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In fluid thermodynamics, Rayleigh–Bénard convection is a type of natural convection, occurring in a planar horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as Bénard cells.
Since it was first proposed, many experimental and real-world applications have been related to the waterwheel dynamics. These include instances like the dynamics for electro-rotation, haline oceanic flow, and Rayleigh–Benard convection. [8]
The choice R(u) = u(1 − u) yields Fisher's equation that was originally used to describe the spreading of biological populations, [3] the Newell–Whitehead-Segel equation with R(u) = u(1 − u 2) to describe Rayleigh–Bénard convection, [4] [5] the more general Zeldovich–Frank-Kamenetskii equation with R(u) = u(1 − u)e-β(1-u) and 0 ...
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. When heat is fed into the system from one direction (usually below), at small values it merely diffuses ( conducts ) from below upward, without causing fluid flow.
Schematic of D2Q9 lattice vectors for 2D Lattice Boltzmann. Unlike CFD methods that solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice.
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 ...
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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 ...