FieldEngineersKitEngineering Reference & ASME Code Basis
1. Core Formula & Variable Definitions
TEMA Standards of the Tubular Exchanger Manufacturers Association, 9th Edition — Section 5 Thermal Relations (LMTD & F) · IAPWS-IF97 Industrial Formulation 1997 — Region 1 liquid water and Region 2 / 4 steam · API Standard 660 — Shell-and-Tube Heat Exchangers for General Refinery Services (context)
Heat duty: Q = ṁh·(hh,in − hh,out) = ṁc·(hc,out − hc,in)
Counterflow LMTD: ΔT1 = Th,in − Tc,out, ΔT2 = Th,out − Tc,in, ΔTlm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2)
Corrected LMTD & area: ΔTlm,corr = F·ΔTlm, A = Q / (U·ΔTlm,corr)
TEMA 9th Ed. Section 5 · IAPWS-IF97 Region 1/2 · API 660 screening context
Water/steam enthalpies from IAPWS-IF97. F is the TEMA 1–2n / multi-shell LMTD correction. Screening only — confirm U, fouling, and mechanical design with TEMA / API 660 and vendor thermal rating software.
- Q (Heat duty) — Hot-side enthalpy (or Cp·ΔT) release = cold-side absorption (kW / BTU/hr).
- ΔT_lm (Log-mean temperature difference) — Counterflow LMTD from terminal differences ΔT₁ and ΔT₂.
- F (TEMA correction factor) — 1-shell / 2n-tube (and N-shell series) F from P and R. Design screen F ≥ 0.75.
- U (Overall heat-transfer coefficient) — User-entered clean/fouled overall U (W/m²·K or BTU/hr·ft²·°F).
- A (Required heat-transfer area) — A = Q / (U · F · ΔT_lm).
- P, R (Temperature effectiveness / capacity ratio) — P = (Tc,out−Tc,in)/(Th,in−Tc,in); R = (Th,in−Th,out)/(Tc,out−Tc,in).
2. Screening Rules Matching This Calculator
Counterflow LMTD, TEMA F for 1/2/4 shell passes, IAPWS-IF97 water/steam enthalpies, and A = Q/(U F ΔT_lm). Mechanical TEMA design, fouling factors, and vendor HTRI ratings are out of scope.
Hero ≈ 349.4 kW · 8.11 m² with ΔT_lm = 40 °C and F ≈ 0.898 (1 shell).
Below 0.75 the approach is too steep for a practical 1-shell 1–2 exchanger — raise shell passes or cut effectiveness P.
Q = ṁ · h_fg at IAPWS saturation temperature equal to the hot terminal.
No baffle design, vibration, or two-phase flow maps. Confirm U and area with the exchanger fabricator.
Quick Reference Lookup Table
| Quantity | Value | Unit | Notes |
|---|---|---|---|
| Q | 349.4 | kW | IAPWS Δh · ṁ |
| ΔT_lm | 40.0 | °C | ΔT₁ = ΔT₂ = 40 |
| F | 0.898 | — | TEMA 1–2n · P≈0.429 · R=1 |
| F·ΔT_lm | 35.9 | °C | Corrected LMTD |
| A | 8.11 | m² | Q/(U F ΔT_lm) |
| ṁ_c (required) | ≈ 10 000 | kg/h | From cold Cp·ΔT |
| Steam condenser 120 °C · 5000 kg/h | Q 3059 · A 29.2 | kW / m² | F ≈ 1 · LMTD 87.3 °C |
| Imperial 194→140 °F · 22 000 lb/hr | Q 1.19 MMBtu/hr · A 87.2 | ft² | U ≈ 211 BTU/hr·ft²·°F |
| Imperial U = 200 · 15 000 lb/hr | Q 752 kBTU/hr · A 59.1 | ft² | 200→150 / 80→130 °F |
| F design floor | 0.75 | — | Warn when F < 0.75 |
Hero reports Q and required area from IAPWS-IF97 enthalpy (or custom Cp) with TEMA F-corrected LMTD. Default water–water duty asserts Q ≈ 349.4 kW, ΔT_lm = 40 °C, F ≈ 0.898, A ≈ 8.11 m².
3. Applicability & Thermal Regime Limits
Fluid and configuration limits for this screening tool. Metallurgy is not computed — select materials from PMS / API 660 separately.
| Group / Regime | Range / Condition | Limit / Criterion | Engineering Notes |
|---|---|---|---|
| Liquid–liquid water (IAPWS Region 1) | 0–600 °C hot · 0–400 °C cold screening | 1 bar abs property reference | Liquid enthalpies evaluated at 1 bar abs. High-pressure liquid lines may need pressure-corrected properties. |
| Steam condenser / cool (IAPWS Region 2/4) | Saturation up to ~374 °C critical approach | Psat from T · Region 1/2 latent heat | Isothermal condenser when Th,in ≈ Th,out. Desuperheat+condense when Th,out < Th,in uses Psat(Th,in). |
| 1-shell temperature cross | Th,out < Tc,out | F often collapses | Temperature cross on a 1-shell unit is inefficient — review 2+ shell passes. |
| Custom Cp fluids | User Cp band | — | Custom path uses constant Cp · ΔT only — not IAPWS. Confirm Cp at mean fluid temperature. |
Code Applicability & Safety Boundaries
- Not a substitute for TEMA mechanical design or API 660 datasheet certification
- F < 0.75 triggers a design-limit warning
- IAPWS screening band ≈ 1–100 bar, 0–600 °C
4. Step-by-Step Worked Example
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Worked Example — Water–Water Cooler
Cool 10 000 kg/h of hot water from 90 °C to 60 °C against cooling water heated from 20 °C to 50 °C in a 1-shell / 2n-tube exchanger with U = 1200 W/m²·K.
Hot-side duty from IAPWS enthalpy
Counterflow LMTD
TEMA F from P, R
Required area
5. How to calculate heat exchanger LMTD and area
- 1
Enter hot and cold terminal temperatures
Set Th,in / Th,out and Tc,in / Tc,out. Counterflow LMTD requires ΔT₁ and ΔT₂ positive.
- 2
Select fluid mode and hot mass flow
Use water (IAPWS), steam condenser/cool, or custom Cp. Enter hot mass flow in kg/h or lb/hr.
- 3
Set shell passes and overall U
Choose 1, 2, or 4 shell passes and the overall heat-transfer coefficient U.
- 4
Read Q, F, LMTD, and A
Hero shows duty and required area. Check F ≥ 0.75 and temperature-cross warnings before locking the datasheet.
6. Frequently Asked Questions & Technical References
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FEK uses counterflow terminal differences ΔT₁ = Th,in−Tc,out and ΔT₂ = Th,out−Tc,in, then ΔT_lm = (ΔT₁−ΔT₂)/ln(ΔT₁/ΔT₂). The TEMA F factor corrects for 1-shell / 2n-tube (and multi-shell) flow.
An F-factor below ≈ 0.75 means the temperature approach is too steep for a practical single-shell unit. Increase shell passes, reduce cold-side rise, or split the duty.
When Th,in ≈ Th,out, FEK treats the hot side as isothermal condensation: Q = ṁ · h_fg at the IAPWS saturation temperature equal to the hot terminal.
Simple Q/(U·LMTD) assumes F = 1 (pure counterflow). Shell-and-tube 1–2 units need A = Q/(U·F·LMTD). For the default water duty, F ≈ 0.898 raises area versus the F = 1 estimate.