Difference between revisions of "Péclet number"
From Encyclopedia of Mathematics
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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: | 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", 3<sup>rd</sup> ed., Cambridge University Press (1974) {{ISBN|0-521-20533-6}} {{ZBL|0293.76001}} | ||
| − | + | {{TEX|done}} | |
Latest revision as of 17:47, 14 November 2023
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=23450
Péclet number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=P%C3%A9clet_number&oldid=23450
This article was adapted from an original article by Material from the article "Péclet number" in BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article