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Log Mean Temperature Difference (LMTD) Heat Exchanger Calculator

The Log Mean Temperature Difference (LMTD) provides the logarithmic average driving temperature force between hot and cold fluid streams along a heat exchanger.

Relative flow direction of hot and cold streams.

Temperature of hot process fluid entering the exchanger.

Temperature of hot process fluid exiting the exchanger.

Temperature of coolant or cold fluid entering the exchanger.

Temperature of cold fluid exiting the exchanger.

Overall heat transfer coefficient U (water-water plate ≈ 1000 - 4000, shell-and-tube ≈ 500 - 1000).

Total effective heat exchange surface area in square meters.

Calculated Result
39.15 °C

Log Mean Temp Difference (LMTD)

Log Mean Temp Difference (LMTD)

39.15°C

Flow Configuration

Counter-Current Flow (Maximum Thermal Efficiency)

Terminal End ΔT

ΔT₁ = 50°C, ΔT₂ = 30°C

Thermal Effectiveness (ε)

57.1%

Total Heat Transfer Duty (Q)

391.52 kW (U = 800 W/m²K, A = 12.5 m²)

Calculation Breakdown

  1. 1. Terminal Temperature DifferencesΔT₁ = Th_in - Tc_out = 90°C - 40°C = 50°C; ΔT₂ = Th_out - Tc_in = 50°C - 20°C = 30°C
  2. 2. LMTD Integration FormulaLMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁ / ΔT₂) = (50 - 30) / ln(50 / 30) = 39.15°C
  3. 3. Total Heat Transfer Duty (Q = U · A · LMTD)Q = 800 W/(m²·K) · 12.5 m² · 39.15°C = 391.52 kW

Terminal Temperature Driving Forces

Interactive visualization based on your current inputs

ΔT (°C)
0.013253850Hot End (ΔT₁)Log Mean (LMTD)Cold End (ΔT₂)LocationΔT (°C)

What Is the Log Mean Temperature Difference (LMTD) Heat Exchanger Calculator?

The Log Mean Temperature Difference represents the logarithmic driving force for heat conduction across heat exchanger boundaries.

How Does the Log Mean Temperature Difference (LMTD) Heat Exchanger Calculator Work?

Integrates Newton’s law of cooling along variable temperature profiles in co-current and counter-current channels.

Log Mean Temperature Difference (LMTD) Heat Exchanger Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}, \quad Q = U \cdot A \cdot \Delta T_{lm}

Log mean temperature difference equals terminal difference ΔT1 minus ΔT2 divided by the natural logarithm of their ratio. Heat duty is U times area times LMTD.

How to Use the Log Mean Temperature Difference (LMTD) Heat Exchanger Calculator

  1. Select counter-flow or parallel-flow configuration.
  2. Enter hot stream inlet and outlet temperatures.
  3. Enter cold stream inlet and outlet temperatures.
  4. Optionally supply overall heat transfer coefficient U and area A to compute kilowatt duty.

Step-by-Step Example Calculation

Counter-Flow Water Chiller (90°C/50°C vs 20°C/40°C)

Input Values:

flowConfiguration:counter-flow
hotInTempC:90
hotOutTempC:50
coldInTempC:20
coldOutTempC:40
overallHeatTransferCoeffU:800
heatExchangerAreaM2:12.5
Worked Steps: With ΔT₁ = 50°C and ΔT₂ = 30°C, LMTD is 39.15°C, yielding 391.52 kW total heat transfer duty at 800 W/(m²·K).

Understanding Your Result

LMTD (°C): Logarithmic mean temperature difference.

Heat Duty (kW): Transferred thermal energy rate.

Terminal End Differences: Local temperature driving forces at entry and exit.

Factors That Affect the Result

  • Counter-flow yields systematically larger LMTD than parallel flow for the same terminal temperatures.

When Should You Use This Calculator?

  • Chemical process condensers, district heating substations, HVAC chillers, and steam boilers.

Assumptions & Limitations

  • Assumes constant overall heat transfer coefficient U and constant specific heats without phase change along the path.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Classical analytical solution to the 1D steady-state heat exchanger governing differential equation.

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