Introduction
LMTD (Log Mean Temperature Difference) is a key concept used in heat exchanger design. It represents the effective temperature difference driving heat transfer between two fluids.
What Is LMTD
LMTD is the logarithmic average of temperature differences between hot and cold fluids at the inlet and outlet of a heat exchanger.
It accounts for the fact that temperature difference changes along the length of the exchanger.
Why LMTD Is Important
Temperature difference is not constant in heat exchangers. LMTD provides a more accurate value than a simple average, ensuring correct heat transfer calculations.
LMTD Formula
The LMTD is calculated using:
ΔT = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2)
Where:
- ΔT1 = temperature difference at one end
- ΔT2 = temperature difference at the other end
How to Determine ΔT1 and ΔT2
Parallel Flow
Both fluids enter from the same side:
- ΔT1 = Th,in − Tc,in
- ΔT2 = Th,out − Tc,out
Counter Flow
Fluids flow in opposite directions:
- ΔT1 = Th,in − Tc,out
- ΔT2 = Th,out − Tc,in
Counterflow generally results in higher efficiency.
Example Calculation
Given:
- Hot fluid: 120°C → 80°C
- Cold fluid: 40°C → 70°C
Counterflow case:
- ΔT1 = 120 − 70 = 50°C
- ΔT2 = 80 − 40 = 40°C
LMTD:
ΔT = (50 − 40) / ln(50 / 40) ≈ 44.7°C
Use in Heat Exchanger Design
LMTD is used in the equation:
Q = U × A × ΔT
This allows calculation of required heat transfer area.
Correction Factor (F)
In real heat exchangers, correction factor (F) is applied:
Q = U × A × F × LMTD
F depends on flow arrangement and exchanger type.
Common Mistakes
- Using arithmetic average instead of LMTD
- Incorrect temperature differences
- Ignoring correction factor
Conclusion
LMTD is essential for accurate heat exchanger design. It provides the true driving force for heat transfer and ensures proper sizing and performance.
