LMTD (Log Mean Temperature Difference) Calculation Guide
Introduction:
LMTD is a crucial parameter used in heat exchanger design to determine the temperature driving force for heat transfer. This logarithmic average accounts for the fact that the temperature difference between hot and cold fluids varies along the heat exchanger.
LMTD Formula:
LMTD = (ΔT1 - ΔT2) / ln(ΔT1/ΔT2)
Where:
ΔT1 = Hot fluid inlet temp - Cold fluid outlet temp
ΔT2 = Hot fluid outlet temp - Cold fluid inlet temp
ln = Natural logarithm
For Counter-flow Heat Exchangers:
ΔT1 = Th,in - Tc,out
ΔT2 = Th,out - Tc,in
For Parallel-flow Heat Exchangers:
ΔT1 = Th,in - Tc,in
ΔT2 = Th,out - Tc,out
Example Calculation:
Let's solve an example for a counter-flow heat exchanger:
Given:
Hot fluid inlet temperature (Th,in) = 95°C
Hot fluid outlet temperature (Th,out) = 45°C
Cold fluid inlet temperature (Tc,in) = 25°C
Cold fluid outlet temperature (Tc,out) = 55°C
Step 1: Calculate ΔT1
ΔT1 = Th,in - Tc,out
ΔT1 = 95°C - 55°C = 40°C
Step 2: Calculate ΔT2
ΔT2 = Th,out - Tc,in
ΔT2 = 45°C - 25°C = 20°C
Step 3: Apply LMTD formula
LMTD = (40°C - 20°C) / ln(40/20)
LMTD = 20 / ln(2)
LMTD = 28.84°C
Important Notes:
LMTD is always positive
Units must be consistent (either °C or K)
For complex heat exchanger configurations, correction factors may be needed
Applications:
Heat exchanger design
Performance evaluation
Sizing calculations
Energy efficiency analysis
Conclusion:
Understanding and correctly calculating LMTD is essential for heat exchanger design and analysis. This logarithmic average provides a more accurate representation of the true driving force for heat transfer compared to a simple arithmetic mean.
