Churchill-Bernstein Equation

In mass transfer dimensionless quantities.

Heat transfer definition

$\overline{Nu}_D \ = 0.3 + \frac{0.62Re_D^{1/2}Pr^{1/3}}{\left[1 + (0.4/Pr)^{2/3} \, \right]^{1/4} \,}\bigg[1 + \bigg(\frac{Re_D}{282000} \bigg)^{5/8}\bigg]^{4/5} \quad PrRe_D \ge 0.2$

where:

Re_D is the Reynolds number with the cylinder diameter as its characteristic length
$\Pr$ is the Prandtl numbers
$\overline{Nu}_D$ is the surface averaged Nusselt number with characteristic length of diameter

The Churchill Bernstein equation is valid for a wide range of Reynolds numbers and Prandtl numbers, as long as the product of the two is greater than or equal to 0.2, as defined above. The Churchill Bernstein equation can be used for any object of cylindrical geometry in which fluid dynamics. The equation yields the surface averaged Nusselt number, which is used to determine the average convective heat transfer coefficient. Newton's law of cooling can then be invoked to determine the heat loss or gain from the object, fluid and/or surface temperatures, and the area of the object, depending on what information is known.

Mass transfer definition

$Sh = 0.3 + \frac{0.62Re_D^{1/2}Sc^{1/3}}{\left[1 + (0.4/Sc)^{2/3} \, \right]^{1/4} \,}\bigg[1 + \bigg(\frac{Re_D}{282000} \bigg)^{5/8}\bigg]^{4/5} \quad ScRe_D \ge 0.2$

where:

$S h$ is the Sherwood number
$S c$ is the Schmidt number

Using the mass-heat transfer analogy, the Nusselt number is replaced by the Sherwood number, and the Prandtl number is replaced by the Schmidt number. The same restrictions described in the heat transfer definition are applied to the mass transfer definition. The Sherwood number can be used to find an overall mass transfer coefficient and applied to Fick's law of diffusion to find concentration profiles and mass transfer fluxes.

References

^ Some examples of said system can be seen here: Cylinder in Cross Flow at Various Velocities. Flometrics (1997). Retrieved on 10/07/2007.

Incropera, Frank (2006). Fundamentals of Heat and Mass Transfer, 6E. Wiley. ISBN 978-0-471-45728-2.
Tammet, Hannes & Kulmala, Markku (June), , . Retrieved on 10/07/2007
Ramachandran Venkatesan; Scott Fogler (2004). "Comments on Analogies for Correlated Heat and Mass Transfer in Turbulent Flow". AIChE Journal 50 (7): 1623-1626. doi:10.1002/aic.10146.
[|Martínez, Isidoro], , . Retrieved on 10/24/2007

Categories: Convection

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Churchill-Bernstein_Equation". A list of authors is available in Wikipedia.