Logarithmic Mean Temperature Difference

In summary, the user was initially confused about which streams to use for the log mean temperature difference in a counter flow heat exchanger. After some discussion and references to resources, they were able to determine the correct calculation, which involved taking the difference between hot and cold temperatures at each end of the exchanger. The method for calculating the LMTD does not affect the overall result.
  • #1
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Homework Statement


Homework Equations


The Attempt at a Solution



I am confused as to which streams I should use for the log mean temperature difference. I am pretty sure it should be the difference in temperature between the two streams on the same side, so I think it's

(700-450)-(1100-960) / ln [(700-450)/(1100-960)], but I am not sure.

The term wasn't well defined, and my search on wikipedia gave the definition as ''The LMTD is a logarithmic average of the temperature difference between the hot and cold streams at each end of the exchanger.''

This is too vague, which end of the exchanger??
 

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  • #3
The way you calculated it is correct. You are not confused about it after all.

Chet
 
  • #4
I am confused, because the only reason I know it had to be that was because I would get a negative logarithm if I did it the other way. Suppose it was such that I didn't get a negative number in the logarithm either way that I subtracted it, then how would I do it??
 
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  • #5
Read the attachment to Post #2.
 
  • #6
Woopydalan said:
I am confused, because the only reason I know it had to be that was because I would get a negative logarithm if I did it the other way. Suppose it was such that I didn't get a negative number in the logarithm either way that I subtracted it, then how would I do it??

You take hot temperature minus cold temperature at one end of the heat exchanger, and hot temperature minus cold temperature at the other end of the heat exchanger. How you do things after that doesn't matter.
 
  • #7
Okay great, I have convinced myself of that now. Thank you!
 

1. What is the significance of Logarithmic Mean Temperature Difference (LMTD)?

The LMTD is an important parameter used in heat transfer calculations to determine the average temperature difference between two fluids in a heat exchanger. It takes into account the varying temperature profiles of both fluids and provides a single value that can be used to calculate the heat transfer rate.

2. How is LMTD calculated?

LMTD is calculated using the formula: LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2), where ΔT1 and ΔT2 are the temperature differences across the hot and cold fluids, respectively. This formula assumes that the temperature difference between the two fluids is constant along the length of the heat exchanger.

3. Can LMTD be negative?

Yes, LMTD can be negative if the temperature difference between the two fluids is reversed. This can happen in counter-flow heat exchangers where the hot and cold fluids flow in opposite directions. In this case, the LMTD would have a negative value, but it still provides a valid measure of the average temperature difference.

4. What is the relationship between LMTD and overall heat transfer coefficient?

LMTD is directly proportional to the overall heat transfer coefficient, which is a measure of the efficiency of the heat transfer process. A higher LMTD indicates a larger temperature difference between the two fluids and therefore a higher heat transfer rate. This means that a higher overall heat transfer coefficient is needed to maintain the same LMTD.

5. What are some limitations of using LMTD in heat transfer calculations?

LMTD assumes that the temperature difference between the two fluids is constant along the length of the heat exchanger. This may not be true in all cases, especially if the fluids have significantly different flow rates or if there are variations in the heat transfer surface. In addition, LMTD does not take into account any heat losses or gains along the length of the heat exchanger, which can affect the accuracy of the calculations.

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