Log Mean Temperature Difference Calculator

Calculator Inputs

Flow arrangement

This sets how ΔT1 and ΔT2 are paired.

Temperature unit

Use one unit consistently for all inputs.

Quick check

LMTD uses only temperature differences

Offsets cancel, but do not mix units.

Hot inlet, Th,in

Hot outlet, Th,out

Cold inlet, Tc,in

Cold outlet, Tc,out

ΔT definitions

Parallel flow

ΔT1 = Th,in − Tc,in · ΔT2 = Th,out − Tc,out

Counterflow

ΔT1 = Th,in − Tc,out · ΔT2 = Th,out − Tc,in

Reset

Formula Used

The log mean temperature difference represents an average driving temperature difference for heat exchange when the temperature difference changes along the exchanger length.

LMTD is defined as: LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2)

ΔT1 and ΔT2 are the temperature differences at the two ends.
If ΔT1 equals ΔT2, then LMTD equals that common difference.
Both ΔT1 and ΔT2 must be positive for a valid logarithm.

How to Use This Calculator

Select the flow arrangement: counterflow or parallel flow.
Choose a single temperature unit and keep it consistent.
Enter hot and cold inlet and outlet temperatures.
Press Calculate to show results above the form.
Use the CSV or PDF buttons to export the computed values.

Example Data Table

Flow	Th,in	Th,out	Tc,in	Tc,out	ΔT1	ΔT2	LMTD
Counterflow	120 °C	80 °C	30 °C	60 °C	60	50	54.85
Parallel flow	150 °C	90 °C	40 °C	75 °C	110	15	45.58
Counterflow	95 °C	65 °C	20 °C	55 °C	40	45	42.46

Example values are rounded for quick reference.

Technical Article

1) Role of LMTD in heat exchanger design

Log mean temperature difference (LMTD) compresses a varying temperature driving force into one effective difference. It is used with Q = U · A · LMTD, where Q is heat duty, U is overall coefficient, and A is area. Because LMTD depends on end temperatures, it is excellent for quick sizing and comparison studies.

2) Choosing the flow arrangement

Counterflow typically maintains a larger temperature gap along the length than parallel flow. For the same inlet and outlet temperatures, counterflow often yields a higher LMTD and therefore needs less surface area. Parallel flow can be acceptable, but it may tighten the outlet “pinch” and reduce the effective driving force.

3) Understanding ΔT1 and ΔT2

The two end differences, ΔT1 and ΔT2, come from the selected arrangement. They must stay positive. If either becomes zero or negative, it usually indicates temperature crossing, swapped streams, or unrealistic targets. Verify which stream is hot and cold at each end before trusting the output.

4) Near-equal end differences

When ΔT1 ≈ ΔT2, the logarithmic form approaches 0/0. Physically, the driving force is nearly constant, so LMTD should equal that common difference. The calculator detects this case to avoid numerical noise.

5) Using LMTD for area and duty checks

Rearranging gives A = Q / (U · LMTD). Example: if Q = 500 kW, U = 800 W/(m²·K), and LMTD = 25 K, then A ≈ 25 m². Keep units consistent and remember LMTD is a temperature difference.

6) Correction factor for complex exchangers

Ideal parallel and counterflow use LMTD directly. Multi-pass and crossflow arrangements often apply a correction factor F: Q = U · A · F · LMTD. Many design practices prefer F above about 0.75 to limit area penalties and sensitivity to maldistribution.

7) Data checks and troubleshooting

Confirm hot inlet > hot outlet and cold outlet > cold inlet for typical heating service. Extremely small approach differences can be feasible but increase area sharply. If the calculator flags invalid differences, revisit end temperatures and flow selection first.

8) Reporting and sensitivity studies

Use exports to document cases and compare outlet targets, fouling allowances that reduce U, or flow arrangement changes. LMTD is best for screening; detailed rating should still consider pressure drop, phase change, and property variation along the length.

FAQs

1) What does LMTD represent?

LMTD is an effective average temperature difference that drives heat transfer when the temperature gap varies along an exchanger. It replaces a changing profile with one value suitable for sizing and quick performance checks.

2) Why must ΔT1 and ΔT2 be positive?

The logarithm in the LMTD formula requires a positive ratio ΔT1/ΔT2. Negative or zero end differences typically mean temperature crossing, swapped streams, or inconsistent inlet/outlet targets.

3) Can I use °F, °C, or K?

Yes. LMTD uses temperature differences, so offsets cancel. Enter all temperatures in one consistent unit. Do not mix units within a single calculation.

4) What if ΔT1 equals ΔT2?

If the end differences match, the driving force is constant. In that special case, LMTD equals the common difference, and the calculator returns that value directly.

5) How is LMTD used to estimate heat duty?

Combine it with overall coefficient and area using Q = U · A · LMTD. If flow is not true parallel or counterflow, include a correction factor: Q = U · A · F · LMTD.

6) When do I need an LMTD correction factor F?

Use F for crossflow exchangers and multi-pass shell-and-tube arrangements where the temperature profile deviates from ideal parallel or counterflow. Design practices often aim for F above roughly 0.75–0.8.

7) Why do counterflow and parallel flow give different values?

They pair the hot and cold end temperatures differently. Counterflow usually maintains a larger temperature gap along the length, producing a higher effective driving force and often reducing required area.