View source for Prandtl number

One of the characteristics of similarity of heat processes in fluids and gasses. The Prandtl number depends only on the thermodynamical state of the medium, and is defined by

<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/p074/p074260/p0742601.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074260/p0742602.png" /> is the kinematic coefficient of viscosity, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074260/p0742603.png" /> is the dynamic coefficient of viscosity, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074260/p0742604.png" /> is the density, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074260/p0742605.png" /> is the coefficient of heat conductivity, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074260/p0742606.png" /> is the coefficient of thermal diffusion, and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074260/p0742607.png" /> is the specific heat capacity of the medium at constant pressure.

The Prandtl number is connected with other characteristics of similarity, the [[Péclet number|Péclet number]] and the [[Reynolds number|Reynolds number]], by the relation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074260/p0742608.png" />.

The Prandtl number is named after L. Prandtl.



====Comments====
The Prandtl number is sometimes also called the Darcy–Prandtl number.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  N. Curle,   H.J. Davies,   "Modern fluid dynamics" , '''II''' , v. Nostrand-Reinhold  (1971)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  S. Chandrasekhar,   "Hydrodynamics and hydrodynamic stability" , Dover, reprint  (1981)  pp. Chapt. VII</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  C.-S. Yih,   "Stratified flows" , Acad. Press  (1980)</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top">  L.D. Landau,   E.M. Lifshitz,   "Fluid mechanics" , Pergamon  (1959)  pp. 203, 208  (Translated from Russian)</TD></TR></table>