How Does Velocity Affect Heat Transfer Coefficient Using the Colburn Equation?

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The discussion revolves around using the Colburn Equation to derive a general expression linking the convection heat transfer coefficient to velocity. Participants suggest expanding the Nusselt number and inquire whether the equation applies to specific fluids or universally. The conversation emphasizes understanding the Reynolds and Prandtl numbers in their expanded forms to facilitate this derivation. Clarification on the applicability of the equation to various fluids is also sought. Overall, the focus is on developing a clear relationship based on established heat transfer principles.
cruckshank
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Hi, I need to use the Colburn Equation, Nu = 0.023Re0.8Pr0.333 to write a simple general expression for the relationship between convection heat transfer coefficient and velocity.

I've been thinking about this for a while, but can't really figure out where to go beyond writing the Reynolds and Prandtl Numbers out in their expanded form.

Thanks in advance!
 
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What about writing the Nusselt number in its expanded form?
 
Is this for a specific fluid, or does it have to work for any fluid?
 

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