Hydromagnetic Stability of a Liquid Film Flowing down an Inclined Conducting Plane

Abstract

The stability analysis is presented for a film of a viscous, electrically conducting liquid flowing down an inclined plane in the presence of a magnetic field applied perpendicular to the plane which is also electrically conducting. The resulting Orr-Sommerfeld equation is solved by a regular parturbation technique for disturbances of wavelengths large compared with the thickness of the film. Conductivity of the plane is found to delay the onset of instability.