Linear Spatial Stability Analysis of Mixed Convection Boundary Layer over a Heated Plate

Abstract

The spatial stability properties of a mixed convection boundary layer developed over a heated horizontal flat plate is investigated under the linear and quasi-parallel assumptions by solving the Orr-Sommerfeld equations. The main aim of this work is to find a critical buoyancy parameter above which a qualitative change in the stability characteristics of the mixed convection boundary layer due to the influence of heat transfer is displayed. The equilibrium flow used here is that given by the similarity solution of [1] which implies the wall temperature to vary as the inverse square root of the distance from the leading edge of the plate. The Orr-Sommerfeld equation has been solved by using the compound matrix method (CMM)-- which locates all the modes in a chosen range of complex wave number, for spatial stability analysis. Cases with different buoyancy parameters have been investigated which were earlier reported incorrectly in [2]. Results indicate modifications of the hydrodynamic mode with certain buoyancy parameter for which continuous existence of instability as the flow develops downstream. The erroneous results in the above mentioned paper is associated with the wrong choice of compound variables used in CMM and the associated dispersion relation satisfied at the wall. Key Words: Mixed Convection Flow; Orr-Sommerfeld Equation; Spatial Stability Analysis; Compound Matrix Method (CMM)