# Péclet number

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://www.encyclopediaofmath.org/index.php?title=P%C3%A9clet_number&oldid=39992