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

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 the two bounding plates are maintained at constant and equal 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 1000 and for angles of inclination ranging from 0° to 90°. It is found that the instability sets in as either transverse travelling wave modes or longitudinal stationary modes and three-dimensional disturbances are not responsible for instability.