Rayleigh-Bénard Plume Dynamics

Thermal convection between heated bottom and cooled top plates

Rayleigh Number Ra = 4000

Prandtl Number Pr = 7

Viscosity ν = 0.06

Convection onset at Ra > Ra_c ≈ 1708. Hot plumes rise from the bottom boundary layer; cold plumes descend from the top. The Nu–Ra scaling relation Nu ~ Ra^β governs heat transport (β ≈ 0.3 in experiments).