The Stability of Natural Convection in a Vertical Fluid Layer Having Side Walls of Different Temperatures and Internal Heat Generation

Abstract

Linear stability theory is applied to the problem of the stability of natural convection in a vertical fluid layer. It is assumed that the two side walls are maintained at constant and different temperatures and the fluid layer is heated by uniformly distributed internal heat sources. The power series method is used to obtain the eigenvalue equation which is then solved numerically. The stability conditions are obtained for wide range of the Prandtl number. The numerical results show that when internal heat sources are present the instability takes the form of travelling waves in the critical state and the critical wave speeds are always negative.