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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 ...
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.
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, turbulent flow.
Fig 2: The grid used for discretisation in Upwind Difference Scheme for positive Peclet number (Pe>0) Fig 3: The grid used for discretisation in Upwind Difference Scheme for negative Peclet number (Pe < 0) By putting these values in equation and rearranging we get the following result,
[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.
It requires that transportiveness changes according to magnitude of peclet number i.e. when pe is zero is spread in all directions equally and as Pe increases (convection > diffusion) at a point largely depends on upstream value and less on downstream value. But central differencing scheme does not possess transportiveness at higher pe since Φ ...
A Nusselt number of order one represents heat transfer by pure conduction. [1]: 336 A value between one and 10 is characteristic of slug flow or laminar flow. [2] A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range. [2]
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 ...