LMTD Heat Exchanger Calculator
Calculate the Log Mean Temperature Difference (LMTD) for counter-flow or parallel-flow heat exchangers. Used by engineers to size heat exchange area and evaluate thermal performance.
About this calculator
The Log Mean Temperature Difference (LMTD) is the effective average temperature driving force across a heat exchanger. For a counter-flow arrangement, the terminal temperature differences are defined as ΔT₁ = T_hot,in − T_cold,out and ΔT₂ = T_hot,out − T_cold,in. The LMTD is then: LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂). When ΔT₁ equals ΔT₂ exactly, LMTD simplifies to that equal value (avoiding a division-by-zero). The LMTD feeds directly into the heat exchanger design equation Q = U × A × LMTD, where Q is the heat duty (W), U is the overall heat transfer coefficient (W/m²·K), and A is the required surface area (m²). Maximizing LMTD reduces the area needed, lowering capital cost.
How to use
A counter-flow heat exchanger cools hot oil from 120 °C to 60 °C using water entering at 25 °C and leaving at 55 °C. Calculate the terminal differences: ΔT₁ = 120 − 55 = 65 °C and ΔT₂ = 60 − 25 = 35 °C. Apply the formula: LMTD = (65 − 35) / ln(65 / 35) = 30 / ln(1.857) = 30 / 0.6190 ≈ 48.5 °C. If the heat duty is 500,000 W and U = 300 W/m²·K, the required area is A = Q / (U × LMTD) = 500,000 / (300 × 48.5) ≈ 34.4 m².
Frequently asked questions
What is the difference between LMTD for counter-flow and parallel-flow heat exchangers?
In a counter-flow exchanger, hot and cold fluids flow in opposite directions, which produces a more uniform temperature difference along the exchanger length and a higher LMTD compared to parallel flow. In a parallel-flow exchanger, both fluids enter from the same end, causing a large ΔT at the inlet that rapidly diminishes toward the outlet. For the same inlet and outlet temperatures, a counter-flow arrangement always yields a higher LMTD, meaning less heat transfer area is needed. This is why counter-flow is almost always preferred in industrial applications.
Why do we use the logarithmic mean instead of the arithmetic mean for temperature difference?
The temperature difference between hot and cold fluids changes continuously along the length of a heat exchanger, and this variation is approximately exponential in nature. The arithmetic mean would overestimate the driving force in most configurations, leading to an undersized exchanger. The logarithmic mean correctly accounts for the exponential decay of temperature difference and provides the true average driving force for heat transfer. This makes the LMTD a thermodynamically rigorous basis for heat exchanger sizing calculations.
When should I apply an LMTD correction factor (F-factor) to my calculation?
An LMTD correction factor F is required when the heat exchanger is not a pure single-pass counter-flow design — for example, shell-and-tube exchangers with multiple tube passes, or cross-flow exchangers. The corrected driving force becomes F × LMTD_counter-flow, where F is always ≤ 1. F values are read from standard charts using two dimensionless ratios (P and R) derived from the four stream temperatures. If F drops below about 0.75, the design is thermally inefficient and an alternative configuration should be considered.