Rayleigh number

The Rayleigh number (Ra) is a dimensionless parameter that expresses the relationship between all the actions that positively contribute to motion in a fluid (floating force) and everything that is negatively opposed (viscosity and thermal diffusivity):


It is, therefore, possible to understand whether there is motion, or not, in conditions of natural convection; or if, due to the effect of the floating force resulting from the density field, which in turn is a consequence of the temperature field, motion in the fluid is triggered or not.

In the case where the Rayleigh number is lower than the critical value (equal to 1708), the buoyancy thrusts due to density gradients within the fluid do not succeed in overcoming the opposition of the kinematic viscosity: motion does not manifest itself, and the heat exchange takes place by simple conduction.

Vice versa, if Ra > 1708, the thrusts are such as to allow the overcoming of the resistance imposed by the product \(\mu\alpha\) and, therefore, the convection motion manifests itself: we are in a regime of natural convection.