The Stability of Natural Convection in a Vertical Fluid Layer with Internal Heat Generation

Abstract

Linear stability theory is applied to the problem of the stability of natural convection which occurs in a vertical fluid layer with uniformly distributed internal heat sources. The two parallel bounding plates are assumed to be maintained at constant and equal temperature. The power series method is adopted to obtain essentially exact values of the critical Reynolds number R c , the critical wavenumber α c and the crtical wave speed c c for ten finite values of the Prandtl number P ranging from 0.01 to 1000. It is shown that the power series method is a powerful tool for linear stability problems when the values of α R M and α R P M are both less than about 8000, where M is the maximum value of \(|\overline{W}{-}c|\), \(\overline{W}\) being the dimensionless velocity profile of the base flow.