Comment calculer nombre de Jakob Ja boiling condensation phase

Calcule nombre de Jakob Ja = cp*dT/hfg rapport chaleur sensible sur chaleur latente changement phase boiling/condensation. Ja<<1 latent dominant; Ja>>1 cryogenics. Max Jakob Allemagne-USA 1879-1955. CEA + EDF + Sanofi + Total + Atlantic + De Dietrich applications.

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Nombre de Jakob Ja rapport adimensionnel chaleur sensible vs chaleur latente changement phase boiling/condensation: Ja = cp * dT / hfg. cp J/(kg*K) (eau 4180; R134a 1430; LN2 2042); dT K subcooling/superheating; hfg J/kg (eau 2257000; R134a 178000; LN2 199000).

Ja* = Ja*(rho_l/rho_v) film condensation.

Stefan St=Ja.

Regimes: Ja<0.01 negligeable latent dominant; 0.01-0.1 mild HVAC; Ja>1 strong cryogenics.

Nusselt 1916.

Rohsenow 1952.

Bromley 1950.

Zuber 1959 CHF. Histoire: Max Jakob (Ludwigshafen Allemagne 1879 - Pittsburgh USA 1955) Munich PhD 1903 + PTR Berlin + IIT Chicago 1936-1955; 1932 Phys Z 33:1023 + 1949 'Heat Transfer' Wiley classic + Max Jakob Award ASME 1961. Nusselt 1916. Rohsenow MIT 1952. Zuber 1959. Bromley 1950.

France recherche Jakob + boiling + condensation: CEA Saclay + Cadarache + Grenoble + Marcoule 16000 + cryogenics + nuclear boiling + ITER fusion partner LHe; CNRS 11000 + LIMSI + LEMTA; Mines Paris PSL CES Sophia 2000; IFPEN Rueil-Malmaison 1700; ONERA Palaiseau 2200 + microgravita; EDF R&D Saclay Chatou 158000 + Code Saturne CFD nuclear cooling boiling water + steam generators; IRSN Fontenay 1740 + nuclear safety boiling crisis; ANDRA 660; Synchrotron SOLEIL Saint-Aubin 500 + cryogenics LHe; CNES Paris Toulouse 2400 + microgravita ISS thermal management.

France universites Jakob + boiling + condensation: Sorbonne Paris 55000 LIMSI; PSL 17000 ENS ESPCI Mines; X Polytechnique 3500 LadHyX Baroud microfluidique; Centrale Supelec 7000 EM2C combustion Candel; INSA Lyon 6000 LMFA + LAGEPP + CETHIL Catherine Coronel HVAC + Frederic Kuznik building + Christophe Marquette boiling; Centrale Lyon 1700; Toulouse III 35000 IMFT Eiff + LAPLACE; Aix-Marseille 80000 IRPHE + IUSTI Pierre Lance thermal + Catherine Bertin boiling thermal; UGA Grenoble 60000 LEGI + LOCIE Annecy Christian Inard + LITEN Grenoble; ENSAM 6000; Bordeaux 50000 + I2M Sebastian Perre + LCBM.

France industrie HVAC + frigorifico + caldaie: Daikin France Vitry-sur-Seine 600 + R32 R134a; Mitsubishi Electric France 400; Carrier France Velizy 300; Atlantic Group La Roche-sur-Yon 1968 9000 + chauffe-eau radiateurs PAC + heat pumps; Saunier Duval Vaillant France 500; De Dietrich Mertzwiller 1684 1500 + chaudieres condensation + heat pumps; Frisquet Meaux 200; Chappee Saint-Gobain 1500; Viessmann France 600; Bosch Thermo 800.

France industrie nucleare + steam generators + cryogenics: EDF 158000 + Bugey Cattenom Tricastin Saint-Laurent Penly Flamanville Gravelines Chinon Belleville Civaux 56 reactors operativi 2024 + steam generators + boiling crisis; Framatome (Areva NP) Courbevoie 14000 + EPR + steam generators + boiling water reactor; Orano (Areva) Chatillon 17500 + La Hague Tricastin uranium + cryogenics; Engie Courbevoie 100000; Total Énergies Courbevoie 102000 + raffinerie + steam generators; CEA 16000 + ITER fusion + Tokamak West + Tore Supra superconducting LHe + cryogenics; Air Liquide Paris 1902 67000 + LN2 LH2 LHe distribution + medical oxygen + cryogenics + ITER partner; McPhy Energy La Motte-Fanjas 100 + green hydrogen electrolyzer + LH2; Symbio Saint-Fons 200 + fuel cells PEM.

France industrie heat pipes spacecraft: Airbus Defence and Space Toulouse + Les Mureaux 11000 + thermal management satellites Sentinel + Galileo + Solar Orbiter; ArianeGroup Issy-les-Moulineaux 9000 + Ariane 6 + cryogenic LH2 LOX; CNES 2400 + heat pipes ammonia methanol; Thales Alenia Space France 7000; Safran Group Paris 92000 + jet engine cooling + LEAP CFM.

