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Heat Exchanger Effectiveness

Effectiveness–NTU analysis of a two-stream heat exchanger. In rating mode the overall conductance UA is known and the tool finds the heat transferred and both outlet temperatures; in sizing mode one outlet temperature is the target and the tool finds the NTU and UA that reach it. Six flow arrangements are covered (counterflow, parallel flow, crossflow with both streams unmixed, crossflow with one stream mixed, and shell-and-tube with one or more shell passes) with the closed-form ε–NTU relations; the log-mean temperature difference and its correction factor are reported as a check, and the ε–NTU chart of the arrangement is drawn with the case on it.

  • Capacity rates, Cmin / Cmax ratio and the maximum possible heat transfer

  • Rating: ε from NTU and the arrangement, heat duty, both outlets; sizing: NTU and UA for a target outlet

  • LMTD and the correction factor F as a cross-check; temperature profiles for counterflow and parallel flow

  • ε–NTU chart of the arrangement at several capacity ratios with the case marked

Heat Exchanger Effectiveness

Unit System: /

Hot Stream (temperatures °F for USCS, °C for SI)




Cold Stream




Exchanger







The ε–NTU Method | Method page
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Heat Exchanger Effectiveness

The ε–NTU Method

Two streams exchange heat across a wall. Each carries a capacity rate C = ṁ cp, the heat needed to change its temperature by one degree per unit time, and the smaller of the two, Cmin, limits what can be exchanged: the most that can ever pass is qmax = Cmin (Th,in − Tc,in), the duty of an infinitely long counterflow exchanger in which the Cmin stream leaves at the other stream's inlet temperature. The effectiveness ε is the actual duty as a fraction of that maximum.

The effectiveness depends on only two numbers once the arrangement is chosen: the number of transfer units NTU = UA/Cmin, the size of the exchanger measured in units of the limiting stream, and the capacity ratio Cr = Cmin/Cmax. The relations are closed forms for counterflow, parallel flow, the mixed crossflow cases and shell-and-tube exchangers, and a close correlation for crossflow with both streams unmixed. At Cr = 0, a condensing or boiling stream, every arrangement gives ε = 1 − e−NTU. Counterflow is best at every NTU; parallel flow is capped at 1/(1 + Cr) because the streams can only approach a common temperature; the others fall between.

Two problems are posed on an exchanger. Rating: UA is known (from the manufacturer, or from U and the area), so NTU and then ε, the duty and both outlets follow directly. Sizing: an outlet temperature is the target, which fixes the duty and the required ε; the NTU that gives it is solved from the arrangement's relation (the tool bisects) and UA = NTU Cmin is what to buy. A target that needs more than the arrangement's limiting ε cannot be met by any size; the tool says so and suggests counterflow.

The older LMTD method writes the same duty as q = F UA ΔTlm with the log-mean difference on the counterflow basis and a correction factor F for other arrangements. The tool reports both as a cross-check; F is 1 for counterflow and falls as the arrangement departs from it. For a design, keep F above about 0.75: below it the exchanger is near a temperature pinch and small changes in the flows move the duty a lot.



References

Incropera, F. P., DeWitt, D. P., Bergman, T. L., and Lavine, A. S. (2007). Fundamentals of Heat and Mass Transfer, 6th ed. John Wiley and Sons, Hoboken, NJ.

Kays, W. M., and London, A. L. (1984). Compact Heat Exchangers, 3rd ed. McGraw-Hill, New York.

American Society of Heating, Refrigerating and Air-Conditioning Engineers (2021). ASHRAE Handbook: Fundamentals. ASHRAE, Peachtree Corners, GA.

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