Péclet number

In fluid dynamics, the Péclet number is a dimensionless number relating the rate of advection of a flow to its rate of diffusion, often thermal diffusion. It is equivalent to the product of the Reynolds number with the Prandtl number in the case of thermal diffusion, and the product of the Reynolds number with the Schmidt number in the case of mass dispersion.

For thermal diffusion, the Péclet number is defined as:

:$mathrm\{Pe\}\_L\; =\; frac\{L\; V\}\{alpha\}\; =\; mathrm\{Re\}\_L\; cdot\; mathrm\{Pr\}.$

For mass diffusion, it is defined as:

:$mathrm\{Pe\}\_L\; =\; frac\{L\; V\}\{D\}\; =\; mathrm\{Re\}\_L\; cdot\; mathrm\{Sc\}$

where

* "L" - characteristic length
* "V" - Velocity
* α - Thermal diffusivity $=\; frac\{k\}\{\; ho\; c\_p\}$
* "D" - mass diffusivity

and

* "k" - Thermal conductivity
* ρ - Density
* $c\_p$ - Heat capacity

In engineering applications the Péclet number is often very large. In such situations, the dependency of the flow upon "downstream" locations is diminished, and variables in the flow tend to become 'one-way' properties. Thus, when modelling certain situations with high Péclet numbers, simpler computational models can be adopted. [Patankar, Numerical Heat Transfer and Fluid Flow, ISBN 0891165223, p 102]

A flow will often have different Péclet numbers for heat and mass. This can lead to the phenomenon of double-diffusive convection.

In the context of particulate motion the Péclet numbers have also been called Brenner numbers, with symbol "Br", in honour of Howard Brenner [Promoted by S. G. Mason in publications from "circa" 1977 onward, and adopted by a number of others.] .

ee also

* Reynolds number
* Prandtl number
* Schmidt number

References