Overall heat transfer coefficient in function of flow rate?

[Alain001]

I did a study on how good the HE could cool by changing both the volume rate.
What I experimentally found out is that
Q = U A ΔTLM
the U (overall heat transfer coefficient) can be written in a function of one of the fluidums mass rate when I keep the other fluidum's mass rate constant:
so U(mass rate fluidum 1)=(a*M+b)/(M+c). So its a rational function with both first order polynoms.
And when I curve fitted it from my experimental data, it had an R square of at least 0,999.

So I know its the correct function, but I have no idea why. I did some research but i couldn't find it anywhere what the correlation is of the OHTC and the mass rate of the fluidums.

Thanks!!
Alain Vanhille

 

[SNORGY]

How well do your data and your correlation compare with the variation in OHTC as functions of the film coefficients which, in turn, are functions of Reynolds Number, Prandtl Number and Nusselt Number? Is it possible that you have just discovered a correlation that appears to agree well with other already established correlations?

 

[IRstuff]

So, have you not consulted any HT textbooks? I would dispute your claim that your results are "correct," given that Nusselt, Reynolds, Prantdl, etc. came up with the current formulation of the heat transfer equations after working for decades on them, and their results have withstood the test of time over the last century. You've spent, what, a year, maybe? You might have something that works for your set of data, but does it work in general? You've made a bunch of simplifying assumptions by holding one side static, will your formula work for a two-sided problem?

The basic physical process is dependent on mass flow, so there should be no surprise that there's a strong dependence on the momentum flow of the fluid. However, the fact that you COULD fit to a polynomial means little if you have no predictable way of determining your fitting coefficients a, b, and c, or any rationale for why they exist. I suggest that you consult your HT texts and read up on Nusselt and Reynolds numbers in particular. If you cannot afford to buy one, there is a rather verbose and obtuse one that can be downloaded for free:

http://web.mit.edu/lienhard/

http://www/ahtt.html.

Now, admittedly, the Nusselt, Reynolds, and Prandtdl number approach are similarly heuristic, in that they are not solutions to obvious equations derived from physics, but, they are mostly based on the apriori, known physical parameters of the scenario.

TTFN
faq731-376

 

[hacksaw]

sounds like a masterful confirmation of the total heat balance under equilibrium conditions

 

[MortenA]

As said by others: Look in any stadard text book. The theory is that when the fluid is more turbulent then the "heat resistance film" is thinner and the heat transfer rate thus higher.

Nu=a*Pr^b*Re^c

and Nu=h*D/k and solve

With regards to fitting: Its very fine, but given enough data point and a sufficient polynomial you can always get Rsq very low.

Best regards

Morten

 

[davefitz]

generally, the convective heat transfer coefficient varies by the 0.8 power of the mass flow, if single phase flow is assumed. The opverall HT coeficient must also include the ffects of fouling, conductivity, and the convective heat transfer coeficient of teh other mass flow that was not varied.

If you are maintining one mass flowrate and varying the other, the ratio of (W*Cp1)/(W*Cp2) will vary, so one would expect a change in heat exchanger effectiveness "e", as per the "compact heat exchanger theory", sometimes called the e-NTU method. I would compare the results of your experiment with that predicted by the e-NTU method.

 

[Alain001]

Alright!
i know the part that the heat resistance film is getting thinner as the fluid is more turbelent, which is more flow rate.

I retried some fittings, and thought about a very logic function and found a new, actually more believable function of
U=a*M/(M+b). So if the flow rate is o, you don't transfer heat so U=o kW/m²K
If the flow rate is infinite the heat transfer is U=a kW/m²K. with in my back mind that you can cool the hot fluid to the temperature of the cold fluid' entrance. This is the maximum heat transfer possible in the cooler.

Does my logic have any flaws?

 

[IRstuff]

Given that it looks nothing like what pretty much everyone else in the world uses?

this is what the standard model says:

TTFN
faq731-376

 

[Alain001]

Where did you find that standard model?
I can't find it anywhere..

 

[MortenA]

Alain, did you try to google Nussels no. or Dittus-Boelter equation?

http://en.wikipedia.org/wiki/Dittus-Boelter_equation#Dittus-Boelter_equation

Best regards Morten

 

[Alain001]

Alright, I got it now! thanks.

I have another question though.
The correction factors, whichs exists for all heat exchangers.How are they determined? Is it experimentally or proven science?

Thanks!

 

[zekeman]

"And when I curve fitted it from my experimental data, it had an R square of at least 0,999."

I don't believe it unless you had maybe two or three data points.

 

[25362]

And, please, don't forget that he value of U can never be greater than the lowest of both heat transfer coefficients in the given heat exchanger.