For 10 points, name this dimensionless constant from fluid dynamics which determines whether a fluid is undergoing conduction or convection.
For a system containing stress-free surfaces, the critical value of this quantity is equal to twenty-seven over 4 times pi to the fourth power. For the Earth's mantle, this quantity is proportional to the product of the fifth power of the depth of the mantle and the radiogenic heat production. In one system, the critical value of this quantity is equal to 1708 at an eigenvalue of 3.2, above which the system forms Benard cells. In one system, this value is proportional to the difference between the surface temperature and the quiescent temperature, all times the cube of the (*) characteristic length. This quantity is proportional to the expansion coefficient and inversely proportional to the thermal diffusivity, and this value is also equal to the product of the Grashof and Prandtl numbers. For 10 points, name this dimensionless constant from fluid dynamics which determines whether a fluid is undergoing conduction or convection.
For a system containing stress-free surfaces, the critical value of this quantity is equal to twenty-seven over 4 times pi to the fourth power.
Rayleigh number