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Difference between revisions of "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:
 
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:
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$$
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\mathrm{Pe} = \frac{v l}{\alpha} = \frac{C_p \rho v}{\lambda/l}
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$$
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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.
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p0719401.png" /></td> </tr></table>
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The Péclet number is related to the [[Reynolds number]] $\mathrm{Re}$ and the [[Prandtl number]] $\mathrm{Pr}$ by $\mathrm{Pe} = \mathrm{Re}\cdot\mathrm{Pr}$.
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p0719402.png" /> is the characteristic linear scale of the heat-transfer surface, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p0719403.png" /> is the velocity of the liquid relative to that surface, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p0719404.png" /> is thermal diffusion coefficient, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p0719405.png" /> is the heat capacity at constant pressure, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p0719406.png" /> is the density, and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p0719407.png" /> is the thermal conductivity coefficient.
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It is named after J. Péclet.
  
The Péclet number is related to the [[Reynolds number|Reynolds number]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p0719408.png" /> and the [[Prandtl number|Prandtl number]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p0719409.png" /> by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p071/p071940/p07194010.png" />.
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====References====
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* 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}}
  
It is named after J. Péclet.
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{{TEX|done}}

Latest revision as of 18:19, 13 December 2016

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 "Péclet number" in BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article