The temperature difference between hot and cold streams changes along a heat exchanger. Log mean temperature difference (LMTD) expresses that changing driving force as one value. Used with the correct flow arrangement, it helps relate heat duty to the area needed for an industrial cooler. The calculation is especially useful when a buyer can supply both streams’ inlet and target outlet temperatures.
What Is the LMTD Formula, and Which Temperatures Go Into It?
For ideal counterflow or parallel flow, calculate the hot-to-cold difference at each end:
LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂)
Here, ln is the natural logarithm. Both differences must be positive and describe the same operating case. Use bulk fluid temperatures at the four ports, not wall or ambient temperatures. The result is a temperature difference, expressed in °C or K.
| Flow arrangement | ΔT₁ | ΔT₂ |
|---|---|---|
| Counterflow | Hot inlet − cold outlet | Hot outlet − cold inlet |
| Parallel flow | Hot inlet − cold inlet | Hot outlet − cold outlet |
The two differences must pair temperatures meeting at the same physical end. Parallel flow brings both inlets together; counterflow brings the hot inlet beside the cold outlet. If they are equal, LMTD equals that common difference; direct substitution would give 0/0.
See the flow arrangement guide for the flow paths, then check your inputs in JED’s LMTD calculator.
Worked Example: Counterflow vs. Parallel-Flow LMTD
Consider these hypothetical inlet and outlet temperatures:
| Stream | Inlet | Outlet |
|---|---|---|
| Hot fluid | 100°C | 60°C |
| Cold fluid | 20°C | 40°C |
For counterflow:
- ΔT₁ = 100 − 40 = 60°C
- ΔT₂ = 60 − 20 = 40°C
- LMTD = (60 − 40) / ln(60 / 40) = 49.33°C
For parallel flow:
- ΔT₁ = 100 − 20 = 80°C
- ΔT₂ = 60 − 40 = 20°C
- LMTD = (80 − 20) / ln(80 / 20) = 43.28°C
For these specified endpoints, counterflow has the higher LMTD. The two calculations compare ideal arrangements. Reversing flow on a real unit will not necessarily preserve the four outlet temperatures.
If a hypothetical duty is 100 kW, U is 500 W/(m²·K), and F is 1, A = Q / (U × F × LMTD). The indicated areas are 100,000 / (500 × 49.33) = 4.05 m² for counterflow and 100,000 / (500 × 43.28) = 4.62 m² for parallel flow. Those estimates assume the same U and duty for both arrangements. A temperature difference of 1°C equals 1 K numerically. LMTD alone does not determine duty. Use flow and fluid properties in the heat duty calculator, then check whether heat lost by the hot stream approximately equals heat gained by the cold stream.
When Does a Real Exchanger Need an LMTD Correction Factor?
In Q = U × A × F × LMTD, Q is heat duty, U the overall heat-transfer coefficient, A the area, and F the correction for the flow arrangement.
Multi-pass shell and tube exchangers and crossflow units may need a correction or a different analysis. F depends on the configuration and temperatures. It should come from the selected flow arrangement or an appropriate thermal model, rather than a guessed constant. The single-pass versus multi-pass guide distinguishes tube passes from flow direction.
For an area estimate, U must reflect the fluids and design basis, including any specified fouling. Pressure drop and available water flow also constrain the design. A larger area calculated from a smaller corrected LMTD is a starting point, not a promise that any particular bundle or shell can meet the duty.
Common LMTD Mistakes That Change the Answer
Pairing the wrong ends. Mark both flow directions before calculating ΔT₁ and ΔT₂. A wrong pairing may look plausible.
Using an arithmetic average. The mean of 80°C and 20°C is 50°C; their LMTD is 43.28°C. This changes an area estimate.
Ignoring equal or nonpositive end differences. Equal positive differences give the same LMTD. For zero or negative values, recheck labels, flow arrangement, and duty.
Mixing operating cases. A peak-load oil inlet and a low-load water outlet cannot define one steady condition. Measure temperatures and flows together at a stable load. Check the heat balance with suitable fluid properties before using the data for design.
The heat exchanger sizing guide lists the remaining project data.
Send Your Temperature Data for a Custom Heat Exchanger Review
JED manufactures custom shell and tube heat exchangers for industrial cooling. Send both media, inlet and measured or target outlet temperatures, flows, pressures, allowable pressure drops, drawings, installation space, and fouling or water-quality information.
Label target outlet temperatures clearly. JED can review the duty, flow arrangement, materials, and manufacturing scope. If an existing cooler is being replaced, include its nameplate and current performance readings so the review addresses the change in duty. Submit the data through our contact form for a custom quotation.
Frequently Asked Questions About LMTD
Can I calculate LMTD if I only know the inlet temperatures?
Two inlets do not determine two outlets. Provide flow rates, fluid properties, and a target outlet for design review. For a known exchanger, an effectiveness–NTU analysis may help estimate unknown outlets.
Can LMTD be used when one fluid is condensing or boiling?
Yes, if its temperature profile is represented correctly. Nearly constant phase-change temperature simplifies the differences; pressure changes, temperature glide, or sensible-heat zones may require a more detailed analysis.
Can the cold outlet be hotter than the hot outlet in counterflow?
Yes. The hot inlet can exceed the cold outlet while the hot outlet exceeds the cold inlet. Check both local end differences and the heat balance. Ideal parallel flow cannot achieve this crossover.
How reliable is LMTD when the measured temperature approach is very small?
Compare the small end difference with the combined uncertainty of the two sensors. If they are similar, the calculated LMTD is sensitive to measurement error. Check calibration and measurement locations before drawing a firm conclusion.
