Calculation for correction factor LMTD in crossflow HEX? 3

[Roykonnecho]

Is there anyone who can tell me what the equation for the correction factor of a LMTD in a crossflow heat exchanger is? I only can find charts of this correction factor, but no equation...

 

[tickle]

It is the same as for any heat exchanger

t = tube
T = shell
i = in
o = out

LMTD = (Ti-to)-(To-ti)/ln[(Ti-to)/(To-ti)]

 

[25362]

Would you please, tell why do you need formulas for the LMTD correction factors in cross-flow if you have the graphs ? Do you have formulas for other exchanger configurations ?

 

[Roykonnecho]

Hi there,

@ tickle: Thanks for your answer, I only need the correction factor for the LMTD, not the calculation for a MTD itself.

@ 25362: I need this formulas because I am working on a effectivity calculation for a specific crossflow heat exchanger and I would like to calculate the EMTD exactly. The charts I have are not precisely enough.

Both persons, thank you for your post!

 

[25362]

If effectiveness is your aim have a look at Holman's HEAT TRANSFER - Mc Graw-Hill

 

[davefitz]

I suggest the use of "compact heat exchangers" by Kayes + London. The exact equations for each HX configuration are provided, based on the e-NTU method. These are the basis of the correction curves found in the literature.

 

[siretb]

Crossflow heata exchangers are more difficult to calculate.
If you do not want to use the set of curves available for the "F" factor (you will find them on the net) , I suggest you get a copy of the july 7, 1996, chemical engineering issue. Richard Turton is the author.
It contains formulas, involving a Bessel function that can be easily programmed, even in a spreadsheet.
It is also fairly easy to write a program, using a relaxation method (guess the temperature profile ; apply for each node or cell q=uA*true delta_t, and iterate).

You state the charts are not precise enough (??) . Could that mean that you are in an area where the effectiveness of your exchanger is very poor?

 

[Roykonnecho]

By not precise enough charts I mean that the charts I have are not for use with the exchanger I have. I am calculating a 4-pass crossflow heat exchanger and all charts I have found are for "more simple" exchangers or just 1-pass cross flow.

Tnx for your post siretb!

 

[siretb]

I would consider using the available charts for 2 shell passes, 4 tube passes (shell & tube), even if your configuration is different.
I have never seen data for F factors for crossflow, with 4 passes (unmixed/unmixed). There are charts for F charts for crossflow, 2 passes. Keep in mind that the hypothesis (mixed or unmixed) will alter the result, and that often the reality in in-between.
My feeling is that some simplification would be OK, unless you are in an area where the F factor gets much below 0.7.
If you do need some accuracy, again a relaxation method is easy to program.
If you need more, we'll need actual data to help more.

 

[Roykonnecho]

Tnx for your post Siretb!