LMTD Calculator for Heat Exchangers
Log mean temperature difference for counterflow, parallel and shell-and-tube heat exchangers, with the F factor, duty Q = U·A·F·LMTD and the area required.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the LMTD Calculator?
The rate at which a heat exchanger moves heat depends on the temperature difference between the two fluids, and that difference changes from one end of the exchanger to the other. The log mean temperature difference (LMTD) is the single average that makes Q = U·A·LMTD exact for a simple counterflow or parallel flow unit with constant properties. With hot water going from 150 °C to 90 °C and cold water from 30 °C to 70 °C, the ends differ by 80 K and 60 K and the LMTD is 69.52 K.
Enter the four terminal temperatures and pick the flow arrangement. The calculator gives both end differences, the LMTD, the arithmetic mean for comparison, and for a shell-and-tube unit with one shell pass and two or more tube passes it calculates the F correction factor from the capacity ratio R and effectiveness P. With an overall heat transfer coefficient U it then gives the duty for a known area, or the area needed for a known duty, in SI or US units.
- Counterflow, parallel flow and shell-and-tube arrangements
- Equal end differences handled without a divide-by-zero
- F factor for 1 shell pass and 2+ tube passes, or a manual F from charts
- Solve for duty Q or required area A in SI or US units
- Counterflow versus parallel flow comparison for the same temperatures
How to use the LMTD Calculator
- Choose counterflow, parallel flow, or shell and tube, and the temperature unit.
- Enter the hot inlet and outlet and the cold inlet and outlet temperatures.
- For shell and tube, either let the calculator find F for a 1-2 exchanger or type F from a chart for other configurations.
- Choose whether to solve for duty or required area, then enter U and the area or duty.
- Read ΔT1, ΔT2, LMTD, F and the result. The table below compares counterflow and parallel flow for the same temperatures.
Worked examples
Water to water counterflow (page default)
Input
Hot 150 → 90 °C, cold 30 → 70 °C, U 500 W/m²·K, A 10 m²
Output
ΔT1 80 K, ΔT2 60 K, LMTD 69.52 K, Q 347.6 kW
The arithmetic mean of 70 K overstates the driving force slightly; the gap grows as the two end differences move apart.
Same duty in parallel flow
Input
Same temperatures, parallel flow, Q 347.6 kW, U 500
Output
LMTD 55.81 K, area 12.46 m²
Parallel flow needs 25% more area than counterflow for the same job.
Shell and tube, one shell pass
Input
Same temperatures, F calculated
Output
R 1.5, P 0.333, F 0.910, area 10.98 m² for 347.6 kW
F of 0.91 is comfortably above the 0.8 rule of thumb, so a single shell is fine for this duty.
Background and insight
The LMTD comes from integrating dQ = U·(Th − Tc)·dA along the exchanger while each stream changes temperature in proportion to the heat it gains or loses. The result is (ΔT1 − ΔT2) / ln(ΔT1/ΔT2). When the two end differences are equal, as in a balanced counterflow exchanger, the formula becomes 0/0 and the limit is simply that common difference; the calculator handles that case directly.
Counterflow always gives the larger LMTD for the same four temperatures, so it needs the least area. It is also the only arrangement where the cold outlet can rise above the hot outlet, called a temperature cross. Parallel flow cannot achieve that, because both streams approach the same outlet temperature.
Real shell-and-tube exchangers are a mix of counterflow and parallel flow, so the counterflow LMTD is multiplied by a correction factor F of 1 or less. For one shell pass and an even number of tube passes F has a closed form, published by Bowman, Mueller and Nagle in 1940 and reproduced in TEMA standards and heat transfer texts. Designers usually keep F above about 0.75 to 0.8; below that the curve is so steep that a small error in temperatures gives a large error in area, and a second shell pass is the better choice.
Common use cases
Preliminary exchanger sizing
Estimate the area a plate or shell-and-tube unit needs before asking vendors for a rated selection.
Checking existing equipment
Back-calculate the duty an installed exchanger can deliver at new operating temperatures, or the U-value it is actually achieving.
Choosing flow arrangement
See how much area counterflow saves over parallel flow, and whether a single-shell design has an acceptable F.
Coursework and exams
Check LMTD, R, P and F values for heat transfer problems with the formulas shown step by step.
Tips and limitations
- Make sure the stream temperatures balance: the heat lost by the hot side (m·cp·ΔT) should equal the heat gained by the cold side.
- Use a design U that includes fouling resistances. Clean U-values can be 20 to 50% higher than the value after months in service.
- If F comes out as "no solution", one shell pass cannot reach those outlet temperatures. Use shells in series or true counterflow.
- For condensers and evaporators where one side stays at constant temperature, F is 1 for any arrangement.
- LMTD assumes constant U and specific heat. For large property changes, split the exchanger into zones and calculate each separately.
Frequently asked questions
What is LMTD in a heat exchanger?
The log mean temperature difference is the effective average temperature difference between the hot and cold fluids. It is the value that makes Q = U x A x LMTD exact for counterflow or parallel flow with constant properties.
What is the LMTD formula?
LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2), where ΔT1 and ΔT2 are the temperature differences between the fluids at the two ends of the exchanger.
What happens to LMTD when ΔT1 equals ΔT2?
The formula becomes 0/0, but the limit is simply the common value. If both ends differ by 40 K, the LMTD is 40 K.
Why is counterflow LMTD higher than parallel flow?
In counterflow the hottest hot fluid meets the hottest cold fluid, keeping the difference more even along the length. In parallel flow the difference starts large and shrinks fast, giving a lower mean.
What is the F correction factor?
A factor of 1 or less that corrects the counterflow LMTD for multi-pass and cross-flow exchangers. It depends on R (the ratio of the hot and cold temperature changes) and P (the cold side effectiveness).
What is a good F factor value?
Most designers aim for F above 0.8 and avoid values below 0.75. Lower F means part of the exchanger is working with little driving force and the design is very sensitive to the temperatures.
How do I calculate heat exchanger area from LMTD?
A = Q / (U x F x LMTD). For 347.6 kW with U 500 W/m²·K, F 1 and LMTD 69.52 K, A = 347,600 / (500 x 69.52) = 10.0 m².
Is there an in-depth guide to the LMTD Calculator?
Yes. “LMTD and the F Correction Factor: Sizing Heat Exchangers” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
Related Tools You May Like
Free, in-browser tools that pair well with this one.