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The differentially heated cavity

  • Computational Heat Transfer
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Abstract

This review discusses recent work dealing with natural convection flow in a differentially heated cavity. The emphasis is placed primarily on work dealing with the non-Boussinesq regime, transitional flow, and turbulent flow. Direction for future work in areas where additional effort is required is also provided.

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References

  • Al-Homoud A A, Bejan A 1979 Experimental study of high Rayleigh number convection in a horizontal cavity with different end temperatures. Tech. Rep.CUMER-79-1, University of Colorado, Boulder, Dept. of Mech. Eng.

    Google Scholar 

  • Arakawa A 1966 Computational designs for long term numerical integration of the equations of fluid motion — Part 1. Two dimensional incompressible flow.J. Comput. Phys. 1: 119–143

    Article  MATH  Google Scholar 

  • Batchelor G K 1954 Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures.Q. Appl. Math. 12: 209–233

    MATH  MathSciNet  Google Scholar 

  • Bejan A 1979 Note on Gill’s solution for free convection in vertical enclosure.J. Fluid Mech. 90: 561–568

    Article  Google Scholar 

  • Bejan A 1980 A synthesis of analytical results for natural convection heat transfer across rectangular enclosures.Int. J. Heat Mass Transfer 23: 723–726

    Article  Google Scholar 

  • Bejan A, Al-Homoud A A, Imberger J 1981 Experimental study of high Rayleigh number convection in a horizontal cavity with different end temperatures.J. Fluid Mech. 109: 283–299

    Article  Google Scholar 

  • Bejan A, Tien C L 1978 Laminar natural convection heat transfer in a horizontal cavity with different end temperatures.J. Heat Transfer 100: 641–647

    Google Scholar 

  • Bergholz R F 1978 Instability of steady natural convection in a vertical fluid layer.J. Fluid Mech. 84: 743–768

    Article  Google Scholar 

  • Briggs D G, Jones D N 1985 Two-dimensional periodic natural convection in a rectangular enclosure of aspect ratio one.J. Heat Transfer 107: 850–854

    Google Scholar 

  • Briggs D G, Jones D N 1989 Periodic two-dimensional cavity flow: effect of linear horizontal thermal boundary conditions.J. Heat Transfer 111: 86–91

    Google Scholar 

  • Catton I 1978 Natural convection in enclosures. InHeat Transfer 1978 (Washington,DC: Hemisphere) vol. 6

    Google Scholar 

  • Chenoweth D R, Paolucci S 1985 Gas flow in vertical slots with large horizontal temperature differences.Phys. Fluids 28: 2365–2374

    Article  Google Scholar 

  • Chenoweth D R, Paolucci S 1986 Natural convection in an enclosed vertical air layer with large horizontal temperature differences.J. Fluid Mech. 169: 173–210

    Article  MATH  Google Scholar 

  • Cormack D E, Leal L G, Imberger J 1974a Natural convection in a shallow cavity with differentially heated end walls. Pt. 1, Asymptotic theory.J. Fluid Mech. 65: 209–229

    Article  MATH  Google Scholar 

  • Cormack D E, Leal L G, Seinfield J H 1974b Natural convection in a shallow cavity with differentially heated end walls. Pt. 2, Numerical solutions.J. Fluid Mech. 65: 231–246

    Article  MATH  Google Scholar 

  • Cowan G H, Lovegrove P C, Quarini G L 1982 Turbulent natural convection heat transfer in vertical single water-filled cavities. InHeat Transfer 1982 (eds) U Grigull, E Hahne, K Stephan, J Straub (WashingtonDC: Hemisphere) vol. 2

    Google Scholar 

  • De Vahl Davis G, Jones I P 1983 Natural convection in a square cavity: a comparison exercise.Int. J. Numer. Meth. Fluids 3: 227–248

    Article  MATH  Google Scholar 

  • Deardorff J W 1973 Three-dimensional numerical modelling of the planetary boundary layers. InWorkshop on micrometerology (Washington,DC: Am. Math. Soc.)

