How to calculate Stanton number St heat exchanger design

Calculate Stanton number St = h/(rho*u*cp) = Nu/(Re*Pr) ratio convective heat transport on flow heat capacity. Reynolds analogy St~Cf/2 turbulent. Heat exchanger + turbomachinery. NIST + MIT + Stanford + GE Aviation + Honeywell + ExxonMobil + Trane Carrier.

Calculation parameters
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How to calculate Stanton number (St) dimensionless ratio fluid dynamics + convective heat transfer measuring boundary heat flux to flow heat capacity: St = h / (rho * u * cp) = Nu / (Re * Pr). h W/(m^2·K) convective heat transfer coefficient; rho kg/m^3 fluid density; u m/s velocity; cp J/(kg·K) constant pressure specific heat.

Reynolds analogy turbulent fully developed St~Cf/2 (Pr~1 gas); Chilton-Colburn 1934 St*Pr^(2/3) = Cf/2 generalized.

Regime classification: St0.1 very high slow flow.

Sir Thomas Edward Stanton (UK 1865-1931) NPL Teddington UK Director Engineering 1899-1928 English mechanical engineer pioneer fluid dynamics + heat transfer + boundary layer + Stanton diagram skin friction.

Reynolds Osborne UK 1874 Manchester analogy heat-momentum + 1883 turbulent transition.

Chilton-Colburn 1934 IEC 26:1183 j_H = j_M = j_F generalized analogy.

USA universities + national labs: NIST National Institute Standards Technology Boulder CO + Gaithersburg MD 1901 3000 thermophysical properties + REFPROP database + heat transfer; MIT Massachusetts Institute Technology Cambridge MA 1861 11000 + Mechanical Engineering + Department Aeronautics Astronautics + Wing-Yet Han + David Hardt + heat transfer; Stanford University Palo Alto CA 1885 17000 + Mechanical Chemical Engineering + Sanjiva Lele computational + Howard Stone fluid mechanics; Caltech Pasadena CA 1891 2300 + GALCIT Graduate Aeronautical Lab + John Brady transport + Tim Colonius computational; Harvard School Engineering Applied Sciences SEAS 1847 + David Weitz soft matter + Howard Stone fluid dynamics; UC Berkeley Lawrence Berkeley National Lab LBNL 1868 45000 + Mechanical Engineering + Chemical Engineering; Princeton 1746 + Mechanical Aerospace + Howard Stone soft matter; University Wisconsin Madison 1848 Chemical Engineering Bird Stewart Lightfoot 1960 textbook + Edmund Patten heat transfer; Cornell Ithaca NY 1865 + Mechanical Aerospace + Sibley School; UPenn 1740 + Bioengineering + Howard Stone microfluidics; Michigan 1817 + Mechanical Engineering + Aerospace; Texas A&M 1876 + Mechanical Engineering + Aerospace;

Georgia Tech 1885 + Aerospace + GTRI; Purdue Lafayette IN 1869 + Aerospace; Penn State University Park 1855 + Aerospace + Combustion Research; Notre Dame IN 1842; Carnegie Mellon Pittsburgh 1900 + Mechanical Engineering.

USA national labs: NREL Golden CO 1977 3000 + thermal energy storage + concentrated solar power CSP heat transfer; ORNL Oak Ridge TN 1943 5000 + Spallation Neutron Source + High Flux Isotope Reactor HFIR; ANL Argonne National Lab Lemont IL 1946 + Advanced Photon Source APS + nuclear thermal hydraulics; LLNL Lawrence Livermore CA 1952 + High Performance Computing CFD heat transfer simulations; SNL Sandia Albuquerque NM + Livermore CA 14000 + Combustion Research Facility CRF Livermore 100 + nuclear; LANL Los Alamos NM 1943 12000 + nuclear thermal hydraulics; PNNL Pacific Northwest Richland WA 1965 5000 + environmental + heat transfer; INL Idaho Falls 1949 5000 + nuclear; AEDC Arnold Tullahoma TN Air Force wind tunnels Mach 14-16.

