Heat exchangers — LMTD and ε-NTU

Heat exchangers show up across HVAC & Refrigeration and Thermal & Fluid Systems, and they're a place candidates report the real exam runs harder than the practice books. The key is knowing which method to reach for — picking wrong wastes the time you don't have.

The two methods, and when to use each

• LMTD (log-mean temperature difference). Use it when you know (or can find) the inlet and outlet temperatures. Heat duty = overall coefficient × area × correction factor × the log-mean temperature difference. The correction factor accounts for real geometries (shell-and-tube, cross-flow) that aren't pure counterflow.
• ε-NTU (effectiveness–number of transfer units). Use it when you don't know an outlet temperature — when solving for LMTD would force iteration. Effectiveness ties the actual heat transfer to the maximum possible, given the flow arrangement and the heat-capacity-rate ratio.

Details that decide the answer

• Counterflow vs. parallel flow changes the temperature profile and the LMTD — counterflow is more effective for the same end temperatures.
• The overall U combines the convective films and any wall/fouling resistances in series.
• Geometry (shell-and-tube, plate-and-frame) sets the correction factor or the effectiveness relation.

Where people lose points

• Using LMTD when an outlet temperature is unknown — and burning minutes iterating instead of switching to ε-NTU.
• Counterflow vs. parallel mix-ups in the LMTD.
• Forgetting the correction factor on a non-counterflow exchanger.
• Dropping fouling from the overall resistance when the problem includes it.

How to study it

Build the habit of asking first: do I know both outlet temperatures? That one question routes you to LMTD or ε-NTU instantly. Then drill both methods on shell-and-tube and cross-flow geometries until the routing and the relations are automatic.

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