In geophysics, the Rayleigh number is of fundamental importance: it indicates the presence and strength of convection within a fluid body such as the Earths mantle. The mantle is a solid that behaves as a fluid over geological time scales. The Rayleigh number for the Earths mantle due to internal heating alone, Ra, is given by:
where:
*H is the rate of radiogenic heat production per unit mass
*η is the dynamic viscosity
*k is the thermal conductivity
*D is the depth of the mantle.
A Rayleigh number for bottom heating of the mantle from the core, Ra, can also be defined as:
where:
*ΔT is the superadiabatic temperature difference between the reference mantle temperature and the core–mantle boundary
*C is the specific heat capacity at constant pressure.
High values for the Earth's mantle indicates that convection within the Earth is vigorous and time-varying, and that convection is responsible for almost all the heat transported from the deep interior to the surface.