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Heat Transfer

LMTD Calculator

The log mean temperature difference (LMTD) is the effective temperature driving force for heat transfer in a heat exchanger. It accounts for the changing temperature difference along the exchanger length. For multi-pass configurations, the LMTD is corrected by a factor F (where 0 < F ≤ 1) to account for the departure from true counter-current flow. This calculator computes both uncorrected and corrected LMTD for preliminary heat exchanger sizing.

TypeInteractive engineering calculator

Calculator

°C
°C
°C
°C
ΔT₁ (hot end)80 °C
ΔT₂ (cold end)60 °C
LMTD69.5212 °C

Preliminary estimate only. Confirm with detailed thermal-hydraulic design before procurement.

Next step: use the Heat Exchanger Area Calculator to estimate the required heat-transfer area.

Choosing between methods? See the LMTD vs NTU Method guide and the NTU Effectiveness Reference.

Formulas

Counter-current LMTD
LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂)
Hot-end ΔT (counter-current)
ΔT₁ = T_h,in − T_c,out
Cold-end ΔT (counter-current)
ΔT₂ = T_h,out − T_c,in
Corrected LMTD
LMTD_corrected = F × LMTD

Diagram

T_h,inT_h,outT_c,inT_c,outΔT₁ΔT₂LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂)Counter-current heat exchanger

Worked example

A counter-current shell-and-tube heat exchanger cools a process stream from 150 °C to 90 °C using cooling water entering at 30 °C and leaving at 70 °C. What is the LMTD?

  1. 01ΔT₁ = T_h,in − T_c,out = 150 − 70 = 80 °C
  2. 02ΔT₂ = T_h,out − T_c,in = 90 − 30 = 60 °C
  3. 03LMTD = (80 − 60) / ln(80/60)
  4. 04LMTD = 20 / ln(1.333)
  5. 05LMTD = 20 / 0.2877 = 69.5 °C
Result

LMTD ≈ 69.5 °C for this counter-current arrangement.

FAQ

When is the LMTD correction factor F needed?
F is needed for any heat exchanger with more than one tube pass or more than one shell pass. A pure counter-current single-pass exchanger has F = 1. Multi-pass configurations (e.g., 1-shell-2-tube-pass) always have F < 1.
What happens when ΔT₁ equals ΔT₂?
When both terminal temperature differences are equal, the LMTD equals that common value. The calculator handles this as a special case to avoid division by zero in the logarithmic formula.
Can I use this for parallel-flow (co-current) heat exchangers?
Yes. Switch to co-current mode. The terminal ΔT definitions change: ΔT₁ = T_h,in − T_c,in and ΔT₂ = T_h,out − T_c,out. Co-current LMTD is always lower than counter-current for the same temperatures.
What is a temperature cross and why is it rejected?
A temperature cross occurs when the cold outlet exceeds the hot outlet (in counter-current) or when the cold stream at any point exceeds the hot stream. This means the assumed flow arrangement is thermodynamically impossible. The calculator flags this as an error.

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