Instability of Laminar Natural Convection Boundary Layer Flow on a Vertical Porous Flat Plate

Abstract

The effects of uniform suction and injection on the linear stability theory of laminar natural convection boundary layer flow along a vertical porous flat plate which is maintained at a constant temperature are studied. The nonsimilar boundary layer equations for the basic steady flow have been solved numerically employing a very efficient finite difference scheme in combination with an iterative method for solving the resulting ordinary differential equations. The temporal neutral stability theory for wavelike disturbances of Tollmien-Schlichting type are then presented for the velocity and temperature functions. The corresponding eigenvalue problem for the disturbance amplitude functions is also solved numerically using a very accurate method. Results are presented graphically for both the basic and disturbance velocity and temperature profiles for some values of the modified local Grashof number G and suction or injection parameter X . The Prandtl number Pr is taken to be 0.73 (air) throughout this paper. The results show clearly the important role that suction or injection parameter X may have on the basic and disturbance flow characteristics in this problem.