USA chemical industry petrochemical: ExxonMobil Spring TX 1999 62000 + ExxonMobil Chemical 22000 + heat exchanger Baytown TX 590000 bpd + Beaumont TX + Baton Rouge LA + Joliet IL refineries + cryogenic LNG; Chevron San Ramon CA 1879 45000 + Chevron Phillips Chemical 8000 petrochemical heat exchanger; Phillips 66 Houston TX 14000; Marathon Petroleum 17000; Valero Energy 10000; Halliburton 40000 oilfield services + heat transfer; Schlumberger 99000; Baker Hughes 55000; Dow Chemical Midland MI 1897 36000 + heat exchanger; DuPont Wilmington DE 1802 23000 + materials + Kevlar Teflon; LyondellBasell 19000 + polymers; Chemours Wilmington DE 6000 + TiO2; Air Products Allentown PA 1940 19000 industrial gases + cryogenic LNG + Air Products Hydrogen Solutions; Linde Danbury CT subsidiary Ireland parent 80000 gases + Engineering Hydrogen + cryogenic LNG; Praxair Linde subsidiary 2018; Honeywell Performance Materials Charlotte NC 13000 + UOP catalysts + heat exchanger; Trinity Industries Dallas TX heat exchanger + tank cars; PCM Group + Fives Cryogenics Hampton VA cryogenic heat exchanger LNG; CB&I Chicago Bridge Iron Pasadena TX engineering construction.

USA HVAC + heat exchanger: Trane Davidson NC 35000 HVAC + heat exchanger + chillers; Carrier Palm Beach Gardens FL 56000 HVAC + heat exchanger + chillers + cooling towers; Johnson Controls Glendale WI 100000 HVAC + heat exchanger + chillers; Daikin Applied Minneapolis MN 6000 HVAC; Lennox International Richardson TX 1895 12000 HVAC residential commercial; Goodman Manufacturing Houston TX HVAC; Rheem Atlanta GA 4000 + Rheem-Ruud water heaters + HVAC; ASHRAE American Society Heating Refrigerating Air-Conditioning Engineers Atlanta 1894 50000 members standards 90.1 90.2; AHRI Air-Conditioning Heating Refrigeration Institute.

USA aerospace turbine engines + cooling: General Electric GE Aerospace Cincinnati OH 50000 + GE Aviation + GE Renewable Energy + GE Power + Steam Turbine + Gas Turbine + HRSG + GE9X 777X engine + LEAP CFM56 partner Snecma Safran; Pratt Whitney East Hartford CT 1925 38000 + PW1000G geared turbofan + F119 F-22 + F135 F-35 engines; Honeywell Aerospace Phoenix AZ 22000 + APUs + cooling systems + AGT1500 Abrams tank turbine engine; Rolls-Royce North America Reston VA + Indianapolis subsidiary UK parent + Trent 1000 7000 1000 engines; Lockheed Martin 116000 + F-22 F-35; Boeing Chicago IL 156000 + commercial 737 747 757 767 777 787 + military F-15 F-18 + B-1 B-2 B-21 + Pratt Whitney engines + Boeing Defense; Raytheon Technologies Waltham MA 180000 + Pratt Whitney + Collins Aerospace + Raytheon Missile Defense.

USA automotive cooling radiators: Tesla Fremont CA + Austin TX + Berlin + Shanghai 140000 + thermal management EV battery cooling; Ford Detroit MI 1903 175000 + cooling radiators + intercooler; GM General Motors Detroit MI 1908 167000 + Pontiac Buick Chevy + Cadillac + cooling; Stellantis Auburn Hills MI ex-Chrysler 80000 + Jeep + RAM + Dodge cooling; Toyota North America Plano TX subsidiary; Honda Marysville OH; Nissan Smyrna TN.

USA boilers + power industry: Babcock & Wilcox Charlotte NC 1867 + nuclear + boilers + steam generators; Westinghouse Pittsburgh PA + nuclear AP1000 + boilers; GE Power + Steam Turbine + Gas Turbine; Siemens Energy USA Orlando FL + steam + gas turbines; Mitsubishi Power USA Lake Mary FL subsidiary Japanese parent + steam gas turbines + HRSG combined cycle.

USA universities transport phenomena: NIST + MIT + Stanford + Caltech + Harvard SEAS + UC Berkeley LBNL + Princeton + Wisconsin Bird Stewart Lightfoot 1960 textbook + Cornell + UPenn + Michigan + Texas A&M + Georgia Tech + Purdue + Penn State + Notre Dame + CMU + UMN + UCLA + UCSD + UNC Chapel Hill.

Stanton formula

St = h/(rho*u*cp) = Nu/(Re*Pr). Reynolds analogy turbulent St~Cf/2 (Pr~1). Chilton-Colburn 1934 St*Pr^(2/3) = Cf/2 generalized.

