoyancy on the stability of mixed convection flow over a horizontal plate has been studied using high accuracy numerical methods. Present analysis is valid when the buoyancy force effects are small compared to forced convection effects. The mixed convection flow problem is formulated by two-dimensional incompressible flow with the buoyancy term represented by the Boussinesq approximation. The non-similar mixed convection boundary layer equations are solved directly by direct integration method without any approximation for non-similar terms. The spatial stability equations are solved using Compound matrix method (CMM). CMM allows finding the correct eigenvalues and removes the stiffness present in the stability system of equations. Neutral curves and critical parameters are reported for assisting and opposing mixed convection flows for air. Results show a qualitative change in instability properties and a double loop of neutral curve appears suddenly at a particular value of buoyancy parameter ( ξ ) for assisting flows. The lower loop of the neutral curve diminishes and disappears as the buoyancy parameter increases for assisting mixed convection flows. The onset of transition occurs due to buoyancy force only for ξ ≥ 0.005 . The reported critical buoyancy parameter value matches very well with the experimental values available in the literature. Results show that the flow becomes less stable as the buoyancy force increases for assisting mixed convection flow and more stable as the buoyancy force increases for the opposing mixed convection flow.