Tube Heat Exchanger : LMTD calculation (2024)

Tube Heat Exchanger : LMTD calculation (1)

What is the LMTD ? How to calculate it ? How to correct it ?

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Section summary
1. Shell-Tube heat exchangers
2. Shell-Tube heat exchanger calculation procedure

1. LMTD : Logarithmic Mean Temperature Difference

Tube Heat Exchanger : LMTD calculation (3)

With

ΔT1 = temperature difference on one side of the heat exchanger (end 1)
ΔT2 = temperature difference on the other side of the heat exchanger (end 2)

The LMTD allows to represent the driving force of heat exchange along the exchanger and accounts for the fact that the difference in between the cold side and the hot side is changing all along the equipment. The use of the LMTD is valid for co-axial heat exchangers.

Typical examples of temperature profiles along co-axial heat exchangers, for co-current and counter current are given below :

Tube Heat Exchanger : LMTD calculation (4)

The LMTD in the case of counter-current is noted LMTDcc.

Example :

Counter current HX with

  • Hot fluid temperature in = 100c
  • Hot fluid temperature out = 75c
  • Cold Fluid temperature in = 20c
  • Cold fluid temperature out = 60c
  • DT1 = 75-20 = 55c
  • DT2 = 100-60 = 40c
  • LMTD = (40-55)/(ln(40/55)) = 47.1 c

2. Correction factor of the LMTD

How to correct the LMTD to account for other configuration than counter current ?

Very few heat exchangers are purely co current or counter current, which allows to apply the LMTD. Most of the them will be partially co current and partially counter current. It is quite easy to visualize it for a 2 pass tube / 1 pass shell heat exchanger for example.

In this case, the LMTD must be corrected by a coefficient F which accounts for those non idealities. F can be calculated from abacus.

Tube Heat Exchanger : LMTD calculation (2024)

FAQs

How to calculate LMTD for heat exchanger? ›

Formula for LMTD calculation -

For a Parallel Flow Heat Exchanger, Hot fluid entering at temperature 100 degree Celsius and exiting at 90 degree Celsius . Cold fluid Entering at 30 degree Celsius and exiting at 50 degree Celsius. Find the LMTD . LMTD = ((100 - 30)-(90-50)) / ln (100-30/90-50) = 53.6 degree Celsius .

Is higher or lower LMTD better? ›

For a given heat exchanger with constant area and heat transfer coefficient, the larger the LMTD, the more heat is transferred. The use of the LMTD arises straightforwardly from the analysis of a heat exchanger with constant flow rate and fluid thermal properties.

What are the limitations of the LMTD method? ›

The LMTD method cannot be used for the determination of heat transfer rate and outlet temperature of the hot and cold fluids for prescribed fluid mass flow rates and inlet temperatures when the type and size of heat exchanger are specified.

What is the possible max value of LMTD correction factor? ›

Explanation: The value of corrected LMTD should be less than the theoretical LMTD considering countercurrent flow. Thus the LMTD correction factor is less than 1. Also for steady state operation of the HE, its value should be more than 0.75.

What is the correction factor equation for LMTD? ›

The Log Mean Temperature Difference (LMTD) correction factor, F, is traditionally expressed in terms of two non-dimensional parameters P=t 2 - t 1/T 1-t 1, and R=T 1 - T 2/t 2 - t 1 in form of charts as the underlying equations are complicated.

What happens when LMTD is zero? ›

If the LMTD is zero, it means that there is no temperature difference between the hot and cold fluids. This can occur in situations where the two fluids are at the same temperature, or where the heat exchanger is not functioning properly.

Which is more accurate, NTU or LMTD? ›

It is convenient to use the LMTD method when the fluid inlet and outlet temperatures are known. However, if only the fluid inlet temperatures are given, the effectiveness-NTU method is more preferably adopted.

Why is LMTD used instead of temperature difference? ›

The LMTD is used because it considers the varying temperature differences along the length of the tube, making it a more accurate representation of the heat transfer effectiveness.

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.

What is the difference between LMTD and MTD? ›

MTD: the sum of values from the first day of the month till the date you are watching. LMTD: same calculation than MTD but for the month before.

How to calculate temperature difference in heat exchanger? ›

The equation of delta t is: ΔT = T2 - T1

The entrance temperature in the heat exchanger at B would be T1. And the outlet from the heat exchanger coming out at D is T2. The cooling water entering the heat exchanger will get warmer on its way through the exchanger. The difference is then the ΔT.

What is the LMTD method of heat transfer? ›

LMTD stands for Logarithmic Mean Temperature Difference. Its used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is logarithmic average of the temperature difference between the hot and cold feeds at each end of the double pipe exchanger.

How do you calculate the heat transfer in a heat exchanger? ›

The formula is Q = U ⋅ A ⋅ Δ T lm , where Q is the total heat transfer, U is the overall heat transfer coefficient, A is the surface area for heat transfer, and Δ T lm is the log mean temperature difference.

What is the formula for heat exchanger efficiency? ›

The heat exchanger efficiency is defined as the ratio of the actual rate of heat transfer in the heat exchanger, q, and the optimal rate of heat transfer, qopt, η = q q opt = q U A ( T ‾ - t ¯ ) The optimum (maximum) rate of the heat transfer is the product of UA of the heat exchanger under consideration and the ...

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