LMTD Calculator

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

Determine the effective temperature difference driving heat transfer in heat exchangers using the logarithmic mean temperature difference method.

Examples

Click on any example to load it into the calculator.

Counterflow Heat Exchanger

Counterflow Heat Exchanger

A typical counterflow heat exchanger with good temperature approach.

Hot In: 90 °C

Hot Out: 50 °C

Cold In: 20 °C

Cold Out: 60 °C

HTC: 600 W/m²·K

Area: 15 m²

Parallel Flow Heat Exchanger

Parallel Flow Heat Exchanger

Parallel flow configuration with moderate temperature difference.

Hot In: 80 °C

Hot Out: 65 °C

Cold In: 25 °C

Cold Out: 45 °C

HTC: 400 W/m²·K

Area: 12 m²

Steam Condenser

Steam Condenser

Steam condensation with cooling water in a shell-and-tube exchanger.

Hot In: 120 °C

Hot Out: 120 °C

Cold In: 15 °C

Cold Out: 35 °C

HTC: 800 W/m²·K

Area: 25 m²

Refrigeration Evaporator

Refrigeration Evaporator

Refrigerant evaporation with air cooling in an evaporator coil.

Hot In: 25 °C

Hot Out: 15 °C

Cold In: -10 °C

Cold Out: -5 °C

HTC: 300 W/m²·K

Area: 8 m²

Other Titles
Understanding LMTD Calculator: A Comprehensive Guide
Master the fundamentals of heat exchanger design and analysis using Log Mean Temperature Difference (LMTD) method. This essential tool helps engineers optimize thermal systems.

What is Log Mean Temperature Difference (LMTD)?

  • Core Concept
  • Mathematical Foundation
  • Why LMTD Matters
Log Mean Temperature Difference (LMTD) is a fundamental concept in heat exchanger design that represents the effective temperature difference driving heat transfer between two fluids. Unlike simple arithmetic mean, LMTD accounts for the logarithmic relationship between temperature differences at the inlet and outlet of the heat exchanger, providing a more accurate representation of the driving force for heat transfer.
The Mathematical Foundation
LMTD is calculated using the formula: LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂), where ΔT₁ is the temperature difference at one end of the heat exchanger and ΔT₂ is the temperature difference at the other end. This logarithmic mean provides a more accurate representation than arithmetic mean because heat transfer rate varies exponentially with temperature difference.
Why LMTD is Critical in Heat Exchanger Design
LMTD is essential because it directly relates to the heat transfer rate through the fundamental equation: Q = UA × LMTD, where Q is heat transfer rate, U is overall heat transfer coefficient, and A is heat transfer area. Accurate LMTD calculation ensures proper sizing of heat exchangers and prediction of thermal performance.
Temperature Difference Variations
In real heat exchangers, the temperature difference between hot and cold fluids varies along the length of the exchanger. The LMTD method provides a single, effective temperature difference that, when used with the overall heat transfer coefficient, gives the correct heat transfer rate for the entire exchanger.

Key LMTD Characteristics:

  • LMTD is always less than or equal to the arithmetic mean temperature difference
  • LMTD approaches the arithmetic mean when temperature differences are nearly equal
  • LMTD is sensitive to the ratio of temperature differences rather than their absolute values
  • LMTD provides the correct driving force for heat transfer calculations

Step-by-Step Guide to Using the LMTD Calculator

  • Data Collection
  • Input Validation
  • Result Interpretation
Using the LMTD calculator requires careful attention to temperature measurements and understanding of heat exchanger operation. Follow these steps to obtain accurate and meaningful results.
1. Gather Temperature Data
Measure or obtain the inlet and outlet temperatures for both hot and cold fluids. Ensure measurements are taken at the actual heat exchanger connections, not at distant locations. Use calibrated temperature sensors and account for any measurement uncertainties.
2. Validate Temperature Relationships
Verify that hot fluid temperatures are consistently higher than cold fluid temperatures. Check that the temperature differences make physical sense - hot fluid should lose heat (outlet < inlet) and cold fluid should gain heat (outlet > inlet).
3. Input Heat Transfer Parameters
Enter the overall heat transfer coefficient (U) and heat transfer area (A) if you want to calculate heat transfer rate. These values depend on the heat exchanger type, fluid properties, and operating conditions.
4. Analyze and Apply Results
The calculator provides LMTD, heat transfer rate, and effectiveness. Use these values to evaluate heat exchanger performance, compare with design specifications, or optimize operating conditions.

