Non-linear convection in a porous medium with inclined temperature gradient and variable gravity effects

Abstract

The energy method is developed to discuss the non-linear stability of convection in a horizontal porous layer subjected to an inclined temperature gradient and a variable gravity field. Both linear and non-linear stability analyses are carried out for a large number of parameter values. The eigenvalue problems in both cases are solved by the Chebyshev tau-QZ method with optimization routine. It is found that the preferred mode at the onset of convection is a longitudinal mode and that a decrease in gravity variation has a stabilizing effect on the system. Comparisons between the linear and energy stability results show that as the horizontal Rayleigh number increases the difference between the two results increases and thus indicates the possibility of subcritical instability.