What Is LMTD?
The Log Mean Temperature Difference (LMTD) is the effective average temperature driving force for heat transfer in a heat exchanger. Because the temperature difference between hot and cold fluids varies along the length of the exchanger, a simple arithmetic mean would be inaccurate. The LMTD properly accounts for the logarithmic nature of heat transfer, providing the correct average driving force for calculating heat duty.
LMTD is used in the fundamental heat exchanger design equation Q = U A LMTD, where Q is the heat transfer rate, U is the overall heat transfer coefficient, and A is the heat transfer area. This method is widely used in chemical engineering, HVAC design, and power plant engineering.
LMTD Formula
For counter-flow: ΔT1 = Th,in - Tc,out and ΔT2 = Th,out - Tc,in
For parallel-flow: ΔT1 = Th,in - Tc,in and ΔT2 = Th,out - Tc,out
Flow Configurations
| Configuration | LMTD | Effectiveness | Use Case |
|---|---|---|---|
| Counter-Flow | Highest | Highest possible | Most efficient design |
| Parallel-Flow | Lower | Limited | When uniform wall temp needed |
| Cross-Flow | Between | Moderate | Compact exchangers (car radiators) |
Frequently Asked Questions
Why is counter-flow more efficient?
In counter-flow, the hot and cold fluids flow in opposite directions, maintaining a more uniform temperature difference along the length. The cold outlet can approach the hot inlet temperature, enabling higher heat recovery. In parallel flow, both outlets approach the same intermediate temperature, limiting the maximum achievable heat transfer.
When does LMTD equal the arithmetic mean?
When the temperature differences at both ends are equal (dT1 = dT2), the LMTD equals both of them. This occurs in special cases like condensers or evaporators where one fluid temperature is constant, or when the heat capacity rates are perfectly balanced in counter-flow.
What is the LMTD correction factor?
For multi-pass shell-and-tube or cross-flow exchangers, the actual effective temperature difference is less than the counter-flow LMTD. A correction factor F (0 to 1) is applied: Q = U A F LMTD. Correction factor charts depend on the number of shell and tube passes and the temperature ratios P and R.