Common Temperature Measurement Points:

  • Shell-and-tube: Measure at shell inlet/outlet nozzles and tube inlet/outlet headers
  • Plate heat exchanger: Measure at inlet and outlet connections for both fluids
  • Air-cooled: Measure air temperature at inlet and outlet, fluid at heat exchanger connections
  • Double-pipe: Measure at the inlet and outlet of both inner and outer pipes

Real-World Applications of LMTD Analysis

  • Industrial Processes
  • HVAC Systems
  • Power Generation
LMTD analysis is fundamental to numerous industrial and commercial applications where heat transfer is critical for process efficiency and system performance.
Industrial Heat Exchangers
In chemical plants, refineries, and manufacturing facilities, LMTD calculations are used to design and optimize heat exchangers for processes like distillation, reaction cooling, and product heating. Accurate LMTD ensures proper heat transfer rates and energy efficiency.
HVAC and Building Systems
Heating, ventilation, and air conditioning systems rely on LMTD for designing chillers, boilers, and air handling units. Proper LMTD calculation ensures adequate heating/cooling capacity and energy-efficient operation.
Power Generation
Power plants use LMTD analysis for condensers, feedwater heaters, and other heat recovery systems. Optimizing LMTD improves thermal efficiency and reduces fuel consumption.
Automotive and Aerospace
Vehicle cooling systems, aircraft heat exchangers, and thermal management systems all depend on accurate LMTD calculations for proper sizing and performance prediction.

Typical LMTD Values by Application:

  • Steam condensers: 10-30°C
  • Liquid-to-liquid heat exchangers: 20-50°C
  • Air-cooled heat exchangers: 30-80°C
  • Refrigeration evaporators: 5-15°C

Common Misconceptions and Correct Methods

  • Arithmetic vs. Logarithmic Mean
  • Flow Configuration Effects
  • Fouling Considerations
Several misconceptions exist about LMTD calculation and application. Understanding these helps avoid design errors and ensures accurate thermal analysis.
Myth: Arithmetic Mean is Sufficient
Using arithmetic mean temperature difference instead of LMTD can lead to significant errors, especially when temperature differences vary considerably along the heat exchanger. Arithmetic mean overestimates the driving force, leading to undersized heat exchangers.
Myth: LMTD Works for All Flow Configurations
LMTD method is most accurate for counterflow and parallel flow configurations. For complex flow arrangements like cross-flow or multi-pass shell-and-tube exchangers, correction factors must be applied to the LMTD.
Reality: Fouling Affects LMTD Performance
Fouling buildup on heat transfer surfaces reduces the overall heat transfer coefficient over time, affecting the actual heat transfer rate even if LMTD remains constant. Regular monitoring and cleaning are essential.
Reality: Temperature Approach Matters
The minimum temperature approach (pinch point) significantly affects LMTD. Smaller temperature approaches result in lower LMTD values, requiring larger heat transfer areas for the same heat duty.

LMTD Correction Factors:

  • Cross-flow, both fluids unmixed: 0.85-0.95
  • Cross-flow, one fluid mixed: 0.90-0.98
  • 1-2 shell-and-tube: 0.80-0.90
  • 2-4 shell-and-tube: 0.85-0.95

Mathematical Derivation and Advanced Concepts

  • LMTD Derivation
  • Effectiveness-NTU Method
  • Multi-Pass Considerations
Understanding the mathematical foundation of LMTD provides insight into its limitations and applications, enabling more sophisticated heat exchanger analysis.
Derivation of LMTD Formula
LMTD is derived by integrating the differential heat transfer equation dQ = U × dA × ΔT along the length of the heat exchanger. The logarithmic form arises from the exponential relationship between temperature difference and heat transfer rate.
Effectiveness-NTU Method Alternative
For complex flow configurations or when outlet temperatures are unknown, the effectiveness-NTU method may be more appropriate than LMTD. This method uses heat exchanger effectiveness and number of transfer units.
Multi-Pass and Complex Configurations
Multi-pass shell-and-tube heat exchangers require LMTD correction factors to account for the deviation from pure counterflow or parallel flow. These factors depend on the number of shell and tube passes.
Variable Properties and Phase Change
When fluid properties vary significantly with temperature or when phase change occurs, LMTD calculations become more complex. Segmented analysis or numerical methods may be required for accurate results.

Advanced LMTD Applications:

  • Cascade heat exchanger systems with multiple temperature levels
  • Heat recovery networks with complex temperature profiles
  • Cryogenic heat exchangers with variable fluid properties
  • Phase-change heat exchangers (condensers and evaporators)