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Heat exchanger: LMTD and area

Enter flows and temperatures of both fluids, the arrangement and the overall coefficient to get the heat duty, outlet temperature, LMTD, F factor, area and the payback when the heat is recovered.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Pre-sizing
Hot fluid
Cold fluid
Exchanger
Heat recovery

If the recovered heat replaces steam or fuel, enter the cost of delivered heat (price per GJ ÷ efficiency).

Economic analysis
—Required heat transfer area
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Temperature profile along the exchanger

Temperatures of both fluids along the area, by the ε-NTU method.

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Heat recovered and area versus hot outlet temperature

Cooling the hot fluid further recovers more heat, but the area grows fast near the limit.

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Project payback

Cash flow of the improvement: investment in year 0 and annual savings escalated at the rate entered, discounted at the MARR.

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The report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

Balance: Q = ṁh · cph · (Th,in − Th,out) = ṁc · cpc · (Tc,out − Tc,in)
LMTD = (ΔT1 − ΔT2) ÷ ln(ΔT1 ÷ ΔT2); counterflow: ΔT1 = Th,in − Tc,out, ΔT2 = Th,out − Tc,in
F factor (1 shell pass, 2+ tube passes): F = √(R²+1) · ln[(1 − P) ÷ (1 − PR)] ÷ {(R − 1) · ln[(2 − P(R + 1 − √(R²+1))) ÷ (2 − P(R + 1 + √(R²+1)))]}
Fouled U: 1 ÷ Ud = 1 ÷ Uclean + Rf; area: A = Q ÷ (Ud · F · LMTD)
Effectiveness: ε = Q ÷ (Cmin · (Th,in − Tc,in)); NTU = Ud · A ÷ Cmin

Assumptions and limits

  • Constant specific heats, no phase change and no losses to ambient.
  • U entered by the user: the actual coefficient depends on velocities, geometry and fluid properties (Kern, Bell-Delaware).
  • The shell-and-tube temperature profile is drawn as an equivalent counterflow (UA corrected by F).
  • Investment proportional to area; pressure drop and pumping cost not included.

Standards and technical documents

  • TEMA, Standards of the Tubular Exchanger Manufacturers Association, 10th ed. (2019): fouling resistances and construction
  • Bowman, R. A.; Mueller, A. C.; Nagle, W. M. (1940). Mean temperature difference in design. Trans. ASME 62
  • Kern, D. Q., Process Heat Transfer; Incropera, F. P. et al., Fundamentals of Heat and Mass Transfer (ε-NTU)
  • ASME BPVC Section VIII, Division 1: shell-and-tube exchangers as pressure vessels

U.S. regulations

  • ASME BPVC Section VIII and state pressure vessel laws: exchangers above code thresholds need code stamp and inspection
  • OSHA 29 CFR 1910.119 (Process Safety Management): mechanical integrity of heat exchangers in covered processes

Frequently asked questions

How do I calculate heat exchanger area?

Run the heat balance to get the duty and the missing temperature, compute the LMTD between the ends and divide: A = Q ÷ (U · F · LMTD). Use a fouled U, as TEMA recommends.

When is the F factor needed?

In shell-and-tube exchangers with more than one tube pass, flow is not pure counterflow. F corrects the LMTD; below 0.8 the design is poor and usually needs shells in series.

What U value should I use?

For estimates: water-water 140–260 Btu/(h·ft²·°F); condensing steam to water 260–700; oil-water 25–70; gas-gas 2–9. Confirm with the manufacturer or a detailed rating.