History and context

Sir Thomas Edward Stanton UK 1865-1931 NPL Teddington UK Director Engineering 1899-1928 + Stanton diagram skin friction + Stanton heat transfer paper + Charlesworth-Stanton 1934 + Bibliography Reynolds Number + pioneer wind tunnel UK first 1908 NPL. Reynolds Osborne UK 1874 Manchester Reynolds analogy heat-momentum + 1883 Reynolds number turbulent transition. Chilton-Colburn 1934 IEC 26:1183 j_H = j_M = j_F. von Karman 1930s analogy + Prandtl mixing length 1925. Bird-Stewart-Lightfoot 1960 Wiley 'Transport Phenomena' classic textbook reference. USA universities: NIST Boulder + Gaithersburg 1901 3000 thermophysical + REFPROP heat transfer; MIT 1861 11000 + Han Hardt; Stanford 1885 17000 + Lele Stone; Caltech 1891 2300 + GALCIT Brady Colonius; Harvard SEAS 1847 + Weitz Stone; UC Berkeley LBNL 1868 45000 + ChemE; Princeton 1746 + Stone soft matter; Wisconsin 1848 BSL textbook + Patten; Cornell 1865 Sibley School; UPenn 1740 + Stone microfluidics; Michigan 1817 + Aerospace; Texas A&M 1876 + Aerospace; Georgia Tech 1885 + GTRI; Purdue 1869; Penn State 1855 + Combustion Research; Notre Dame 1842; CMU 1900. USA national labs: NREL 3000 CSP heat storage; ORNL 5000 + SNS HFIR; ANL Lemont + APS; LLNL Livermore HPC CFD; SNL CRF Livermore 100; LANL 12000; PNNL 5000; INL Idaho 5000; AEDC Tullahoma Mach 14-16. USA chemical: ExxonMobil 62000 + Chemical 22000 + Baytown 590k bpd + Beaumont + Baton Rouge + Joliet; Chevron 45000 + Chevron Phillips 8000;

Phillips 66 14000 + Marathon 17000 + Valero 10000 + Halliburton 40000 + Schlumberger 99000 + Baker Hughes 55000; Dow 36000 + DuPont 23000 + LyondellBasell 19000 + Chemours 6000; Air Products 19000 + Linde 80000 + Praxair Linde 2018 + Honeywell 13000 + UOP catalysts + Trinity heat exchanger + CB&I + PCM Fives Cryogenics LNG. USA HVAC: Trane 35000 + Carrier 56000 + Johnson Controls 100000 + Daikin Applied 6000 + Lennox 12000 + Goodman + Rheem 4000 + ASHRAE 50000 + AHRI. USA aerospace: GE Aerospace Cincinnati 50000 + GE9X + LEAP CFM56; Pratt Whitney 38000 + PW1000G + F119 F135 F-22 F-35; Honeywell Aerospace Phoenix 22000; Rolls-Royce 7000; Lockheed Martin 116000; Boeing 156000; Raytheon 180000. USA automotive: Tesla 140000 EV thermal; Ford 175000; GM 167000; Stellantis 80000; Toyota Honda Nissan subsidiaries. USA boilers: Babcock & Wilcox 1867; Westinghouse AP1000; GE Power; Siemens Energy USA Orlando; Mitsubishi Power Lake Mary FL.

Stanton table

  • St = h/(rho*u*cp)
  • St = Nu/(Re*Pr)
  • St ~ Cf/2 Pr~1: Reynolds analogy
  • St*Pr^(2/3) ~ Cf/2: Chilton-Colburn 1934
  • St<1e-4 very low: high velocity
  • 1e-4-1e-3 low: turbulent pipe
  • 1e-3-1e-2 moderate: transitional
  • 1e-2-0.1 high: laminar BL
  • St>0.1 very high: microfluidic
  • Water h pipe 1k-10k W/m²K
  • Air HVAC 25-100 W/m²K
  • Oil 100-500 W/m²K
  • Steam condensing 5k-30k
  • Boiling water 5k-50k
  • Pr water 20°C ~7
  • Pr air 0.7
  • Pr oil 100-1000
  • Stanton 1897-1928 NPL UK
  • Reynolds 1874: heat-momentum
  • Chilton-Colburn 1934 IEC 26:1183
  • USA NIST 1901: 3000 REFPROP
  • USA MIT 1861: 11000 Han Hardt
  • USA Stanford: Lele Stone
  • USA Wisconsin BSL 1960 textbook
  • USA NREL Golden 3000: CSP heat storage
  • USA SNL CRF Livermore: 100 combustion
  • USA AEDC Tullahoma: Mach 14-16
  • USA Trane 35000: HVAC heat exchanger
  • USA Carrier 56000: HVAC chiller
  • USA GE Aerospace 50000: GE9X LEAP
  • USA Pratt Whitney 38000: F119 F135
  • USA ExxonMobil 62000: Baytown 590k
  • USA Babcock Wilcox 1867: nuclear boilers

