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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 critical Rayleigh number can be obtained analytically for a number of different boundary conditions by doing a perturbation analysis on the linearized equations in the stable state. [16] The simplest case is that of two free boundaries, which Lord Rayleigh solved in 1916, obtaining Ra = 27 ⁄ 4 π 4 ≈ 657.51. [ 17 ]
A comprehensive review of thermomagnetic convection (in A. Mukhopadhyay, R. Ganguly, S. Sen, and I. K. Puri, "Scaling analysis to characterize thermomagnetic convection", International Journal of Heat and Mass Transfer 48:3485-3492, (2005)) also shows that this form of convection can be correlated with a dimensionless magnetic Rayleigh number.
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.
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 heat addition causes a decrease in stagnation pressure, which is known as the Rayleigh effect and is critical in the design of combustion systems. Heat addition will cause both supersonic and subsonic Mach numbers to approach Mach 1, resulting in choked flow. Conversely, heat rejection decreases a subsonic Mach number and increases a ...
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