Rayleigh Number
When a thin layer of fluid is heated from below or cooled from above, the upward heat transfer can be achieved by conduction, that is, in the absence of motion on the part of the fluid because its viscosity cannot be overcome by the buoyancy forces. However, this can occur only in the rather extreme case of a very thin and very viscous fluid
For a horizontal fluid layer of thickness H in contact with a lower temperature T along its top surface and with a higher temperature T + ?T along its bottom, the threshold separating the quiet from the convective regime is expressed in terms of the Rayleigh number:
Ra = ?g?T(H^3)/??
in which ? is the thermal expansion coefficient, ? the kinematic viscosity, and ?
is the thermal diffusivity.
No convective motion occurs at low values of the Rayleigh number, Ra < 1708, and the fluid transports heat exclusively by molecular heat diffusion. At Rayleigh numbers slightly exceeding the critical value of 1708, convection occurs in alternating patterns of upward and downward motion.