Numerical examples

Example 1 - Water pipe flow. h=5000 W/(m²K), rho=1000, u=1.5, cp=4186. St=7.96e-4. Low turbulent pipe heat exchanger. USA: ExxonMobil Baytown 590k bpd + Chevron + UOP Honeywell catalysts.

Example 2 - Air HVAC. h=50, rho=1.2, u=5, cp=1005. St=8.29e-3. Moderate transitional. USA: Trane 35000 + Carrier 56000 + Johnson Controls 100000 + Daikin Applied + Lennox + Rheem.

Example 3 - Via Nu-Re-Pr. Nu=100, Re=5e4, Pr=0.7. St=2.86e-3. USA: research MIT + Stanford + Caltech + Wisconsin BSL textbook.

Example 4 - Compact heat exchanger. h=10000, rho=1000, u=3, cp=4186. St=7.96e-4. USA: PCM Fives Cryogenics LNG + CB&I + ExxonMobil.

Example 5 - Engine oil cooler. h=500, rho=880 oil, u=0.5, cp=1900. St=5.98e-4. USA: GE Aerospace 50000 + Pratt Whitney 38000 + Tesla 140000 EV thermal + Ford GM Stellantis.

Limits

  1. Reynolds analogy assume Pr~1 (gas). Water Pr=7, oil Pr=1000 invalid. Chilton-Colburn correction.
  2. Boundary layer laminar vs turbulent: Nu(Re,Pr) different.
  3. Variable properties: rho cp k mu vary T temperature.
  4. Phase change boiling/condensation: St formula not apply.
  5. Geometry: tube banks plates compact spirals correlations.
  6. Reynolds range turbulent Re>10000.
  7. Roughness wall enhance St + Cf.
  8. Multi-component diffusion Lewis Le=Sc/Pr.
  9. Compressibility M>0.3 recovery factor.
  10. Numerical CFD RANS LES DNS predict Nu.

Common errors

St vs Nu vs Pr: St = Nu/(Re*Pr).

Reynolds analogy Pr=1 only.

Cp vs Cv: pressure vs volume constant.

Bulk vs film T: properties evaluation.

Phase change: specific correlations.

Practical applications

  1. Heat exchanger industrial: USA ExxonMobil 62000 Baytown 590k bpd + Chevron 45000 + Halliburton 40000 + Schlumberger 99000 + Baker Hughes 55000.
  2. Power plant turbine cycles: GE Power + Steam Turbine + Gas Turbine + HRSG + Babcock Wilcox 1867 + Westinghouse AP1000 + Siemens Energy USA Orlando + Mitsubishi Power Lake Mary FL.
  3. HVAC residential commercial: Trane 35000 + Carrier 56000 + Johnson Controls 100000 + Daikin Applied 6000 + Lennox 12000 + Goodman + Rheem + ASHRAE.
  4. Automotive cooling: Tesla 140000 EV thermal management + Ford 175000 + GM 167000 + Stellantis 80000 + Toyota Honda Nissan subsidiaries.
  5. Aerospace turbine engines: GE Aerospace Cincinnati 50000 GE9X LEAP + Pratt Whitney East Hartford 38000 PW1000G F119 F135 + Honeywell Aerospace Phoenix 22000 APUs + Rolls-Royce.
  6. Microreactor microfluidic: 10x Genomics + Bio-Rad + MIT + Caltech + Stanford + Harvard SEAS Stone Weitz + UC Berkeley.
  7. Cryogenic LNG heat exchanger: ExxonMobil + Chevron + Air Products 19000 + Linde 80000 + PCM Fives Cryogenics Hampton VA + CB&I.
  8. Boiling + condensation: GE Power boilers + Babcock Wilcox + Westinghouse + ORNL HFIR.
  9. Solar thermal CSP: NREL Golden CO 3000 + SNL Sandia + LANL + Crescent Dunes Tonopah NV.
  10. University research heat transfer: NIST + MIT 11000 + Stanford 17000 + Caltech 2300 + Berkeley LBNL 45000 + Wisconsin BSL legacy + Cornell + UPenn + Michigan + Princeton + Texas A&M + Georgia Tech.

