LMTD Heat Exchanger Calculator

Log Mean Temperature Difference (LMTD) LMTD is the effective driving temperature difference for heat transfer in heat exchangers. Q = U × A × LMTD Where: Q = heat duty (W or kW) U = overall heat transfer coefficient (W/m²K) A = heat transfer area (m²) LMTD = log mean temperature difference (K or °C)

LMTD Formula LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂) Where ΔT₁ and ΔT₂ are the temperature differences at each end of the exchanger.

Counterflow vs Parallel Flow Counterflow: hot and cold streams flow in opposite directions. ΔT₁ = T_hot,in − T_cold,out | ΔT₂ = T_hot,out − T_cold,in Best LMTD, and the most efficient configuration. Parallel flow: both streams flow in the same direction. ΔT₁ = T_hot,in − T_cold,in | ΔT₂ = T_hot,out − T_cold,out Less efficient, and a temperature cross is not possible.

LMTD Correction Factor F For multi-pass shell-and-tube exchangers, apply correction factor F: Q = U × A × F × LMTD_counterflow F depends on temperature efficiency and number of passes (charts in TEMA/HEDH). F = 1 for pure counterflow. Typically F runs 0.8 to 1.0 for 2-pass shell-and-tube.

Overall Heat Transfer Coefficient U Typical U values (W/m²K): Water to water: 1,000 to 2,500 | Gas to gas: 10 to 50 | Steam to water: 1,000 to 3,500 Oil to water: 300 to 900 | Condensing steam: 1,500 to 8,000 Gas to liquid: 20 to 200

Energy Balance Hot side: Q = ṁ_h × Cp_h × (T_h,in − T_h,out) Cold side: Q = ṁ_c × Cp_c × (T_c,out − T_c,in)

The temperature cross, and why the flow arrangement is not a detail

Feed 120°C hot water in and ask for 80°C on the cold outlet while the hot side leaves at 60°C. In counterflow that is ordinary: the cold outlet meets the hot inlet, so 80 against 120 leaves a 40 degree driving difference and the cold stream leaves hotter than the hot stream does. In parallel flow the same job is impossible. Both streams walk toward a common temperature from the same end, so the cold outlet can never pass the hot outlet, and asking for it gives a negative ΔT₂ that has no logarithm.

That is why almost every real exchanger is counterflow or as close to it as the geometry allows. It is not a small efficiency edge. It decides whether the duty is achievable at all.

Why the log mean and not the plain average

The driving difference is not constant along the exchanger, and the local heat flux is proportional to it. Averaging the two ends works only when they are close. Take a case with ΔT₁ = 40 and ΔT₂ = 40: both means give 40. Now stretch it to 90 and 10. The arithmetic mean still says 50, the log mean says 36.4. Size on 50 and you buy an exchanger 27% smaller than the duty needs, which will simply never make its outlet temperature. The gap grows with the ratio between the two ends, and past a ratio of about 2 is where guessing an average starts to cost real money.

A quick sanity rule for U

A U value is dominated by whichever side has the worst film coefficient, which almost always means the gas side. Adding a second gas stream does not average the two; it drags the result down to something near the weaker one. So a gas-to-liquid exchanger sits near 20 to 200 W/m²K while liquid-to-liquid sits ten times higher, and that single fact explains why air-cooled equipment is physically enormous compared with a water-cooled unit of the same duty.