Log Mean Temperature Difference
Also known as: LMTD, logarithmic mean temperature difference
The Log Mean Temperature Difference (LMTD) method is a fundamental tool for calculating heat transfer rates in heat exchangers. It defines the effective temperature difference between two fluids as the logarithmic average of the temperature differences at the inlet and outlet. This method enables engineers to size and analyze heat exchangers systematically using the basic heat transfer equation Q = U A LMTD.
Key highlights
- Provides exact analytical solution for counterflow arrangement
- Mathematically elegant and thermodynamically rigorous
- Enables straightforward heat exchanger sizing calculations
- Well-established empirical correction factors available
Intuition
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How it works
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When to use it
Use LMTD method when inlet and outlet temperatures are known or can be readily determined. It is particularly suitable for rating problems (determining heat transfer rate for a given exchanger) and design problems with known temperature specifications. Avoid using when temperature change is small (use arithmetic mean) or when complex internal flow patterns exist.
Strengths & limitations
- Provides exact analytical solution for counterflow arrangement
- Mathematically elegant and thermodynamically rigorous
- Enables straightforward heat exchanger sizing calculations
- Well-established empirical correction factors available
- Requires knowledge of outlet temperatures (not always available initially)
- Can be computationally iterative for design problems with unknown outlet conditions
- Correction factors for cross-flow are empirical and less accurate for extreme configurations
- Assumes constant overall heat transfer coefficient along the length
Common pitfalls
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Applications
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Frequently asked
Why use logarithmic mean instead of arithmetic mean?
Temperature change in a heat exchanger is exponential, not linear. The logarithmic mean correctly weights the temperature differences accounting for this exponential variation. Using arithmetic mean overestimates heat transfer for most configurations.
What is the correction factor F and when do I need it?
F accounts for deviation from ideal counterflow. For true counterflow, F = 1. For parallel flow or cross-flow, F < 1 and depends on dimensionless parameters P and R. Correction charts are available in heat transfer textbooks.
How do I solve design problems when outlet temperature is unknown?
Use an iterative approach: assume an outlet temperature, calculate LMTD and Q, verify energy balance, and adjust until convergence. Many software tools automate this process.
Sources
- 1.Kern, D. Q. (1950). Process Heat Transfer. McGraw-Hill.
- 2.Incropera, F. P., DeWitt, D. P., Bergman, T. L., & Lavine, A. S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.). Wiley.ISBN 978-0470055540
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ScholarGate. (2026, June 3). Log Mean Temperature Difference. ScholarGate. https://scholargate.app/thermodynamics/log-mean-temperature-difference