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In the context of particulate motion the Péclet number has also been called Brenner number, with symbol Br, in honour of Howard Brenner. [ 2 ] The Péclet number also finds applications beyond transport phenomena, as a general measure for the relative importance of the random fluctuations and of the systematic average behavior in mesoscopic ...
[1] [2] [3] The effect is named after the British fluid dynamicist G. I. Taylor, who described the shear-induced dispersion for large Peclet numbers. The analysis was later generalized by Rutherford Aris for arbitrary values of the Peclet number. The dispersion process is sometimes also referred to as the Taylor-Aris dispersion.
Solution in the central difference scheme fails to converge for Peclet number greater than 2 which can be overcome by using an upwind scheme to give a reasonable result. [1]: Fig. 5.5, 5.13 Therefore the upwind differencing scheme is applicable for Pe > 2 for positive flow and Pe < −2 for negative flow. For other values of Pe, this scheme ...
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.
When Pe=0 (no flow, or pure diffusion), Figure shows that solution, may be interpolated using a simple linear average between the values at x=0 and x=L. When the Peclet number has an intermediate value, the interpolated value for at x=L/2 must be derived by applying the power law equivalent. The simple average convection coefficient formulation ...
Small values of the Prandtl number, Pr ≪ 1, means the thermal diffusivity dominates. Whereas with large values, Pr ≫ 1, the momentum diffusivity dominates the behavior. For example, the listed value for liquid mercury indicates that the heat conduction is more significant compared to convection, so thermal diffusivity is dominant. However ...
is a typical velocity of the flow, is a typical length scale of the flow, is the magnetic diffusivity. The mechanism by which the motion of a conducting fluid generates a magnetic field is the subject of dynamo theory. When the magnetic Reynolds number is very large, however, diffusion and the dynamo are less of a concern, and in this case ...
The turbulent Schmidt number is commonly used in turbulence research and is defined as: [3] = where: is the eddy viscosity in units of (m 2 /s); is the eddy diffusivity (m 2 /s).; The turbulent Schmidt number describes the ratio between the rates of turbulent transport of momentum and the turbulent transport of mass (or any passive scalar).