The temperature difference between two fluids varies along a heat exchanger. The log mean temperature difference is the correct average to use in q = UA·ΔT when sizing exchangers.
How to use the LMTD Calculator
- Flow arrangement
- Hot inlet
- Hot outlet
- Cold inlet
- Cold outlet
- Correction factor F
- UA (W/K, optional)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the flow arrangement and enter the inlet and outlet temperatures of both fluids, the correction factor F (1 for pure counter or parallel flow) and optionally UA.
Inputs explained
| Field | What to enter |
|---|---|
| Flow arrangement | Choose one: Parallel flow, Counter flow |
| Hot inlet | Units: °C, °F, K |
| Hot outlet | Units: °C, °F, K |
| Cold inlet | Units: °C, °F, K |
| Cold outlet | Units: °C, °F, K |
| Correction factor F | A number |
| UA (W/K, optional) | A number |
What each result means
- Corrected LMTD (F·LMTD) = [Correction factor F]×[LMTD]
- Heat duty U·A·F·LMTD = [UA (W÷K, optional)]×[Correction factor F]×[LMTD]÷1000
Example values
How the main result changes when Hot inlet changes and everything else stays at the example values above:
| Hot inlet (°C) | LMTD (K) |
|---|---|
| 45 | 15.417 |
| 67.5 | 31.0994 |
| 90 | 42.0551 |
| 112.5 | 51.4941 |
| 135 | 60.0884 |
| 180 | 75.7415 |
Formula
Counter: ΔT₁ = T_h,in − T_c,out, ΔT₂ = T_h,out − T_c,in · Parallel: ΔT₁ = T_h,in − T_c,in, ΔT₂ = T_h,out − T_c,out
LMTD = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂), q = U·A·F·LMTD
Worked example
Inputs — Flow arrangement: Counter flow; Hot inlet: 90 °C; Hot outlet: 50 °C; Cold inlet: 15 °C; Cold outlet: 40 °C; Correction factor F: 1; UA (W/K, optional): 1,000.
Results — ΔT₁ = 50 K; ΔT₂ = 35 K; LMTD = 42.0551 K; Corrected LMTD (F·LMTD) = 42.0551 K; Heat duty U·A·F·LMTD = 42.0551 kW.
Key terms
- LMTD
- Log mean temperature difference.
Frequently asked questions
Why use a logarithmic mean?
The temperature difference decays exponentially along the exchanger.
Why is counter-flow better?
It keeps a more uniform temperature difference and allows temperature cross.
What if ΔT₁ = ΔT₂?
The LMTD equals that common value.
What is the F factor?
A correction for multi-pass and cross-flow exchangers.