Some Further Results on the Bénard Problem

Abstract

The exact solution of the sixth‐order differential equation which governs the stability of a viscous fluid contained between two rigid walls and heated from below is briefly reviewed and extended to include detailed results on the curve of neutral stability and the cell pattern at the onset of instability. Two approximate methods of solution are then discussed which employ a Fourier or Fourier‐type expansion and which require the solution of only a fourth‐ or a second‐order differential equation. A comparison of these approximate results with the exact solution gives some insight into the relative accuracy of these methods when applied to other more general problems for which an exact solution cannot be obtained.