Rayleighnumero

Rayleigh number, often denoted as Ra, is a dimensionless number that describes the ratio of buoyancy forces to viscous forces and describes the onset of convection in a fluid. It is named after Lord Rayleigh. The Rayleigh number is crucial in the study of natural convection and heat transfer in fluids.

The Rayleigh number is defined as the product of the Grashof number and the Prandtl number. The Grashof number (Gr) represents the ratio of buoyancy forces to viscous forces, while the Prandtl number (Pr) represents the ratio of momentum diffusivity to thermal diffusivity. Mathematically, Ra = Gr * Pr.

The specific formula for the Rayleigh number varies slightly depending on the context, but a common form for fluids heated from below is Ra = (g * β * ΔT * L³) / (ν * α), where g is the acceleration due to gravity, β is the coefficient of thermal expansion, ΔT is the temperature difference across the fluid layer, L is the characteristic length of the fluid layer, ν is the kinematic viscosity, and α is the thermal diffusivity.

A critical value of the Rayleigh number exists, below which heat transfer occurs primarily through conduction, and above which convection becomes the dominant mode of heat transfer. For a fluid layer heated from below with rigid boundaries, this critical Rayleigh number is approximately 1708. When Ra exceeds this value, instabilities arise, leading to the formation of convective cells and increased heat transport. The Rayleigh number is a key parameter in understanding phenomena such as atmospheric convection, ocean currents, and heat transfer in boiling and condensation processes.

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