 Rayleigh number

The Rayleigh number compares buoyancy driving with viscous and thermal diffusion. For a layer of thickness $h$, temperature drop $\Delta T$, density $\rho$, thermal expansion coefficient ${\alpha }_T$, gravitational acceleration $g$, thermal diffusivity $\kappa$, and dynamic viscosity $\mu$,Thermal convection begins when this exceeds a geometry-dependent critical value.

The Rayleigh number (Ra) is a dimensionless number that characterizes the flow and stability of fluids in a system when buoyancy forces are significant compared to viscous forces. It is particularly important in the study of convection, particularly natural convection, where fluid motion is induced by differences in temperature and thus density.