France industrie microchannel boiling: STMicroelectronics Crolles + Tours + Le Mans + Rousset 6500 + microchannel boiling MEMS sensors + Tours + 300 mm wafer; Soitec Bernin Isere 2200; Schneider Electric Rueil-Malmaison 135000 + automation + thermal management.

Formule Jakob

Définition: Ja = cp*dT/hfg.

Histoire

Max Jakob (Ludwigshafen 1879 - Pittsburgh 1955) Munchen + PTR Berlin + IIT Chicago + 1932 Phys Z 33:1023 + 1949 'Heat Transfer' Wiley + Max Jakob Award ASME 1961. Nusselt 1916. Rohsenow MIT 1952. Zuber 1959. Bromley 1950.

France recherche: CEA 16000 + ITER + Tokamak West Tore Supra superconducting LHe; CNRS 11000; Mines Paris PSL 2000; IFPEN 1700; ONERA 2200; EDF R&D 158000 Code Saturne nuclear cooling boiling water + steam generators; IRSN 1740; SOLEIL 500 cryogenics LHe; CNES Paris Toulouse 2400.

France universites: Sorbonne 55000 LIMSI; PSL 17000; X 3500 LadHyX Baroud microfluidique; Centrale Supelec 7000 EM2C; INSA Lyon 6000 LMFA + CETHIL Coronel HVAC + Kuznik building + Marquette boiling; Centrale Lyon 1700; Toulouse III 35000 IMFT + LAPLACE; Aix-Marseille 80000 IRPHE + IUSTI Bertin boiling; UGA Grenoble 60000 LEGI + LOCIE Inard + LITEN; ENSAM 6000; Bordeaux 50000 I2M Sebastian Perre.

France HVAC: Daikin France 600; Atlantic Group 9000 chauffe-eau PAC; De Dietrich 1500 chaudieres condensation; Saunier Duval 500; Frisquet 200; Chappee 1500; Viessmann 600; Bosch Thermo 800.

France nucleare cryogenics: EDF 158000 Bugey Cattenom Tricastin Penly Flamanville 56 reactors steam generators; Framatome 14000 EPR steam generators; Orano 17500 La Hague Tricastin; Engie 100000; Total Énergies 102000; CEA 16000 ITER + Tokamak West Tore Supra LHe + cryogenics; Air Liquide 67000 LN2 LH2 LHe ITER partner; McPhy 100 H2 electrolyzer; Symbio 200 PEM.

France spacecraft heat pipes: Airbus DS Toulouse Les Mureaux 11000 Sentinel Galileo Solar Orbiter; ArianeGroup 9000 Ariane 6 LH2 LOX; CNES 2400 ammonia methanol; Thales Alenia Space France 7000; Safran 92000 LEAP CFM.

France microchannel: STMicroelectronics Crolles 6500 300 mm wafer; Soitec Bernin 2200; Schneider Electric 135000.

Tableau valeurs

  • Ja = cp*dT/hfg
  • Ja* = Ja*(rho_l/rho_v)
  • Stefan St = Ja
  • Ja<0.01 negligeable
  • 0.01-0.1 mild
  • Ja>1 strong
  • Eau cp=4180 hfg=2257000
  • R134a cp=1430 hfg=178000
  • LN2 cp=2042 hfg=199000
  • Nusselt 1916
  • Rohsenow 1952
  • Bromley 1950
  • Zuber 1959 CHF
  • Jakob 1932 + 1949
  • France CEA 16000: ITER LHe
  • France EDF 158000: 56 reactors steam generators
  • France Framatome 14000: EPR
  • France Air Liquide 67000: LH2 LN2 LHe ITER
  • France Atlantic 9000: PAC
  • France De Dietrich 1500: condensation
  • France Airbus DS 11000: spacecraft heat pipes
  • France ArianeGroup 9000: LH2 LOX
  • France Thales Alenia Space 7000
  • France Safran 92000: LEAP CFM
  • France STM Crolles 6500: microchannel

Exemples numériques

Exemple 1 - Eau subcool 10K. Ja=0.0185. France: De Dietrich + Atlantic + Saunier Duval chaudieres.

Exemple 2 - Eau superheat 50K. Ja=0.0926. France: EDF Bugey Cattenom + Framatome EPR steam generators.

Exemple 3 - R134a 10K. Ja=0.0803. France: Daikin + Mitsubishi + Carrier France chillers.

Exemple 4 - LN2 cryo 100K. Ja=1.026. France: CEA ITER + Air Liquide LHe + Tokamak West Tore Supra superconducting + SOLEIL.

Exemple 5 - Steam gen 5K. Ja=0.0123. France: EDF 56 reactors + Framatome EPR + Air Liquide hydrogen + Westinghouse partnership.

Limites

  1. Boiling régimes Rohsenow Bromley.
  2. CHF Zuber.
  3. Subcooled vs saturated.
  4. Surface effects.
  5. Pressure Mostinski.
  6. Mixture glide.
  7. Microchannel.
  8. Falling film.
  9. Heat pipe limits.
  10. Cryogenics LHe.

