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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 ...
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom .
Genius (also known as the Genius Math Tool) is a free open-source numerical computing environment and programming language, [2] similar in some aspects to MATLAB, GNU Octave, Mathematica and Maple. Genius is aimed at mathematical experimentation rather than computationally intensive tasks. It is also very useful as just a calculator.
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 equation is named after Lord Rayleigh, who introduced it in 1880. [2] The Orr–Sommerfeld equation – introduced later, for the study of stability of parallel viscous flow – reduces to Rayleigh's equation when the viscosity is zero. [3] Rayleigh's equation, together with appropriate boundary conditions, most often poses an eigenvalue ...
It was fun to try to peck out words. 53045 looked like “shoes.” 5508 resembled “boss.” 37818 was “Bible” and 7734 was “hell.” This eventually led to the forbidden number 5318008.
Although named for Edgar Buckingham, the π theorem was first proved by the French mathematician Joseph Bertrand in 1878. [1] Bertrand considered only special cases of problems from electrodynamics and heat conduction, but his article contains, in distinct terms, all the basic ideas of the modern proof of the theorem and clearly indicates the theorem's utility for modelling physical phenomena.
The constants σ, ρ, and β are system parameters proportional to the Prandtl number, Rayleigh number, and certain physical dimensions of the layer itself. [3] The Lorenz equations can arise in simplified models for lasers, [4] dynamos, [5] thermosyphons, [6] brushless DC motors, [7] electric circuits, [8] chemical reactions [9] and forward ...