The log mean temperature difference method is a core tool for sizing and analyzing heat exchangers when two fluids exchange thermal energy through a wall. It converts a changing temperature difference along the exchanger into one effective average driving force. This matters because the local heat-transfer rate is larger where the fluid temperatures are farther apart and smaller where they are closer together.
Engineers use the method to estimate heat-transfer area, heat duty, and outlet temperatures in devices such as condensers, boilers, radiators, and process heat exchangers.
The method combines the heat-transfer design equation Q = UAΔTlm with an energy balance on the hot and cold streams. For a heat exchanger with temperature differences ΔT1 and ΔT2 at the two ends, the log mean temperature difference is ΔTlm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2). Counterflow usually gives a larger LMTD than parallel flow for the same inlet and outlet temperatures, so it often needs less surface area for the same heat duty.
Real multi-pass and crossflow exchangers often require a correction factor F, giving Q = UAFΔTlm.
Key Facts
- Heat exchanger design equation: Q = UAΔTlm.
- Log mean temperature difference: ΔTlm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2).
- Hot-stream energy balance: Q = mh ch (Th,in - Th,out).
- Cold-stream energy balance: Q = mc cc (Tc,out - Tc,in).
- For parallel flow, ΔT1 = Th,in - Tc,in and ΔT2 = Th,out - Tc,out.
- For counterflow, ΔT1 = Th,in - Tc,out and ΔT2 = Th,out - Tc,in.
Vocabulary
- LMTD
- The log mean temperature difference is the effective average temperature difference that drives heat transfer along a heat exchanger.
- Overall heat-transfer coefficient
- The overall heat-transfer coefficient U measures the combined ability of convection, wall conduction, and fouling layers to transfer heat.
- Heat duty
- Heat duty Q is the rate of thermal energy transferred from one fluid to the other.
- Counterflow
- Counterflow is a heat exchanger arrangement where the hot and cold fluids move in opposite directions.
- Correction factor
- The correction factor F adjusts the ideal LMTD result for exchanger arrangements that are not simple parallel flow or counterflow.
Common Mistakes to Avoid
- Using the arithmetic average temperature difference instead of LMTD is wrong because the temperature driving force usually changes nonlinearly along the exchanger.
- Mixing up ΔT1 and ΔT2 for parallel and counterflow is wrong because each flow arrangement pairs different end temperatures.
- Forgetting the correction factor F for crossflow or multi-pass exchangers is wrong because Q = UAΔTlm applies directly only to ideal one-pass parallel or counterflow cases.
- Using inconsistent units for U, A, and Q is wrong because W, m2, and W/(m2 K) must combine so the temperature difference is in K or °C.
Practice Questions
- 1 A counterflow heat exchanger has Th,in = 120 °C, Th,out = 70 °C, Tc,in = 25 °C, and Tc,out = 60 °C. Calculate ΔT1, ΔT2, and ΔTlm.
- 2 A heat exchanger has U = 500 W/(m2 K), A = 12 m2, and ΔTlm = 35 K. Calculate the heat-transfer rate Q.
- 3 For the same inlet and outlet temperatures, explain why a counterflow heat exchanger often requires less heat-transfer area than a parallel-flow heat exchanger.