The Stability of Natural Convection in an Inclined Fluid Layer with Internal Heat Generation. II

Abstract

Linear stability theory is applied to the problem of the stability of natural convection that occurs in an inclined fluid layer with uniformly distributed internal heat sources. It is assumed that one bounding plate is a thermally perfect insulator and the other bounding plate is maintained at constant temperature. The power series method is used to obtain the eigenvalue equation which is then solved numerically with the aid of the Muller method. The stability conditions are obtained for Prandtl numbers ranging from 0.001 to 100 and for angles of inclination ranging from -90° to 90°. It is found that the instability sets in as either transverse travelling wave modes or longitudinal stationary modes and that three-dimensional disturbances are not responsible for instability.