    Google Scholar 

  • Drummond J E, Korpela S A 1987 Natural convection in a shallow cavity.J. Fluid Mech. 182: 543–564

    Article  Google Scholar 

  • Duxbury D 1979An interferometric study of natural convection in enclosed plane air layers with complete and partial central vertical divisions. Ph D thesis, University of Salford, UK

    Google Scholar 

  • Eckert E R G, Carlson W O 1961 Natural convection in an air layer enclosed between two vertical plates with different temperatures.Int. J. Heat Mass Transfer 2: 106–120

    Article  Google Scholar 

  • Elder J W 1965a Laminar free convection in a vertical slot.J. Fluid Mech. 23: 77–98

    Article  Google Scholar 

  • Elder J W 1965b Turbulent free convection in a vertical slot.J. Fluid Mech. 23: 99–111

    Article  Google Scholar 

  • Fenstermacher P R, Swinney H L, Gollub J P 1979 Dynamical instabilities and the transition to chaotic Taylor vortex flow.J. Fluid Mech. 94: 103–128

    Article  Google Scholar 

  • Fusegi T, Hyun J M, Kuwahara K, Farouk B 1991 A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure.Int. J. Heat Mass Transfer 34: 1543–1557

    Article  Google Scholar 

  • George W K, Capp S P 1979 A theory for natural convection turbulent boundary layers next to heated vertical surfaces.Int. J. Heat Mass Transfer 22: 813–826

    Article  MATH  Google Scholar 

  • Giel P W, Schmidt F W 1986 An experimental study of high Rayleigh number natural convection in an enclosure. InHeat Transfer 1986 (eds) C L Tien, V P Carey, J K Ferrell (Washington:DC: Hemisphere) vol. 4

    Google Scholar 

  • Gill A E 1966 The boundary-layer regime for convection in a rectangular cavity.J. Fluid Mech. 26: 515–536

    Article  Google Scholar 

  • Gill A E, Davey A 1969 Instabilities of a buoyancy-driven system.J. Fluid Mech. 35: 775–798

    Article  MATH  Google Scholar 

  • Gollub J P, Benson S V 1980 Many routes to turbulent convection.J. Fluid Mech. 100: 449–470

    Article  Google Scholar 

  • Gorman M, Swinney H L 1982 Spatial and temporal characteristics of modulated waves in the circular Couette system.J. Fluid Mech. 117: 123–142

    Article  Google Scholar 

  • Graebel W P 1981 The influence of Prandtl number on free convection in a rectangular cavity.Int. J. Heat Mass Transfer 23: 125–131

    Article  Google Scholar 

  • Gray D D, Giorgini A 1976 The validity of the Boussinesq approximation for liquids and gases.Int. J. Heat Mass Transfer 19: 545–551

    Article  MATH  Google Scholar 

  • Haldenwang P 1986 Unsteady numerical simulation by Chebyshev spectral methods of natural convection at high Rayleigh number.J. Fluid Mech. 144: 389–401

    Google Scholar 

  • Hara T 1958 Heat transfer by laminar free convection about a vertical flat plate with large temperature difference.Bull. JSME 1: 251–254

    Google Scholar 

  • Hart J E 1972 Stability of thin non-rotating Hadley circulations.J. Atmos. Sci. 29: 687–697

    Article  Google Scholar 

  • Hart J E 1983 Low Prandtl number convection between differentially heated end walls.Int. J. Heat Mass Transfer 26: 1069–1074

    MATH  MathSciNet  Google Scholar 

  • Imberger J 1974 Natural convection in a shallow cavity with differentially heated end walls. Pt. 3, Experimental results.J. Fluid Mech. 65: 247–260

    Article  Google Scholar 

  • Ivey G N 1984 Experiments on transient natural convection in a cavity.J. Fluid Mech. 144: 389–401

    Article  Google Scholar 

  • Iyer P A 1973 Instabilities in buoyancy-driven boundary-layer flows in a stably stratified medium.Boundary-Layer Meterology 5: 53–66

    Article  Google Scholar 

  • Jakob M 1949Heat transfer (New York: Wiley)

    Google Scholar 

  • Keunecke V K -H 1970 Stehende interne Wellen in rechteckigen Becken (Standing internal waves in rectangular tanks).Deutsche Hydrographische Zeitschrift 23: 61–79

