LMTD Calculator (Heat Exchanger)
Use this calculator to find the logarithmic mean temperature difference (LMTD) for a parallel flow or counterflow heat exchanger. Enter all temperatures in the same unit (°C, K, or °F).
If both U and A are entered, the calculator also estimates heat duty using Q = U × A × LMTD.
What Is Logarithmic Mean Temperature Difference?
The logarithmic mean temperature difference (LMTD) is an effective average temperature driving force used in heat exchanger design. Because the temperature difference between hot and cold streams changes from one end of the exchanger to the other, a simple arithmetic average can be misleading. LMTD gives a physically correct average for steady-state heat transfer.
Engineers use LMTD in the classic heat exchanger equation:
where Q is heat transfer rate, U is overall heat transfer coefficient, and A is heat transfer area.
LMTD Formula
For two terminal temperature differences, ΔT1 and ΔT2, the formula is:
If ΔT1 and ΔT2 are equal, then LMTD is simply that same value.
How ΔT values are defined
- Parallel flow: ΔT1 = Th,in − Tc,in, ΔT2 = Th,out − Tc,out
- Counterflow: ΔT1 = Th,in − Tc,out, ΔT2 = Th,out − Tc,in
Why LMTD Matters in Heat Exchanger Design
In thermal engineering, LMTD is central to sizing shell-and-tube exchangers, plate exchangers, condensers, and coolers. A higher LMTD means a stronger driving force and often a smaller required heat transfer area for the same duty. A lower LMTD implies you need more area, better heat transfer coefficients, or different operating temperatures.
When comparing counterflow heat exchangers and parallel flow heat exchangers, counterflow usually gives a larger LMTD under similar boundary conditions. That is one reason counterflow arrangements are often preferred for compact and efficient thermal systems.
How to Use This Calculator
- Select the flow arrangement (counterflow or parallel flow).
- Enter hot-side inlet and outlet temperatures.
- Enter cold-side inlet and outlet temperatures.
- Click Calculate LMTD.
- Optionally, add U and A to estimate heat duty Q.
Tip: Keep all input temperatures in one consistent unit. Since LMTD is a temperature difference, °C and K differences are numerically the same.
Worked Example
Suppose you have a counterflow exchanger with:
- Th,in = 180°C
- Th,out = 120°C
- Tc,in = 40°C
- Tc,out = 95°C
Then:
- ΔT1 = 180 − 95 = 85°C
- ΔT2 = 120 − 40 = 80°C
LMTD = (85 − 80) / ln(85/80) ≈ 82.48°C
If U = 450 W/m²·K and A = 12 m², then Q ≈ 450 × 12 × 82.48 ≈ 445 kW.
Common Input Mistakes
- Using mixed temperature units (for example, one value in °C and others in °F).
- Choosing the wrong flow pattern for the exchanger.
- Entering temperatures that cause one terminal ΔT to be zero or negative for the selected model.
- Assuming LMTD applies directly to strongly transient systems without steady-state assumptions.
Final Notes
This logarithmic mean temperature difference calculator is ideal for quick checks, design estimates, and education. For detailed exchanger rating and sizing, engineers often combine LMTD with correction factors, fouling assumptions, pressure-drop constraints, and pinch analysis. Still, as a first-pass tool, LMTD remains one of the most useful concepts in practical heat transfer.