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In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh [1]) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. [ 2 ] [ 3 ] [ 4 ] It characterises the fluid's flow regime: [ 5 ] a value in a certain lower range denotes laminar flow ; a value in a higher range ...
The L and D subscripts indicate the length scale basis for the Grashof number. The transition to turbulent flow occurs in the range 10 8 < Gr L < 10 9 for natural convection from vertical flat plates. At higher Grashof numbers, the boundary layer is turbulent; at lower Grashof numbers, the boundary layer is laminar, that is, in the range 10 3 ...
Richardson numbers higher than indicate that the flow problem is pure natural convection and the influence of forced convection can be neglected. [ 3 ] Like for natural convection, the nature of a mixed convection flow is highly dependent on heat transfer (as buoyancy is one of the driving mechanisms) and turbulence effects play a significant role.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
where S T, T T denote the salinity and temperature at top layer, S B, T B denote the salinity and temperature at bottom layer, Ra is the Rayleigh Number, and Pr is the Prandtl Number. The sign of Ra S and Ra T will change depending on whether it stabilizes or destabilizes the system.
[3] [4] k is the thermal conductivity of the fluid, L is the characteristic length with respect to the direction of gravity, Ra L is the Rayleigh number with respect to this length and Pr is the Prandtl number (the Rayleigh number can be written as the product of the Grashof number and the Prandtl number).
Figure 1(a-d) shows the evolution of salt fingers in heat-salt system for different Rayleigh numbers at a fixed R ρ. It can be noticed that thin and thick fingers form at different Ra T . Fingers flux ratio, growth rate, kinetic energy, evolution pattern, finger width etc. are found to be the function of Rayleigh numbers and R ρ .Where, flux ...
The Richardson number can also be expressed by using a combination of the Grashof number and Reynolds number, =. Typically, the natural convection is negligible when Ri < 0.1, forced convection is negligible when Ri > 10, and neither is negligible when 0.1 < Ri < 10.