Onset of Convection in a Liquid Film Flowing

Abstract

The thermal instability of a vicsious liquid film flowing down an inclined plane heated from below is studied analytically. The effects of Biot number at the free surface, the inclination, the Prandtl number and the Reynolds number on instability for the longitudinal and traverse rolls have shown that the longitudinal rolls have priority of occurence over the transverse rolls. For small Biot numbers with Pr = 7 and 100, the thermal entry region is more unstable than the fully developed region, but for large Biot numbers this situation is reversed.