Nusselt number equation for internal flow 3

[hongxiangping]

Hi, I'm just going through a calculation left by an old senior from my company to determine Nusselt number for gas flow inside tube for a simple cross-flow heat exchanger performance estimation, and he was using the formula as below:

Nu = 0.023(Re^0.8)(Pr^0.4)[(Tb/tf)^0.8]

where
Tb is the bulk temperature, which is the arithmetic mean between hot end and cold end of the gas
tf = Tb - LMTD/4

1. Anyone seen this formula for tf before, who can tell me what does this term means?
2. My understanding is that this equation is a Colburn equation, with temperature correction, but what does this temperature correction mean? What does this power of 0.8 refers to?
3. I understand that another formula to calculate Nusselt number for this internal flow is the modified second Petukhov equation by Gnielinski:

Nu = {(f/8)(Re-1000)Pr}/{1+12.7[(f/8)^(0.5)][(Pr^(2/3))-1]}

Anyone has any idea which equation can give the better accuracy? The corrected Colburn equation or the modified second Petukhov equation?

The person who prepared this calculation is no longer contactable, so will be appreciated if anyone can guide me through this. Thank you very much!

 

[kfoh]

I am not completely sure, but the standard Gnielinsky correlation gives a better result normally. The Dittus Boelter format is weaker in its performance either in low or high Re, not sure anymore.
The factor 0.8 seems to be of empircal nature. If you do not have the paper you need to test it against others.

 

[hongxiangping]

Dear kfoh,

Thank you for your reply. I would prefer to go for the Gnielinsky correlation now, it also covers a wide range of Re and Pr value.

 

[BigInch]

Colburn calculates the heat transfer coefficient.
Bulk temperature is the temperature of the fluid "bulk" i.e. near the centreline of flow.
The other is the pipe wall temperature, not the beginning and end of the pipe.
The 0.23 and 0.8 exponent are from the Colburn equation.
Grashof calculates the inside heat transfer coefficient between fluid and pipe wall for laminar flow.
Heat transfer coefficient is deduced from the Nusselt Number

.

 

[hongxiangping]

Dear BigInch,

Thank you for your input, now I have a better idea as on the temperature correction factor with exponent of 0.8.

On the other hand, I have never seen the Nu equation presented by you. Do you mind telling me where does this correlation comes from, i.e. the reference paper introducing this equation? I presumed this is for internal flow in a circular pipe only (correct me if I'm wrong). Also, this equation is valid for what range of Re and Pr? I'm curious to find out whether there has been more accurate calculation to determine Nu, after Gnielinski.

 

[BigInch]

That frame is copied from a Stoner Pipeline Simulator user manual.
I think you can also find it in "Heat Transfer" by Holeman, not sure because I left the book at my flat in Spain.
All Re numbers, as the transition coefficient is used to bridge from the laminar to the fully turbulent regions.
You might take a look here as well. It shows a number of correlations and their coefficients.

 

[IRstuff]

I think that's "Holman" Chp 5 through 7 discuss convection, but there are MANY equations for Nusselt number, and possibly every author has their own pet equations. I can't see the posted image at work, but equations similar to those in the OP are in Chp 6 of Holman 10th ed.

TTFN
faq731-376

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[georgeverghese]

It is important to keep the big picture in mind when chasing after accuracy in these htc values - there is more uncertainty in shellside htc than there is in tubeside, and the fouling factors and tube id / od surface roughness smudge out everything to a certain extent !

 

[hongxiangping]

Dear BigInch,

Noted and thanks again for your useful information.

Dear IRstuff,

Thank you. I will look into Holman's book as well. The current reference I frequently referred to is Yunus Cengel's "Heat Transfer" book.

Dear georgeverghese,

Thanks for your comment, I agree with you, as external htc, tube metal conductivity, and fouling conductance at tube id/od also will affect the overall htc.