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🌡️ LMTD Calculator

Calculate the Logarithmic Mean Temperature Difference for heat exchangers.

Inputs

Invalid temperature differences. Ensure Hot > Cold at all points.

Results

ΔT₁
0.0 °F
ΔT₂
0.0 °F
LMTD
Error °F

Temperature Profile

Position along Heat ExchangerTemperatureTh,inTh,outTc,outTc,in ΔT₁ΔT₂

Calculator Description

The Logarithmic Mean Temperature Difference (LMTD) represents the effective average driving force for heat transfer in a heat exchanger, where the temperature difference between the hot and cold fluids varies along its length. Because that difference changes exponentially, a logarithmic mean is used instead of a simple arithmetic average.

What this calculator finds

This calculator computes a heat exchanger's LMTD from the inlet and outlet temperatures of the hot and cold fluids, supporting both counter-flow and parallel-flow arrangements.

Why it matters

  • Sizing the required heat-transfer area A in the design equation Q = U · A · LMTD
  • Comparing how counter-flow versus parallel-flow arrangements affect performance
  • Evaluating the performance and verifying the heat duty of existing exchangers

Formula

LMTD Equation

The LMTD is the logarithmic mean of the temperature differences ΔT₁ and ΔT₂ at the two ends of the exchanger. How those end differences are defined depends on the flow arrangement.

LMTD=ΔT1−ΔT2ln⁡ ⁣(ΔT1ΔT2)\text{LMTD} = \dfrac{\Delta T_1 - \Delta T_2}{\ln\!\left(\dfrac{\Delta T_1}{\Delta T_2}\right)}
  • LMTD — Logarithmic mean temperature difference [°C or K]
  • Counter-flow — ΔT₁ = T_h,in − T_c,out | ΔT₂ = T_h,out − T_c,in
  • Parallel-flow — ΔT₁ = T_h,in − T_c,in | ΔT₂ = T_h,out − T_c,out
  • T_h, T_c — Hot / cold fluid temperatures; subscripts in/out mean inlet/outlet [°C]

How the formula works

  • A larger LMTD means a greater driving force, so the same duty can be handled with less area.
  • For the same inlet/outlet temperatures, counter-flow always yields a larger LMTD than parallel-flow, making it more efficient.
  • If ΔT₁ = ΔT₂ the log expression becomes 0/0, so LMTD is then defined as that common value (the arithmetic mean).

Worked example

In counter-flow with hot fluid 120 °C → 80 °C and cold fluid 30 °C → 70 °C, ΔT₁ = 120 − 70 = 50 °C and ΔT₂ = 80 − 30 = 50 °C. Since they are equal, LMTD = 50 °C. If instead ΔT₁ = 50 and ΔT₂ = 30, then LMTD = (50 − 30) / ln(50/30) ≈ 39.2 °C.

Useful Tips

Practical tips

  • For shell-and-tube or cross-flow exchangers, apply a correction factor F: ΔT_eff = F × LMTD (F ≤ 1).
  • Design for counter-flow when possible to obtain a larger LMTD and reduce heat-transfer area.

Limitations & cautions

  • The LMTD method assumes a constant overall heat-transfer coefficient U and constant specific heats throughout the exchanger.
  • For phase change (condensation/boiling) or strongly varying properties, split the exchanger into zones for accuracy.
  • When outlet temperatures are unknown, the ε-NTU method is often more convenient than LMTD.