ZERO LMTD for Shell and Tube exchanger 2

[Nik456]

Hi,

I am performing exchanger design and found that my LMTD is zero as my heating and cooling flow are same.

Does it mean that the design is not correct?

Thanks!

 

[SNORGY]

This might be one of those cases where you find that application of L'Hopital's Rule allows you to demonstrate that the LMTD is not zero, but rather, the temperature difference of interest is the arithmetic mean temperature difference.

Regards,

SNORGY.

 

[srfish]

In this case the LMTD would only be zero if the inlet temperature on one side is equal to the outlet temperature on the other side. The math may be correct in the design but the result is not practical.

 

[Nik456]

In my case, cold side Inlet T: 25C and outlet T: 45C, and Hot side Inlet T: 75C and outlet T: 55C. I checked that temperature approach is more than 10F (per article publisehd in cheresources.com); but LMTD for counter current flow comes 0.

Do I have to consider parallel flow?

Another question is,

How do i know when to use LMTD OR arithmetic mean temperature difference?

 

[rmw]

You have a math mistake or you are calculating LMTD incorrectly.

rmw

 

[OilToil]

Snorgy is correct, sometimes LMTD does not work, as described as a 'special case' at this website:

http://www.cheresources.com/heat_transfer_basics.shtml

I believe the correct temperature difference to use in this case is 30F.

 

[OilToil]

Oops, that should be 30C, my mistake.

 

[SNORGY]

When stuff like this happens, it's good to know that the NTU-Effectiveness method will probably work. It's a bit more calculation intensive, but it should work.

Regards,

SNORGY.

 

[SNORGY]

Might want to transfer this thread to the "Heat Transfer & Thermodynamics engineering" forum.

Regards,

SNORGY.

 

[25362]

The definition of log mean of a and b implies a[≠]b, and if a = b, then log mean = a.

 

[EmmanuelTop]

If you draw a Q-T curve for both streams, you'll see that the temperature difference across the exchanger is constantly 30 degC and that is exactly what 25362 says: for equal temperature differences on both ends of an exchanger, LMTD is equal to the temperature difference on any exchanger end.

http://antwrp.gsfc.nasa.gov/apod/astropix.html

 

[sshep]

It is not true that LMTD calculates to zero, using the formula LMTD=(GTTD-LTTD)/ln(GTTD/LTTD), where GTTD and LTTD =greatest and least terminal temp differences. It actually evaluates to LMTD=0/0 which is indeterminate.

We can solve the limit as GTTD->LTTD by LeHopital's rule which says that limit f(x)/g(x)= limit f'(x)/g'(x).

You can correct my math, but I think this comes out as:
lim(x->c) of (x-c)/ln(x/c)=
lim(x->c) of d(x-c)/d(ln(x)-ln(c))=
lim(x->c) of dx/(dx/x)=
lim(x->c) of x = c
or for your case
LMTD = GTTD = LTTD = 10

best wishes,
sshep

 

[ione]

The use of de L’Hospital’s rule is correct when the LMTD is indeterminate, but I think the result should be

LMTD= ?T1= ?T2

Where

?T1= Thot in – Tcold out

?T2= Thot out – Tcold in

In the OP's specific case: LMTD = 30 °C

 

[Homayun]

I think none of the temperatures you have specified can be that acurate: In this case it does make a difference 24.99 and 25.00C..

The LMTD is actually 30C.

If you use for instance your cold inlet Temp of 24.999 C instead of 25.00 C, you'll get the 30C LMTD. The result would be the same for each of the other streams....For instance, if you take 74.99C for your Hot-in, instead of 75.00, the LMTD would again be 30.

I really wonder what HTRI would do! It probably would not converge unless one of the temperatures is adjusted.

 

[sshep]

You are right about the 30F- my mistake. Knowing the answer to the 0/0 problem already, I blew right through those posts only remembering his note about 10F.

GTTD=LTTD is a fairly common calculation "problem"- as would be encountered when a stream recovers heat from itself before and after a simple unit operation. This has nothing to do with any "temperature inaccuracy", it is just a mathematical qwerk.

HTRI or any other heat exchanger design program will NOT have difficulty with such a problem since these programs will use localized temp differences, and any "integration" will be numerical. Even Aspen-plus in shortcut mode has no problem, the programing caters for it. It is only hand calcs and excel that will fail with divide by zero errors.

best wishes,
sshep