effects of thermal nonequilibrium and non-uniform temperature gradients on the onset of convection in a heterogeneous porous medium

the simultaneous effect of local thermal nonequilibrium (ltne), vertical heterogeneity of permeability, and non-uniform basic temperature gradient on the criterion for the onset of darcy–benard convection is studied. the eigenvalue problem is solved numerically using the galerkin method. the interaction of various types of permeability heterogeneity and non-uniform basic temperature gradient functions on the stability characteristics of the system is analyzed. it is observed that the linear variation (about the mean) of the permeability and the basic temperature gradient with depth has no added effect on the criterion for the onset of convection. however, the concurrent variation in heterogeneous permeability and non-uniform basic temperature gradient functions has more stabilizing effect on the system, while opposite is the trend when the effect of non-uniform basic temperature gradient alone is present.