Pattern selection for Darcy-Bénard convection with local thermal nonequilibrium

A weakly nonlinear analysis is performed on the classical Darcy-Bénard problem to determine the effects of local thermal nonequilibrium on the planform of convection immediately post-onset. It is found that two-dimensional rolls are always favoured.Although disturbances which are perpendicular to the roll whose stability is being assessed usually form the most dangerous mode of instability,it is also found that there are regions of parameter space where the cross-roll instability becomes inoperative as an instability mechanism.