Erreurs courantes

Confondre Ja Stefan.

cp liquid vs vapor.

hfg pression.

Modified Ja.

Subcool vs superheat.

Applications

  1. HVAC France: Daikin France 600 + Atlantic Group 9000 + De Dietrich 1500 + Saunier Duval Frisquet Chappee Viessmann Bosch Thermo.
  2. Steam generators France: EDF 158000 56 reactors Bugey Cattenom Tricastin Penly Flamanville + Framatome 14000 EPR + Engie + Total Énergies.
  3. Cryogenics France: CEA 16000 ITER + Tokamak West Tore Supra LHe + Air Liquide 67000 ITER partner + McPhy + Symbio.
  4. Heat pipes spacecraft France: Airbus DS Toulouse 11000 + ArianeGroup 9000 LH2 LOX + CNES 2400 + Thales Alenia 7000 + Safran 92000 LEAP CFM.
  5. Nuclear cooling boiling France: EDF 56 reactors + Framatome EPR + Orano La Hague + IRSN + CEA Cadarache.
  6. Microchannel France: STM Crolles 6500 + Soitec Bernin 2200 + Schneider Electric.
  7. Solar thermique France: CNIM Themis Targassonne + EDF Renouvelables + DLR Almeria CSP.
  8. Petrochemie steam: Total Énergies 102000 Donges Gonfreville Lavera + Petroineos + Esso.
  9. Cogeneration France: EDF + Engie + Total Énergies + Veolia 220000.
  10. Universites heat transfer: X LadHyX + Centrale Supelec EM2C + INSA Lyon CETHIL Coronel Kuznik Marquette + Aix-Marseille IRPHE IUSTI Bertin + UGA LEGI LOCIE.

Mis à jour en juillet 2026

Questions fréquentes

Qu est-ce que le nombre de Jakob?

Ja = cp*dT/hfg rapport adimensionnel chaleur sensible vs chaleur latente changement phase. Ja<0.01 latent dominant; 0.01-0.1 mild HVAC; Ja>1 cryogenics. Max Jakob Allemagne-USA 1879-1955 + 1932 Phys Z 33:1023. France: CEA 16000 ITER + EDF 158000 56 reactors + Air Liquide 67000 + Atlantic 9000 + Airbus DS 11000.

Comment calculer Jakob?

Procedure: (1) Ja = cp*dT/hfg; (2) cp J/(kg*K) (eau 4180; R134a 1430; LN2 2042); (3) dT K; (4) hfg J/kg (eau 2257000; R134a 178000); (5) régime. Eau: Ja=0.0185. R134a: Ja=0.08. LN2: Ja=1.03. France: X LadHyX Baroud + Centrale Supelec EM2C + INSA Lyon CETHIL Marquette.

Qu est-ce que Nusselt film condensation?

Nusselt film condensation 1916 Wilhelm Nusselt Allemagne 1882-1957 + Z VDI 60:541 classic + analytical solution + Nu = 0.943*(g*rho_l*(rho_l-rho_v)*hfg*L^3/(mu_l*k_l*dT))^(1/4). France: EDF Bugey Cattenom + Framatome EPR + Atlantic De Dietrich chaudieres.

Quels régimes classifie Ja?

Ja<0.01 negligeable; 0.01-0.1 mild HVAC; 0.1-1 moderate; Ja>1 strong cryogenics LN2 LH2 + Leidenfrost. France: Daikin R134a + EDF BWR + CEA ITER LHe + Airbus DS heat pipes spacecraft.

Qui etait Max Jakob?

Max Jakob (Ludwigshafen Allemagne 1879 - Pittsburgh USA 1955) Universitat Munchen PhD 1903 + PTR Berlin 1903-1934 + Illinois Institute Technology Chicago 1936-1955 fled Nazi Germany Jewish; 1932 Phys Z 33:1023 Jakob number eponym + 1949 'Heat Transfer Volume I' Wiley classic + Max Jakob Award ASME 1961.

Qu est-ce que Rohsenow correlation?

Rohsenow correlation Warren Rohsenow MIT Mech Eng 1948-1992 + 1952 Trans ASME 74:969 classic + nucleate pool boiling + C_sf surface coefficient + 'Handbook of Heat Transfer' 3rd ed 1998 McGraw-Hill 1500 pages classic editor. France: INSA Lyon CETHIL Marquette + Aix-Marseille IUSTI Bertin boiling.

Quelles applications de Jakob?

Applications: HVAC Daikin France 600 + Atlantic 9000 + De Dietrich 1500 chaudieres condensation + Saunier Duval; steam generators nuclear EDF 158000 56 reactors Bugey Cattenom Tricastin Penly Flamanville + Framatome 14000 EPR; cryogenics CEA 16000 ITER + Tokamak West Tore Supra LHe + Air Liquide 67000 ITER partner; heat pipes spacecraft Airbus DS Toulouse 11000 + ArianeGroup 9000 LH2 LOX + CNES 2400 + Thales Alenia 7000; microchannel STM Crolles 6500 + Soitec Bernin.

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