What is a good value of the LMTD correction factor F?

Design practice typically requires F ≥ 0.75 for shell-and-tube and cross-flow exchangers. If F is much lower (e.g., below 0.7), the configuration is thermally inefficient and you may need more surface area or a different flow arrangement.

Can this LMTD calculator size a heat exchanger?

Yes. If you know the required heat duty Q and an estimate of the overall heat transfer coefficient U, the calculator can compute the required heat transfer area A = Q / (U · F · LMTD). You can then compare A with the area of a candidate exchanger from vendor data.

LMTD Calculator – Log Mean Temperature Difference

Compute log mean temperature difference (LMTD), heat duty, and required heat transfer area for parallel-flow, counter-flow, and cross-flow heat exchangers using the LMTD method.

Flow arrangement

For cross-flow and multi-pass shell-and-tube, LMTD is multiplied by a correction factor F (typically 0.75–0.95).

Hot fluid

Inlet temperature Th,in

Outlet temperature Th,out

Cold fluid

Inlet temperature Tc,in Outlet temperature Tc,out

What is LMTD (Log Mean Temperature Difference)?

In a heat exchanger, the temperature difference between the hot and cold fluids changes along the length of the exchanger. The log mean temperature difference (LMTD) is an effective average temperature driving force that allows you to use the simple design equation:

\( Q = U \cdot A \cdot \Delta T_{\text{lm}} \) (for pure parallel or counter-flow)
\( Q = U \cdot A \cdot F \cdot \Delta T_{\text{lm}} \) (for cross-flow / shell-and-tube)

Here:

Q = heat duty (W, kW, BTU/hr)
U = overall heat transfer coefficient (W/m²·K or BTU/hr·ft²·°F)
A = heat transfer area (m² or ft²)
\(\Delta T_{\text{lm}}\) = log mean temperature difference
F = LMTD correction factor (dimensionless, typically 0.75–1.0)

LMTD formula

For a single-pass parallel-flow or counter-flow heat exchanger, define the terminal temperature differences:

\( \Delta T_1 = T_{h,\text{in}} - T_{c,\text{out}} \)
\( \Delta T_2 = T_{h,\text{out}} - T_{c,\text{in}} \)

The log mean temperature difference is then:

\( \Delta T_{\text{lm}} = \dfrac{\Delta T_1 - \Delta T_2}{\ln\left(\dfrac{\Delta T_1}{\Delta T_2}\right)} \)

If \(\Delta T_1\) and \(\Delta T_2\) are almost equal, the expression becomes numerically unstable. In that case, this calculator automatically switches to the arithmetic mean:

\( \Delta T_{\text{lm}} \approx \dfrac{\Delta T_1 + \Delta T_2}{2} \quad \text{when } |\Delta T_1 - \Delta T_2| \ll \Delta T_1, \Delta T_2 \)

Using the LMTD method for design

1. Sizing a heat exchanger (find area A)

Specify the required heat duty \(Q\) from process requirements.
Estimate or obtain an overall heat transfer coefficient \(U\) from correlations or vendor data.
Enter inlet and outlet temperatures for both fluids and compute LMTD.
Apply a correction factor \(F\) if the exchanger is not pure counter- or parallel-flow.
Compute the required area:

\( A = \dfrac{Q}{U \cdot F \cdot \Delta T_{\text{lm}}} \)

2. Rating a heat exchanger (find Q)

Use known geometry to get the area \(A\) and an estimate of \(U\).
Measure or specify inlet and outlet temperatures.
Compute LMTD and apply correction factor \(F\).
Compute the heat duty:

\( Q = U \cdot A \cdot F \cdot \Delta T_{\text{lm}} \)

When do you need the correction factor F?

The simple LMTD expression assumes a true counter-flow or parallel-flow exchanger. Real industrial exchangers often use:

1–2, 2–4, or multi-pass shell-and-tube configurations
Cross-flow arrangements (both fluids unmixed or one mixed)
Condensers and boilers with phase change on one side

In these cases, the temperature distribution is more complex and the effective driving force is smaller than the ideal LMTD. A correction factor \(F\) is applied:

\( \Delta T_{\text{effective}} = F \cdot \Delta T_{\text{lm}} \)

Typical design practice is to require F ≥ 0.75. If F is much lower, the exchanger is thermally inefficient and you may need more area or a different configuration.

Common pitfalls and checks

Sign of ΔT: Both \(\Delta T_1\) and \(\Delta T_2\) must be positive. If one is negative, the specified outlet temperatures are inconsistent with the assumed hot/cold assignment.
Temperature units: LMTD is based on temperature differences, so °C and K (or °F and °R) are interchangeable as long as you are consistent.
Approach temperature: Very small terminal temperature differences (e.g. < 3–5 K) may be difficult to achieve in practice and can lead to very large required areas.

FAQ

What is LMTD in a heat exchanger?

LMTD (log mean temperature difference) is the effective average temperature difference between hot and cold fluids in a heat exchanger. It accounts for the fact that the temperature difference changes from inlet to outlet and is used in the design equation \( Q = U \cdot A \cdot \Delta T_{\text{lm}} \).

When can I use the simple LMTD formula without a correction factor?

You can use the simple LMTD formula directly for single-pass parallel-flow and single-pass counter-flow exchangers with no phase change and reasonably uniform U. For cross-flow and multi-pass shell-and-tube exchangers, you should apply a correction factor F.

What is a typical value of the LMTD correction factor F?

For well-designed shell-and-tube or cross-flow exchangers, F is often in the range 0.8–0.95. Many design guidelines recommend F ≥ 0.75. If your estimated F is lower, consider changing the configuration or increasing area.

Can this calculator handle both SI and US units?

Yes. You can enter temperatures in °C, °F, or K; U in W/m²·K or BTU/hr·ft²·°F; and area in m² or ft². The calculator converts everything internally to consistent SI units and reports results with appropriate units.