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At a critical Rayleigh number of 1708, [5] instability sets in and convection cells appear. 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 ]
This work laid the foundation for the study of Rayleigh–Bénard convection, the buoyancy-driven flow of fluid confined between horizontal conducting surfaces, with the higher temperature at the bottom; and Bénard–Marangoni convection, the surface-tension-driven flow of a fluid with an upper free surface and a heated, conducting surface at ...
Another instance of the Marangoni effect appears in the behavior of convection cells, the so-called Bénard cells. One important application of the Marangoni effect is the use for drying silicon wafers after a wet processing step during the manufacture of integrated circuits. Liquid spots left on the wafer surface can cause oxidation that ...
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 ...
A fluid under Rayleigh–Bénard convection: the left picture represents the thermal field and the right picture its two-dimensional Fourier transform. Convection, especially Rayleigh–Bénard convection, where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a pattern-forming system.
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
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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 ...