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

The energy method is developed to discuss the non-linear stability of conve ction in a horizontal porous layer subjected to an inclined temperature gra dient and a variable gravity field. Both linear and non-linear stability an alyses are carried out for a large number of parameter values. The eigenval ue problems in both cases are solved by the Chebyshev tau-QZ method with op timization routine. It is found that the preferred mode at the onset of con vection is a longitudinal mode and that a decrease in gravity variation has a stabilizing effect on the system. Comparisons between the linear and ene rgy stability results show that as the horizontal Rayleigh number increases the difference between the two results increases and thus indicates the po ssibility of subcritical instability. (C) 2001 Elsevier Science Ltd. All ri ghts reserved.