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Grashof number: relates the gravity body forces and the viscous forces
L is the length scale and is the thermal expansion coefficient
A high Grashof number, Gr > 1, means that the flow is going to cycle a lot since the buoyancy forces are dominating. If the Grashof number is low, Gr < 1, then the viscous forces dominate the buoyancy forces, meaning that the fluid will not circulate very much and hence less convection occurs.
When air is subject to a high temperature gradient, the Grashof number tends to be high and the air cycles freely, due to a low viscosity. Contrastingly if wax is subject to a high temperature gradient, the Grashof number will tend to be low due to larger viscous forces.
Rayleigh number: relates inertial force to the buoyancy force
This is often used for studying things like wind, where the wind provides a driven flow and buoyancy is introduced by convection.
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