Nonlinear convection with inclined temperature gradient and horizontal mass flow

The energy method, which gives sufficient condition for the stability, is developed for the convection problem in a thin horizontal layer, subjected to an applied inclined temperature gradient and horizontal mass flow. The boundaries are considered to be rigid and perfectly conducting. Both linear and nonlinear stability analyses, which are valid for moderately large Prandtl number, are carried out. The eigenvalue problem is solved by the compound matrix method and the effects of various parameters in the stability results are pointed out. Comparison between the results of the linear theory and the energy stability theory show a marked difference in the stability boundaries. (C) 1997 Elsevier Science Ltd.