Thermal Engineering2D

LMTD Calculator - Log Mean Temperature Difference

Q: When is LMTD correction factor F needed?

For multi-pass shell-and-tube exchangers (1-2, 2-4 pass) or cross-flow, multiply LMTD by correction factor F (0.5-1.0) from TEMA charts based on P and R parameters.

Q: What if ΔT1 = ΔT2?

The formula gives 0/0, but as ΔT1→ΔT2, LMTD→ΔT (the arithmetic mean). The calculator will handle this case by using ΔT directly.

Q: How do I convert temperature between °C and °F?

°F = °C × 9/5 + 32. For example, 50°C = 122°F. LMTD is a temperature difference, so ΔT in °C equals ΔT in K, and ΔT in °F equals ΔT in °R.

Calculate Log Mean Temperature Difference (LMTD) for heat exchanger design and analysis.

Inputs

Enter your values below

Temperature Difference at End 1 (ΔT1)*C

Temperature Difference at End 2 (ΔT2)*C

Result

LMTD

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Enter values and click Calculate

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Formula

(dt1 − dt2) ÷ log(dt1 ÷ dt2)

Result unit: K

LMTD = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2). For counter-current: ΔT1 = Th_in − Tc_out, ΔT2 = Th_out − Tc_in. For equal ΔT at both ends, LMTD = ΔT.

Introduction

LMTD represents the effective average temperature driving force in a heat exchanger. Used in Q = U·A·LMTD. For counter-current flow (preferred), ΔT is taken at each end. For parallel flow, both streams enter at the same end.

How This Calculator Works

LMTD = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2). For counter-current: ΔT1 = Th_in − Tc_out, ΔT2 = Th_out − Tc_in. For equal ΔT at both ends, LMTD = ΔT.

Step-by-step process:

Enter your input values in the calculator above
The engine converts all inputs to SI base units (meters, kg, Pa)
The formula is evaluated: (dt1 - dt2) / log(dt1 / dt2)
Result is formatted with the appropriate unit and precision

Calculation Example

ΔT1 = 60°C, ΔT2 = 40°C → LMTD = 49.3 K (the arithmetic mean would be 50, very close when ΔT ratio < 2).

Inputs: dt1=60, dt2=40

Result: 49.3 K

Unit Conversion for LMTD

**Temperature units**

- °F = °C × 9/5 + 32

- K = °C + 273.15

- ΔT in °C = ΔT in K; ΔT in °F = ΔT in °R

**Heat duty units**

- 1 kW = 3412 BTU/hr

- 1 W = 3.412 BTU/hr

LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂). Because LMTD is a ratio of temperature differences, it is unit-consistent as long as both ΔT₁ and ΔT₂ use the same temperature unit.

Engineering Applications

•Heat exchanger design
•Process thermal rating
•Boiler/condenser design
•HVAC coil selection

Frequently Asked Questions

When is LMTD correction factor F needed?

For multi-pass shell-and-tube exchangers (1-2, 2-4 pass) or cross-flow, multiply LMTD by correction factor F (0.5-1.0) from TEMA charts based on P and R parameters.

What if ΔT1 = ΔT2?

The formula gives 0/0, but as ΔT1→ΔT2, LMTD→ΔT (the arithmetic mean). The calculator will handle this case by using ΔT directly.

How do I convert temperature between °C and °F?

°F = °C × 9/5 + 32. For example, 50°C = 122°F. LMTD is a temperature difference, so ΔT in °C equals ΔT in K, and ΔT in °F equals ΔT in °R.

Related Calculators

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Engineering Disclaimer: Calculations are for reference and educational purposes only. Always verify results independently for engineering design. See full disclaimer.

Reviewed by: Industrial Engineering Team

References: ASME B31.3, ASTM A36, Perry's Chemical Engineers' Handbook

Methodology: Engineering calculation methodology