LMTD Calculator — Log Mean Temperature Difference

Formel

How this is calculated

In a heat exchanger, the temperature difference between the hot and cold streams varies along the length of the exchanger — it is large at one end and smaller at the other. You cannot simply average the two terminal differences (ΔT at each end) because the relationship is logarithmic, not linear, along the exchanger length. The Log Mean Temperature Difference (LMTD) is the logarithmic average that correctly weights the driving force: LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂). When ΔT₁ equals ΔT₂ (both ends are the same), the formula reduces to LMTD = ΔT₁ by L'Hôpital's rule.

The arrangement of the fluids matters: in a counterflow exchanger the hot and cold fluids travel in opposite directions, so the hot fluid inlet faces the cold fluid outlet. This produces a more uniform temperature profile and allows the cold fluid to exit at a temperature closer to the hot fluid inlet — theoretically approaching the same temperature if the exchanger is long enough. In a parallel-flow (co-current) exchanger both fluids enter from the same end, giving a steep initial ΔT that declines rapidly; the maximum exit temperature of the cold fluid is always below the hot fluid outlet temperature. For the same duty (Q), counterflow needs a smaller heat-transfer area, so it is the more common design.

Once LMTD is known, it enters the fundamental heat-exchanger design equation: Q = U × A × LMTD, where Q is the heat duty (W or kW), U is the overall heat-transfer coefficient (W/m²·K) and A is the heat-transfer area (m²). This calculator computes LMTD only; U and A must be supplied from other data.