Calculate the log mean temperature difference (LMTD) from four terminal temperatures. Choose countercurrent or parallel flow, inspect the end differences, and see how the streams meet at each end of the heat exchanger.
02 Read the driving force
Log mean temperature difference
°C
Enter four temperatures to begin.
- End 1 · ΔT₁
- End 2 · ΔT₂
03 Check the terminal temperatures
Formula and method
The LMTD is the effective temperature driving force for an ideal two-stream heat exchanger. Use the natural logarithm:
ΔTlm = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂)
| Flow arrangement | End 1: ΔT₁ | End 2: ΔT₂ |
|---|---|---|
| Countercurrent (opposite directions) | Th,in − Tc,out | Th,out − Tc,in |
| Parallel (same direction) | Th,in − Tc,in | Th,out − Tc,out |
If the two positive end differences are equal, their common value is the LMTD. The engine uses a numerically stable logarithm for nearly equal values. Temperature differences have no offset: 1 °C difference = 1 K, and 1 °F difference = 5/9 K.
Assumptions and validity
- Steady operation, negligible heat exchange with the surroundings, and approximately constant overall heat-transfer coefficient. For sensible heating or cooling, heat capacities are treated as constant.
- The hot stream cools or remains isothermal; the cold stream heats or remains isothermal. Isothermal temperatures can represent a phase-change segment, but this tool does not check phase equilibrium.
- Both end differences must be positive. A zero difference is a pinch limit; a negative difference violates this model. In countercurrent flow, the cold outlet may exceed the hot outlet if both physical end differences stay positive.
- This is an uncorrected LMTD for ideal parallel or countercurrent flow. Crossflow and multipass arrangements require a separately established correction factor, F. For those cases, ΔTeffective = F × ΔTlm,countercurrent.
- Four temperatures alone do not establish a heat balance, heat duty, exchanger area, pressure drop, or equipment suitability. Check stream properties and energy balances separately.
Worked example
A countercurrent exchanger cools a hot stream from 150 to 90 °C while heating a cold stream from 20 to 60 °C. At end 1, ΔT₁ = 150 − 60 = 90 °C. At end 2, ΔT₂ = 90 − 20 = 70 °C.
LMTD = (90 − 70) / ln(90/70) = 79.582 °C = 79.582 K. The result lies between the two end differences, 70 and 90 °C. Select “Load example” above to reproduce it, then change to parallel flow to compare the same terminal temperatures.
Sources and calculation version
- U.S. Department of Energy, Mechanical Science, DOE-HDBK-1018/1-93, Volume 1, module ME-02, pages 6–8: flow arrangements, LMTD equation, and worked benchmark.
- ASHRAE Handbook—Fundamentals, Chapter 4: Heat Transfer, section 5, Mean Temperature Difference Analysis: assumptions, equal-difference limit, and correction factors.
Changelog: engine 1.0.0 introduces countercurrent and parallel flow, °C/K/°F/°R units, stable equal-difference handling, and input validation. Parameter source: your four temperatures; no property dataset is used. Engineering review status: independent review pending.