Calculate the log mean temperature difference (LMTD) for heat exchangers in counterflow and parallel flow, with required area and effectiveness.
The Log Mean Temperature Difference (LMTD) is the driving force for heat transfer in a heat exchanger. It provides the effective average temperature difference between the hot and cold fluids, accounting for the fact that the temperature difference varies along the length of the exchanger. The LMTD is always less than or equal to the arithmetic mean temperature difference.
Heat exchangers are ubiquitous in engineering: condensers, evaporators, radiators, HVAC coils, oil coolers, and process heaters all rely on LMTD calculations for proper sizing. The fundamental design equation Q = U × A × LMTD connects the heat duty (Q), overall heat transfer coefficient (U), heat transfer area (A), and the LMTD.
This LMTD Calculator computes the LMTD for both counterflow and parallel-flow arrangements from the four terminal temperatures. It also calculates the arithmetic mean temperature difference, ΔT ratio, heat exchanger effectiveness, and the required surface area when U and Q are provided. Preset buttons cover common industrial applications, and a reference table provides typical U values for different fluid combinations.
Use this page to turn terminal temperatures into an effective heat-transfer driving force and then estimate exchanger area once duty and overall U are known. It keeps the temperature endpoints, LMTD, and area estimate together so the exchanger sizing step is easier to follow. That is useful when you want a quick sizing check before moving to a more detailed heat-exchanger model.
LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂) Counterflow: ΔT₁ = Thi − Tco, ΔT₂ = Tho − Tci Parallel Flow: ΔT₁ = Thi − Tci, ΔT₂ = Tho − Tco Heat Transfer: Q = U × A × LMTD Area: A = Q / (U × LMTD)
Result: LMTD = 76.1°C, AMTD = 80°C
A counterflow heat exchanger with hot fluid cooling from 150 to 90°C and cold fluid heating from 20 to 60°C has an LMTD of 76.1°C.
LMTD is the effective average temperature difference that drives heat transfer through the exchanger. Because that driving force changes from one end of the exchanger to the other, a simple arithmetic mean usually misstates the true average.
Once duty, U value, and LMTD are known, the required area follows directly from Q = U x A x LMTD. That makes LMTD one of the core screening tools in preliminary exchanger sizing, long before you build a full thermal design package.
Pure counterflow and parallel-flow formulas are the cleanest cases. Shell-and-tube multipass units, cross-flow exchangers, and arrangements with leakage or bypass need a correction factor or an effectiveness-NTU approach instead of relying on raw LMTD alone.
Because the logarithmic mean correctly accounts for how the temperature difference changes along the exchanger length. The arithmetic mean ignores that changing profile, so it usually overstates the driving force.
When ΔT₁ = ΔT₂ (balanced heat exchanger), LMTD = AMTD. As the ΔT ratio approaches 1, the difference vanishes.
Counterflow always gives a higher LMTD for the same terminal temperatures, meaning less heat transfer area is needed. It is preferred in most applications.
During phase change (condensation or boiling), the temperature stays constant. Use the appropriate LMTD formula with constant temperature for that fluid.
For cross-flow and multipass exchangers, the basic LMTD is multiplied by a factor below 1 to reflect the fact that the real temperature pattern is less ideal than pure counterflow. It is a practical way to account for flow arrangements that do not match the simple textbook case.
U depends on the convection coefficients on both sides and the wall conductance. Reference tables, handbooks, and preliminary calculations can provide estimates.