The stability of natural convection due to internal heat sources in a vertical fluid layer

Linear stability theory is applied to the problem of stability of natural convection that occurs in a vertical 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 essentially exact values of the critical Grashof number Gc, the critical wavenumber αc and the critical frequency ωc are obtained for a wide range of the Prandtl number P.