LMTD Calculator

LMTD stands for Log Mean Temperature Difference. It is the logarithmic average of the temperature difference between the hot and cold fluids at each end of a heat exchanger. Engineers use LMTD to account for the fact that the temperature difference between the two fluids changes along the length of the exchanger, making a simple arithmetic average inaccurate.

The LMTD formula is: ΔTlm = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂), where ΔT₁ and ΔT₂ are the temperature differences between the hot and cold fluids at each end of the heat exchanger. The exact values of ΔT₁ and ΔT₂ depend on whether the exchanger operates in parallel-flow or counter-flow configuration.

In a parallel-flow (co-current) heat exchanger, both fluids enter from the same side, so ΔT₁ = T_hot_in − T_cold_in and ΔT₂ = T_hot_out − T_cold_out. In a counter-flow heat exchanger, the fluids travel in opposite directions, giving ΔT₁ = T_hot_in − T_cold_out and ΔT₂ = T_hot_out − T_cold_in. Counter-flow typically yields a higher LMTD and therefore greater heat transfer efficiency.

The temperature difference between hot and cold fluids varies non-linearly along the heat exchanger length. A simple arithmetic mean overestimates the effective driving force for heat transfer. LMTD accounts for this non-linear variation by using a logarithmic average, giving a more accurate representation of the mean driving force for heat transfer calculations.

First, identify your flow configuration (parallel or counter-flow). Second, calculate ΔT₁ and ΔT₂ based on the inlet and outlet temperatures of each fluid. Third, apply the LMTD formula: (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂). If ΔT₁ equals ΔT₂, then LMTD simply equals that temperature difference (the logarithm becomes indeterminate, but the limit equals the value itself).

For heat exchangers that are neither purely parallel nor counter-flow — such as shell-and-tube or cross-flow designs — the true mean temperature difference is less than the counter-flow LMTD. A correction factor F (between 0 and 1) is applied: ΔTm = F × LMTD_counter_flow. The factor F depends on the exchanger geometry and the temperature ratios R and P, and is typically read from published charts or calculated from empirical correlations.

When ΔT₁ equals ΔT₂, the standard LMTD formula produces an indeterminate form (0/0). However, by applying L'Hôpital's rule, the limit resolves to LMTD = ΔT₁ = ΔT₂. This means the LMTD is simply equal to the uniform temperature difference across the exchanger.

LMTD calculations are used in the design and sizing of heat exchangers across many industries. Common applications include HVAC systems (chillers, condensers, cooling coils), industrial process heat exchangers, power plant condensers and feedwater heaters, automotive radiators, and chemical reactor cooling systems. The LMTD value feeds directly into the heat transfer equation Q = U × A × LMTD, where U is the overall heat transfer coefficient and A is the heat transfer area.