Heat exchanger LMTD — Quick answer
LMTD (Log Mean Temperature Difference) is the effective driving force for heat transfer in a counter-flow or parallel-flow heat exchanger. Heat duty Q = UA × LMTD.
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2)
Q = U × A × LMTD × F (correction factor)
- ΔT1, ΔT2 — temperature differences at the two ends of the exchanger
- U — overall heat-transfer coefficient (W/m²K)
- A — heat-transfer surface area (m²)
- F — correction factor for shell-and-tube (typ 0.85–1.0)
- Q — heat duty (W)
Worked example: Hot fluid 80°C → 60°C, cold fluid 20°C → 50°C, counter-flow. ΔT1 = 80−50 = 30, ΔT2 = 60−20 = 40. LMTD = (40 − 30) / ln(40/30) = 34.76°C. With U = 500 W/m²K, A = 2 m²: Q = 500 × 2 × 34.76 = 34,760 W.
Typical overall heat-transfer coefficients U (W/m²K)
| Service | U (W/m²K) |
|---|
| Water-to-water (shell-tube) | 850–1,700 |
| Steam-to-water condenser | 1,000–3,500 |
| Air-to-water (finned tube) | 30–60 |
| Oil-to-oil | 100–350 |
| Refrigerant evaporator | 500–2,500 |
| Plate heat exchanger (water) | 3,000–6,000 |
Standard / source: TEMA (Tubular Exchanger Manufacturers Association); ASME Section VIII (pressure vessels).
Used for: Process heat-exchanger sizing, HVAC chiller specification, refrigeration evaporator design, industrial cooling-tower performance.
Standards & method
✓ Formula independently verified 12 July 2026- Governing standard
- LMTD method · TEMA (Tubular Exchanger Manufacturers Association) standards for mechanical design
- Method
- LMTD (log mean temperature difference)
- Equations applied
- Q = ṁ·cp·ΔT
- LMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁/ΔT₂)
- Q = U·A·LMTD·F
- Core formula
Q = U·A·ΔT_lm·F · ΔT_lm = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂)- Why this matters
- The F correction factor is not optional for anything other than pure counter-flow — a 1-2 shell-and-tube exchanger can have F ≈ 0.8, meaning about 25% more area than the raw LMTD suggests. And fouling factors must be included, or the exchanger will meet duty when new and fall short within a year.
- Independently verified
- 12 July 2026 — Formula re-derived from first principles and checked numerically against worked reference cases, including the ΔT₁ = ΔT₂ singularity.
Why this matters: A temperature cross is rejected with a clear error rather than returning a thermodynamically impossible result. Counter-flow and parallel-flow ΔT definitions are handled separately.
Results are for guidance. Verify against the current edition of the governing standard and have a licensed engineer review before construction or installation.
LMTD Formula
The Log Mean Temperature Difference (LMTD) represents the temperature driving force for heat transfer in flow systems.
For Counter-Flow:
- ΔT1 = T_Hot In - T_Cold Out
- ΔT2 = T_Hot Out - T_Cold In
For Parallel-Flow:
- ΔT1 = T_Hot In - T_Cold In
- ΔT2 = T_Hot Out - T_Cold Out
Frequently Asked Questions
How to calculate LMTD?
⌄
Determine the temperature differences at both ends of the exchanger (delta T1 and delta T2). The LMTD is the difference between these two values divided by the natural logarithm of their ratio.
What is the LMTD method for heat exchanger design?
⌄
The Log Mean Temperature Difference (LMTD) method: Q = U × A × ΔTlm × F. Where Q is heat duty (W), U is the overall heat transfer coefficient (W/m²·K), A is heat transfer area (m²), ΔTlm is the log mean temperature difference (°C), and F is a correction factor for non-pure counterflow arrangements (F=1.0 for pure counterflow; 0.7–0.95 for shell-and-tube). The LMTD is: ΔTlm = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2).
What is the NTU-effectiveness method for heat exchangers?
⌄
The NTU (Number of Transfer Units) method: NTU = U×A/Cmin. Effectiveness ε = Q_actual/Q_max = Q_actual/(Cmin × (Th,in − Tc,in)). This method is preferred when outlet temperatures are unknown or for performance rating of existing units. For a counterflow heat exchanger: ε = (1 − exp(−NTU(1−Cr))) / (1 − Cr×exp(−NTU(1−Cr))), where Cr = Cmin/Cmax.
What is fouling factor and how does it affect heat exchanger performance?
⌄
Fouling factor (Rf, m²·K/W) accounts for thermal resistance added by deposits (scale, biofilm, corrosion) on surfaces over time. The overall heat transfer coefficient including fouling: 1/U = 1/ho + Rfo + tw/kw + Rfi + 1/hi. TEMA standards specify fouling factors: cooling water — 0.0002 m²K/W; steam — 0.0001; crude oil — 0.0003–0.0005. Fouling can reduce U by 20–50%, so adequate cleaning access and water treatment are essential.
What are typical overall heat transfer coefficients (U)?
⌄
Typical U values for common services: Water-to-water (shell-and-tube) — 800–1,500 W/m²·K; Steam condensers — 1,000–6,000 W/m²·K; Water-to-oil — 100–400 W/m²·K; Air-to-water heat exchangers — 25–250 W/m²·K; Gas-to-gas — 10–50 W/m²·K. Air-side coefficients are low, which is why air-cooled exchangers require large fin surfaces to compensate.
What is the difference between counterflow and parallel-flow heat exchangers?
⌄
In counterflow, hot and cold fluids flow in opposite directions — the temperature difference is more uniform along the length, maximising heat transfer for a given area. In parallel flow, both fluids enter at the same end — the temperature difference is large at entry but shrinks toward zero at exit, limiting effectiveness. Counterflow achieves higher effectiveness and is used in most industrial shell-and-tube, plate, and double-pipe heat exchangers.