LMTD Calculator
Free calculate log mean temperature difference for heat exchanger design. Get instant, accurate results with our easy-to-use calculator.
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What is LMTD?
LMTD (Log Mean Temperature Difference) is the logarithmic average of the temperature differences between hot and cold fluids at each end of a heat exchanger. It's used to calculate heat transfer rates when the temperature difference varies along the flow path.
In heat exchangers, the temperature difference between hot and cold fluids changes continuously along the length. The LMTD provides an effective average temperature difference that can be used in the heat transfer equation: Q = U × A × LMTD.
LMTD is essential for designing and analyzing heat exchangers, including shell-and-tube, plate, and other configurations. It accounts for the varying temperature difference more accurately than a simple arithmetic mean.
LMTD Formula
Where:
- • ΔT₁ = Temperature difference at one end
- • ΔT₂ = Temperature difference at the other end
- • ln = Natural logarithm
For counter-flow:
ΔT₁ = T_h,in - T_c,out, ΔT₂ = T_h,out - T_c,in
For parallel-flow:
ΔT₁ = T_h,in - T_c,in, ΔT₂ = T_h,out - T_c,out
How to Calculate
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1
Convert all temperatures to same units
Convert to Kelvin or consistent Celsius/Fahrenheit for calculations.
-
2
Calculate temperature differences
For counter-flow: ΔT₁ = T_h,in - T_c,out, ΔT₂ = T_h,out - T_c,in
For parallel-flow: ΔT₁ = T_h,in - T_c,in, ΔT₂ = T_h,out - T_c,out
-
3
Calculate LMTD
LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁ / ΔT₂). If ΔT₁ = ΔT₂, use arithmetic mean.
Practical Examples
Example 1: Counter-Flow Heat Exchanger
Hot: 80°C → 50°C, Cold: 20°C → 40°C. Calculate LMTD.
Solution:
ΔT₁ = 80 - 40 = 40°C, ΔT₂ = 50 - 20 = 30°C
LMTD = (40 - 30) / ln(40/30) = 10 / ln(1.333)
LMTD ≈ 34.8°C
Example 2: Parallel-Flow Heat Exchanger
Hot: 80°C → 50°C, Cold: 20°C → 40°C.
Solution:
ΔT₁ = 80 - 20 = 60°C, ΔT₂ = 50 - 40 = 10°C
LMTD ≈ 27.9°C (lower than counter-flow!)
Applications
Heat Exchanger Design
Sizing heat exchangers, calculating required heat transfer area, and optimizing thermal performance.
Thermal Systems
Designing HVAC systems, refrigeration, power plants, and industrial thermal processes.
Process Engineering
Analyzing heat transfer in chemical processes, optimizing energy efficiency, and process design.
Education
Teaching heat transfer principles, understanding logarithmic averages, and heat exchanger analysis.
Frequently Asked Questions
Why use LMTD instead of average temperature difference?
LMTD accounts for the logarithmic variation in temperature difference along the heat exchanger. It's more accurate than arithmetic mean, especially when temperature differences vary significantly.
What is the difference between counter-flow and parallel-flow?
Counter-flow: fluids flow in opposite directions - more efficient, higher LMTD. Parallel-flow: fluids flow in same direction - less efficient, lower LMTD. Counter-flow is generally preferred.
What if ΔT₁ = ΔT₂?
If temperature differences are equal, LMTD = ΔT (arithmetic mean). This occurs when one fluid has constant temperature (e.g., condensing or evaporating).
How is LMTD used in heat transfer calculations?
Heat transfer rate: Q = U × A × LMTD, where U is overall heat transfer coefficient and A is heat transfer area. LMTD provides the effective driving force for heat transfer.
What about cross-flow and multi-pass heat exchangers?
For non-counter-flow configurations, use LMTD with a correction factor F: Q = U × A × LMTD × F. The F factor accounts for the flow arrangement and is typically 0.7-1.0.