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Gravity causes denser parts of the fluid to sink, which is called convection. Lord Rayleigh studied [2] the case of Rayleigh-Bénard convection. [6] When the Rayleigh number, Ra, is below a critical value for a fluid, there is no flow and heat transfer is purely by conduction; when it exceeds that value, heat is transferred by natural ...
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 ...
Heat transfer is a discipline of ... thus influencing its own transfer. The latter process is often called "natural convection". ... The Rayleigh number can be ...
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 ]
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 ...
As the heat flow is increased, above a critical value of the Rayleigh number, the system undergoes a bifurcation from the stable conducting state to the convecting state, where bulk motion of the fluid due to heat begins. If fluid parameters other than density do not depend significantly on temperature, the flow profile is symmetric, with the ...
Bodenstein number: Bo or Bd = / = Max Bodenstein: chemistry (residence-time distribution; similar to the axial mass transfer Peclet number) [2] Damköhler numbers: Da = Gerhard Damköhler: chemistry (reaction time scales vs. residence time)