Long-wave instability of an advective flow in an inclined fluid layer with perfectly heat-conducting boundaries

Stability of a steady convective flow in a plane inclined layer with perfectly heat-conducting solid boundaries in the presence of a uniform longitudinal temperature gradient to long-wave perturbations is studied. The boundaries of the domain of stability to long-wave perturbations are found, and the critical Grashof numbers for the most dangerous even helical perturbations are determined.