Updated July 2026

Frequently Asked Questions

What is the Stanton number?

St = h/(rho*u*cp) = Nu/(Re*Pr) dimensionless ratio convective heat transfer / flow heat capacity. h W/(m^2·K); rho kg/m^3; u m/s; cp J/(kg·K). Reynolds analogy turbulent St~Cf/2 (Pr~1). Sir Thomas Stanton NPL UK 1897-1928. Chilton-Colburn 1934. USA: NIST Boulder REFPROP + MIT 11000 + Stanford + Caltech GALCIT + Wisconsin BSL textbook + GE Aerospace Cincinnati 50000 + Pratt Whitney 38000.

How to calculate Stanton?

Procedure: (1) St = h/(rho*u*cp) with h W/(m^2·K) + rho kg/m^3 + u m/s + cp J/(kg·K); or (2) St = Nu/(Re*Pr) via Nusselt-Reynolds-Prandtl. Example water pipe h=5000 + rho=1000 + u=1.5 + cp=4186: St=7.96e-4. USA: ExxonMobil Baytown 590k bpd + Trane Carrier HVAC + GE Aerospace LEAP CFM56 + Pratt Whitney F119 F135.

What is Reynolds analogy?

Reynolds analogy: turbulent fully developed Pr~1 (gas) St ~ Cf/2 Cf skin friction. Example Cf=0.005 → St=0.0025. Chilton-Colburn 1934 IEC 26:1183 St*Pr^(2/3) = Cf/2 generalized Pr different from 1 (water Pr=7 oil Pr=1000). Reynolds Osborne 1874 Manchester analogy heat-momentum. USA: research MIT + Stanford Lele + Caltech Brady + Wisconsin BSL + GE Aerospace + Pratt Whitney.

What flow regimes does St classify?

St<1e-4 very low: weak heat transfer high velocity; 1e-4-1e-3 low: turbulent pipe heat exchanger; 1e-3-1e-2 moderate: transitional; 1e-2-0.1 high: laminar boundary layer; St>0.1 very high: microfluidic heat pipes slow flow strong heat transfer. USA: industry ExxonMobil + Trane Carrier HVAC + GE Power + Siemens Energy USA + Mitsubishi Power.

Who was Sir Thomas Stanton?

Sir Thomas Edward Stanton (UK 1865-1931 Camberley Surrey) Owens College Manchester + Liverpool University + NPL National Physical Laboratory Teddington English mechanical engineer pioneer fluid dynamics + heat transfer + boundary layer; Director Engineering NPL 1899-1928 Stanton diagram + skin friction + Stanton heat transfer + Charlesworth-Stanton 1934 + Bibliography Reynolds Number + pioneer UK first wind tunnel 1908 NPL aeronautical research. USA: research NIST + Wisconsin BSL textbook + GE Pratt Whitney aero engines.

What is Chilton-Colburn analogy?

Chilton-Colburn 1934 paper Industrial Engineering Chemistry 26:1183 'Mass transfer (absorption) coefficients prediction'; St*Pr^(2/3) = Cf/2 generalizes Reynolds analogy for Pr different from 1 (water Pr=7, oil Pr=1000). Extension also mass transfer Sh*Sc^(2/3) j_H=j_M=j_F. Used industrial heat + mass transfer correlations design. USA: GE Aerospace + Pratt Whitney + ExxonMobil + UOP Honeywell catalysts + research MIT + Stanford.

What applications of St?

Applications: heat exchanger industrial USA ExxonMobil 62000 + Halliburton 40000 + Schlumberger 99000 + UOP Honeywell catalysts; power turbines GE Power + Babcock Wilcox 1867 + Westinghouse AP1000 + Siemens Energy USA Orlando + Mitsubishi Power Lake Mary FL; HVAC Trane 35000 + Carrier 56000 + Johnson Controls 100000 + Daikin + Lennox; aerospace GE Aerospace 50000 GE9X + Pratt Whitney 38000 PW1000G F119 F135 + Honeywell 22000 APUs; automotive cooling Tesla 140000 EV thermal + Ford GM Stellantis.

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