Heat Exchanger LMTD Calculator
Calculates the Log Mean Temperature Difference (LMTD) for counter-flow or parallel-flow heat exchangers, then uses it to find the required heat transfer area or rate. Used in the design and rating of industrial heat exchangers.
Last updated: May 2026
About this calculator
The LMTD method determines an effective mean driving temperature difference across a heat exchanger. For counter-flow or parallel-flow configurations, define ΔT₁ = T_h,in − T_c,out and ΔT₂ = T_h,out − T_c,in. The log mean temperature difference is LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂). When ΔT₁ ≈ ΔT₂, the arithmetic mean is used instead to avoid division by near-zero values. The heat transfer rate is then Q = U · A · F · LMTD, where U is the overall heat transfer coefficient, A is the heat transfer area, and F is a correction factor (F = 1 for pure counter-flow or parallel-flow; tabulated values apply to shell-and-tube configurations). The LMTD accounts for the fact that temperature differences vary along the exchanger length, giving a single representative value.
How to use
A counter-flow water-to-water exchanger: hot fluid enters at 90 °C, exits at 60 °C; cold fluid enters at 20 °C, exits at 50 °C. ΔT₁ = 90 − 50 = 40 °C; ΔT₂ = 60 − 20 = 40 °C. Since ΔT₁ = ΔT₂, LMTD = (40 + 40)/2 = 40 °C (arithmetic mean applies). If U = 800 W/(m²·K) and A = 2 m², then Q = 800 × 2 × 1.0 × 40 = 64 000 W = 64 kW. Now change cold outlet to 55 °C: ΔT₁ = 90 − 55 = 35 °C, ΔT₂ = 60 − 20 = 40 °C. LMTD = (35 − 40)/ln(35/40) = −5/ln(0.875) = −5/(−0.1335) ≈ 37.5 °C.
Frequently asked questions
What is the difference between counter-flow and parallel-flow LMTD in heat exchangers?
In a counter-flow heat exchanger, hot and cold fluids flow in opposite directions, which maintains a more uniform temperature difference along the entire length and produces a higher LMTD for the same inlet and outlet conditions. In a parallel-flow arrangement, both fluids enter at the same end, the temperature difference is largest at the inlet and smallest at the outlet, yielding a lower LMTD and therefore requiring more area for the same duty. Counter-flow is thermodynamically superior and is the preferred configuration whenever space and pressure-drop constraints allow. The LMTD formula is the same for both; only the assignment of ΔT₁ and ΔT₂ changes.
When should I use the LMTD correction factor F in heat exchanger calculations?
The correction factor F is needed whenever the flow arrangement deviates from ideal counter-flow, such as in multi-pass shell-and-tube exchangers, cross-flow heat exchangers, or mixed-flow configurations. F is always ≤ 1, and values below 0.75 are generally considered inefficient and a signal to reconsider the exchanger geometry. F is determined from standardised charts or correlations based on two dimensionless temperature ratios (P and R) that compare the thermal effectiveness to the theoretical maximum. For a single-pass pure counter-flow or parallel-flow exchanger, F = 1 exactly.
How do I use LMTD to find the required heat transfer area for a new heat exchanger?
Rearrange the fundamental equation to A = Q / (U · F · LMTD). First calculate the required duty Q from energy balances on both fluid streams (Q = ṁ · cp · ΔT for each side). Then estimate or look up the overall heat transfer coefficient U, which depends on fluid types, flow velocities, and fouling factors — typical values range from 200 W/(m²·K) for gas-to-gas to 2000 W/(m²·K) for liquid-to-liquid exchangers. Calculate LMTD from the four terminal temperatures and apply the appropriate F factor. The resulting area guides initial sizing before detailed mechanical design begins.