How to Calculate Log Mean Temperature Difference (LMTD)
Log mean temperature difference (LMTD) is the foundational temperature-driving force used in heat exchanger design and performance validation. It compresses the changing temperature difference between hot and cold streams into a single equivalent value that can be paired with heat-transfer coefficients and surface area.
This walkthrough explains how to compute LMTD from four measured temperatures, validate the data for temperature cross, and interpret the result alongside operational metrics such as the immersion cooling heat rejection guide and energy planning tools like the thermal storage sizing calculator.
Definition and physical meaning
LMTD is the logarithmic mean of the temperature differences at each end of a heat exchanger. Because the driving temperature difference changes along the flow path, a simple arithmetic average would misstate the actual heat-transfer potential. The logarithmic mean corrects that bias and yields the effective temperature difference used in steady-state sizing.
The result is expressed in temperature-difference units such as kelvin. A value reported in kelvin is numerically identical to degrees Celsius for differences, so you can interpret the result alongside equipment specifications without unit conversion.
Variables and units
Capture the four terminal temperatures using the same unit system. The most common are degrees Celsius or degrees Fahrenheit. Do not mix units within the same calculation.
- Th,in – Hot-side inlet temperature (deg C or deg F).
- Th,out – Hot-side outlet temperature (deg C or deg F).
- Tc,in – Cold-side inlet temperature (deg C or deg F).
- Tc,out – Cold-side outlet temperature (deg C or deg F).
- ΔT1 – Temperature difference at one end: Th,in − Tc,out.
- ΔT2 – Temperature difference at the other end: Th,out − Tc,in.
LMTD formula
The log mean temperature difference is calculated from the two terminal temperature differences.
ΔT1 = Th,in − Tc,out
ΔT2 = Th,out − Tc,in
LMTD = (ΔT1 − ΔT2) ÷ ln(ΔT1 ÷ ΔT2)
When ΔT1 equals ΔT2, the logarithm simplifies and LMTD equals either terminal difference. This occurs in perfectly balanced temperature profiles.
Step-by-step calculation workflow
Step 1: Measure steady-state temperatures
Record the hot and cold inlet and outlet temperatures once the system reaches a steady operating point. If the process is transient, average the readings over a stable interval.
Step 2: Compute the terminal temperature differences
Subtract the cold outlet from the hot inlet to obtain ΔT1, and subtract the cold inlet from the hot outlet to obtain ΔT2. Both values must be positive; otherwise, you have a temperature cross or swapped sensors.
Step 3: Apply the logarithmic mean formula
Insert ΔT1 and ΔT2 into the LMTD equation. The result is the effective temperature driving force used in heat exchanger rating and in formulas such as Q = U × A × LMTD.
Step 4: Compare with thermal performance expectations
Benchmark the computed LMTD against design expectations or historical performance. If LMTD is lower than expected, the exchanger may be fouled or operating outside design flow rates, so check auxiliary metrics like the energy use intensity workflow for system-wide impacts.
Validation and limits
Validate that ΔT1 and ΔT2 are both positive. A negative or zero value signals temperature cross, which invalidates the logarithm and may indicate sensor placement errors or unexpected heat transfer direction.
LMTD assumes steady-state conditions and either counterflow or parallel flow. For multi-pass or crossflow exchangers, apply an LMTD correction factor before using the value in design calculations. Document the correction factor and its source in technical reports.
Connecting LMTD to heat-duty calculations
LMTD becomes operational when paired with the overall heat-transfer coefficient and surface area. In performance testing, calculate Q from flow rate and specific heat on both sides, then compare Q with U × A × LMTD to see whether fouling or flow imbalance is degrading performance.
If the measured heat duty falls short of the predicted value, inspect the exchanger for scaling, validate flow instrumentation, and confirm that bypass valves are closed. Small shifts in LMTD often magnify into significant duty losses, so trending LMTD over time can expose early-stage fouling before it reaches shutdown thresholds.
Worked example: counterflow heat exchanger
A process stream enters the hot side at 180 deg C and exits at 120 deg C. The cold stream enters at 60 deg C and exits at 90 deg C. ΔT1 is 90 deg C and ΔT2 is 60 deg C. LMTD is (90 − 60) ÷ ln(90 ÷ 60) = 74.00 K, which can be used directly in heat-transfer calculations.
Embed: Log mean temperature difference calculator
Use the embedded calculator to compute LMTD, validate that your temperature differences are positive, and capture the intermediate ΔT values for documentation.