6 replies to this topic

[arsalz100]

Hi  ,in calculation of heat exchanger we use LMTD and  and  to calcualte temp difference across slab or plate we use arthemicatic temperature diff . why we use LMTD in Heat exhangers and log mean radius ?

[Bobby Strain]

If you studied calculus and differential equations, you can use that knowledge to answer your own question.

 

Bobby

[latexman]

Every heat transfer textbook I've seen derives the LMTD.  Open your textbook and read.

[thorium90]

The derivation of LMTD can be easily googled too..

 

The following website will be a good read

http://www-old.me.ga...aura/node5.html

Edited by thorium90, 18 April 2013 - 10:36 AM.

[markymaark]

Besides the obvious answers above..

 

The LMTD is just a more accurate depiction of the temperature difference from point A to point B.  In reality it is not as simply as the arithmetic average between of the start pointA and end pointB.

[Shivshankar]

Arsalz,

 

I hope you know mathematical meanings of following terms.

 

*Mean temperature difference

 

*Arithmetic temperature difference

 

*Log mean temperature difference.

 

 The temperature change that takes place across the heat exchanger from the inlet to the outlet is not linear i.e the temperature difference between the hot and cold fluids varies along the heat exchanger exponentially.

 

and log is the inverse of exponentiation*.

 

So in mathematical terms, for making non-linearity more linear, this method is used for greater accuracy.

 

LMTD is a non-linear approximation of a heat transfer curve, while AMTD is a linear approximation

 

So if you decide to calculate non-linearity by AMTD (which is linear) then that will be less accurate so we calculate it with using LMTD method.

 

* - check on wikipedia.

 

Read attachment.

 

For derivation check below link,

 

%5Burl="http://www.eng.cam.ac.uk/~cnm24/files/EngineeringIIAHeatandMassTransfer/DerivationofLMTD"]http://www.eng.cam.ac.uk/~cnm24/files/EngineeringIIAHeatandMassTransfer/DerivationofLMTD[/url](Length).doc

 

Regards

Shivshanakar

Attached Files

•  LMTD.GIF   43.56KB   10 downloads

Edited by Shivshankar, 19 April 2013 - 09:36 AM.

[thorium90]

*Mean temperature difference

 

*Arithmetic temperature difference

 

*Log mean temperature difference.

 

 

 

Shivshankar, you are confusing others by implying mean and arithmetic are different. I think you meant arithmetic mean. One has to be specific on the type of mean used as there are also other means like geometric mean, harmonic mean etc, although they have other uses.

 

Furthermore, your explanation of exponential temperature change is not entirely accurate. Perhaps you can also think about exchangers where one or both sides experience phase change, for example in condensing or vaporizing exchangers, how this would change the log mean approximation. Recall the assumptions used in the derivation of the equation. Also, think about the drawbacks of the method and you may then understand why other methods like NTU method are also used.

 

I believe both you and the OP can understand the logic behind LMTD for heat exchangers once you are able to do the derivation on your own.

Edited by thorium90, 19 April 2013 - 03:53 PM.