LMTD Calculator

Calculate Logarithmic Mean Temperature Difference (LMTD) and correction factors for heat exchanger design • Counter-flow & Parallel-flow • Shell & Tube configurations

The Logarithmic Mean Temperature Difference (LMTD) is the correct average temperature difference for heat exchanger design. This calculator provides LMTD values, correction factors (Ft), and visual temperature profiles for both counter-current and co-current flow configurations.

LMTD Calculator for Heat Exchangers

Hot fluid inlet temperature
Hot fluid outlet temperature
Cold fluid inlet temperature
Cold fluid outlet temperature
Select heat exchanger configuration

Temperature Profile

— Hot Fluid — Cold Fluid
LMTD Value
—
°C
AMTD (Arithmetic Mean)
—
Ratio LMTD/AMTD: —

LMTD Formulas

Counter-Current Flow:

\[ \text{LMTD} = \frac{(T_1 - t_2) - (T_2 - t_1)}{\ln\left(\frac{T_1 - t_2}{T_2 - t_1}\right)} \]

Co-Current (Parallel) Flow:

\[ \text{LMTD} = \frac{(T_1 - t_1) - (T_2 - t_2)}{\ln\left(\frac{T_1 - t_1}{T_2 - t_2}\right)} \]

LMTD Correction Factor (Ft) for Shell & Tube:

\[ \Delta T_{\text{true}} = F_t \times \text{LMTD}_{\text{counter-current}} \]

LMTD Correction Factor (Ft)

In shell-and-tube heat exchangers with multiple passes, the flow pattern is a mixture of counter-current and co-current flow. The LMTD correction factor Ft adjusts the ideal counter-current LMTD to account for this deviation.

Temperature Ratio (R):

\[ R = \frac{T_1 - T_2}{t_2 - t_1} \]

Thermal Efficiency (S):

\[ S = \frac{t_2 - t_1}{T_1 - t_1} \]

Correction Factor for 1-2 Exchanger:

\[ F_t = \frac{\sqrt{R^2 + 1} \ln\left[\frac{1-S}{1-RS}\right]}{(R-1) \ln\left[\frac{2-S(R+1-\sqrt{R^2+1})}{2-S(R+1+\sqrt{R^2+1})}\right]} \]

Reference: Coulson & Richardson, Chemical Engineering Vol. 6.

Interpretation Guidelines

  • Ft = 1.0: Pure counter-current flow (ideal case)
  • Ft > 0.8: Acceptable design; efficient heat transfer
  • Ft < 0.8: Poor design; consider increasing number of shell passes
  • Ft < 0.75: Not recommended; temperature cross likely occurring

Counter-Current vs Co-Current Flow

Counter-current flow (hot and cold fluids flow in opposite directions) is the most efficient configuration, producing the highest LMTD and requiring minimum heat transfer area. The cold fluid outlet temperature can exceed the hot fluid outlet temperature (temperature cross).

Co-current (parallel) flow (both fluids flow in same direction) produces lower LMTD and requires larger heat transfer area. The cold fluid can never be heated above the hot fluid outlet temperature.

When to Use LMTD vs AMTD

Method Formula Application
LMTD (ΔT1 − ΔT2) / ln(ΔT1/ΔT2) Standard design; accurate for all cases
AMTD (ΔT1 + ΔT2) / 2 Quick estimate when ΔT1 ≈ ΔT2

References & Further Reading

  • • Coulson, J.M. & Richardson, J.F. (1993). Chemical Engineering Volume 6: Chemical Engineering Design (3rd ed.). Butterworth-Heinemann.
  • • Kern, D.Q. (1950). Process Heat Transfer. McGraw-Hill.
  • • Ludwig, E.E. (1965). Applied Process Design for Chemical and Petrochemical Plants, Vol. 3. Gulf Publishing.
  • • TEMA Standards (2019). Tubular Exchanger Manufacturers Association Standards (10th ed.). TEMA Inc.

Frequently Asked Questions

Why is LMTD used instead of arithmetic mean?

Because the temperature difference between fluids varies exponentially along the exchanger length. LMTD correctly integrates this variation, while arithmetic mean overestimates the driving force.

What does a low correction factor (Ft < 0.8) indicate?

A low Ft indicates the exchanger operates inefficiently with significant deviation from counter-current flow. Consider using multiple shell passes in series.

What are R and S parameters?

R (temperature ratio) = (T1 − T2)/(t2 − t1). S (thermal efficiency) = (t2 − t1)/(T1 − t1). Both are dimensionless and used to calculate Ft.