Heat Exchanger LMTD Calculator

Calculate log mean temperature difference and heat transfer in parallel and counter-flow heat exchangers.

U×A: overall HT coefficient × area
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LMTD Represents the Effective Temperature Driving Force

In a heat exchanger, the temperature difference between hot and cold streams usually changes from one end to the other, so one arithmetic difference cannot represent the whole device. For a simple exchanger, the log mean temperature difference is ΔTlm=(ΔT1−ΔT2)/ln(ΔT1/ΔT2). Heat transfer is then Q=UAΔTlm for the corresponding ideal flow arrangement.

Counter-flow often maintains a larger effective temperature difference than parallel flow for the same terminal temperatures, enabling more effective heat exchange. Multipass shell-and-tube arrangements can require an LMTD correction factor because their temperature pattern is not pure parallel or counter-flow.

Q=UAΔTlm,   ΔTlm=(ΔT1−ΔT2)/ln(ΔT1/ΔT2)
SymbolMeaningWhy it appears / units
UOverall heat-transfer coefficientW/(m²·K).
AHeat-transfer aream².
ΔTlmLog mean temperature differenceK or °C difference.
QHeat-transfer rateW.

If the two terminal temperature differences become nearly equal, the LMTD approaches that common value. Temperature differences must be paired correctly for the chosen flow configuration.

An LMTD must lie between the two positive terminal temperature differences. If ΔT1 and ΔT2 are equal, the limiting value of the logarithmic mean is that same temperature difference. A result outside the endpoint range indicates a pairing, sign, or unit problem.

Worked Examples

Example 1: Counter-flow: T_hi=80, T_ho=50, T_ci=20, T_co=40
ΔT₁=80-40=40, ΔT₂=50-20=30
Result: LMTD=34.8°C
Counter-flow is more efficient
Example 2: Parallel-flow same temps
ΔT₁=80-20=60, ΔT₂=50-40=10
Result: LMTD=27.9°C — 20% lower!
Counter-flow gives higher LMTD → smaller HX
Example 3: LMTD from two end differences
ΔT1=60K, ΔT2=30K
Result: ΔTlm≈43.3K
The log mean lies between the two terminal differences.
Example 4: Heat duty
U=500W/m²K, A=10m², LMTD=43.3K
Result: Q≈216.5kW
Overall coefficient, area, and effective driving force multiply directly.

Common Mistakes

⚠️
Using an arithmetic average for large temperature-difference changes

The temperature driving force varies exponentially along ideal exchangers, which leads to the logarithmic mean.

⚠️
Pairing terminal temperatures incorrectly

Parallel and counter-flow definitions of ΔT1 and ΔT2 differ. Draw the stream directions before subtracting temperatures.

⚠️
Ignoring correction factors for multipass designs

Some exchanger arrangements require Q=UAFΔTlm with a correction factor F below 1.

Frequently Asked Questions

Why counter-flow is better?
In counter-flow, cold fluid meets the hottest part of the hot fluid at one end and the warmest part at the other. This maintains a more uniform temperature difference along the exchanger, giving higher LMTD and better efficiency.
NTU method vs LMTD?
LMTD: use when both inlet and outlet temperatures are known. NTU-effectiveness: use when only inlet temperatures are known and you want to size the exchanger. Both give same result for simple configurations.
Why use a logarithmic mean?
Integrating the local heat-transfer driving force along an exchanger leads to the log-mean expression when U is approximately constant.
What if ΔT1 equals ΔT2?
The direct formula appears 0/0, but its mathematical limit is that common temperature difference.
Why can counter-flow be more effective?
It can maintain a useful temperature difference over more of the exchanger length and can allow the cold outlet temperature to exceed the hot outlet temperature.
When should the effectiveness-NTU method be used instead?
The ε-NTU method is convenient when outlet temperatures are unknown but inlet conditions, heat-capacity rates, UA, and exchanger arrangement are known.
Why must the terminal temperature differences be defined consistently in LMTD?
LMTD uses the two end temperature differences for the same flow arrangement. For a counterflow exchanger, pair hot-in with cold-out and hot-out with cold-in; for parallel flow, pair inlet with inlet and outlet with outlet. Reversing one pairing can produce a meaningless logarithm or an incorrect driving force.

Formula Explorer connections

Interpretation: This formula tracks heat, temperature, work, entropy or transport in a thermodynamic system. Assumption: Use absolute temperature where required and consistent energy units. Constant properties, equilibrium, ideal gases or negligible losses may be assumed.

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