# Péclet number

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One of the characteristic numbers for processes of convective heat transfer. The Péclet number characterizes the relation between the convective and molecular heat-transport processes in a flow of liquid: $$\mathrm{Pe} = \frac{v l}{\alpha} = \frac{C_p \rho v}{\lambda/l}$$ where $l$ is the characteristic linear scale of the heat-transfer surface, $v$ is the velocity of the liquid relative to that surface, $\alpha$ is thermal diffusion coefficient, $C_p$ is the heat capacity at constant pressure, $\rho$ is the density, and $\lambda$ is the thermal conductivity coefficient.

The Péclet number is related to the Reynolds number $\mathrm{Re}$ and the Prandtl number $\mathrm{Pr}$ by $\mathrm{Pe} = \mathrm{Re}\cdot\mathrm{Pr}$.

It is named after J. Péclet.

#### References

• J. M. Kay, R. M. Nedderman, "An Introduction to Fluid Mechanics and Heat Transfer", 3rd ed., Cambridge University Press (1974) ISBN 0-521-20533-6 Zbl 0293.76001
How to Cite This Entry:
Péclet number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=P%C3%A9clet_number&oldid=39992
This article was adapted from an original article by Material from the article "PÃ©clet number" in BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article