Long-Wave Instability of Advective Flows in Inclined Layer with Solid   Heat Conductive Boundaries
  We investigate the stability of the steady convective flow in a plane tilted layer with ideal thermal conductivity of solid boundaries in the presence of uniform longitudinal temperature gradient. Analytically found the stability boundary with respect to the long-wave perturbations, find the critical Grashof number for the most dangerous among them of even spiral perturbation. 
R. V. Sagitov, A. N. Sharifulin
physics.flu-dyn math-ph math.MP