    Article  Google Scholar 

  • Kirdyashkin A G, Semenov V I 1984 Spectra of temperature fluctuations in a vertical layer with thermogravitational convection.High Temperature 21: 558–565

    Google Scholar 

  • Kirdyashkin A G, Semenov V I, Berdnikov V S, Gaponov V A 1983 Structure of the temperature field in a vertical layer with thermal gravitational convection.High Temperature 20: 750–757

    Google Scholar 

  • Korpela S A 1974 A study of the effect of Prandtl number on the stability of the conduction regime of natural convection in an inclined slot.Int. J. Heat Mass Transfer 17: 215–222

    Article  Google Scholar 

  • Korpela S A, Gözüm D, Baxi C B 1973 On the stability of the conduction regime of natural convection in a vertical slot.Int. J. Heat Mass Transfer 16: 1683–1690

    Article  Google Scholar 

  • Kraichnan R H 1967 Inertial ranges in two-dimensional turbulence.J. Phys. Fluids 10: 1417–1423

    Article  Google Scholar 

  • Kutateladze S S, Ivakin V P, Kirdyashkin A G, Kekalov A N 1977 Turbulent natural convection in a vertical layer.High Temperature 15: 458–464

    Google Scholar 

  • Kutateladze S S, Ivakin V P, Kirdyashkin A G, Kekalov A N 1978 Thermal free convection in a liquid in a vertical slot under turbulent flow conditions.Heat Transfer — Soviet Res. 10: 118–125

    Google Scholar 

  • Kutateladze S S, Kirdyashkin A G, Ivakin V P 1972a Turbulent natural convection on a vertical plate and in a vertical layer.Int. J. Heat Mass Transfer 15: 193–202

    Article  Google Scholar 

  • Kutateladze S S, Kirdyashkin A G, Ivakin V P 1972b Turbulent natural convection at an isothermal vertical plate.High Temperature 10: 76–79

    Google Scholar 

  • Lankhorst A M, Hoogendoorn C J 1988 Three-dimensional numerical calculations of high Rayleigh number natural convective flows in enclosed cavities. InProc. 1988 National Heat Transfer Conf., ASME HTD-96 (New York:ASME) 3: 463–470

    Google Scholar 

  • Lauriat G 1980 Numerical study of natural convection in a narrow vertical cavity: an examination of high-order accuracy schemes.ASME Paper 80-HT-90

  • Le Quéré P 1990 A note on multiple and unsteady solutions in two-dimensional convection in a tall cavity.J. Heat Transfer 112: 965–974

    Article  Google Scholar 

  • Le Quéré P, Alziary de Roquefort T 1985 Computation of natural convection in two-dimensional cavities with Chebyshev polynomials.J. Comput. Phys. 57: 210–228

    Article  MATH  Google Scholar 

  • Le Quéré P, Alziary de Roquefort T 1986 Transition to unsteady natural convection in a differentially heated cavity InHeat Transfer 1986 (eds) C L Tien, V P Carey, J K Ferrell (Washington,DC: Hemisphere) vol. 4

    Google Scholar 

  • Le Quéré P, Alziary de Roquefort T 1988 Sur l’ existence de solutions périodiques multiples aux équations de Boussinesq.C. R. Acad. Sci. Paris, II 306: 681–687

    Google Scholar 

  • Le Quéré P, Masson R, Perrot P 1992 A Chebyshev collocation algorithm for 2D non-Boussinesq convection.J. Comput. Phys. 103: 320–335

    Article  MATH  Google Scholar 

  • Lee T S, Son G H, Lee J S 1988 Numerical predictions of three-dimensional natural convection in a box. InProc. 1st KSME-JSME Thermal and Fluids Eng. Conf. 2: 278–283

    Google Scholar 

  • Lee Y, Korpela S A, 1983 Multicellular natural convection in a vertical slot.J. Fluid Mech. 126: 91–121

    Article  MATH  Google Scholar 

  • Leonardi E, Reizes J A 1979 Natural convection in compressible fluids with variable properties. InNumerical methods in thermal problems (eds) R W Lewis, K Morgan (Swansea,UK: Pineridge)

    Google Scholar 

  • Leonardi E, Reizes J A 1981 Convective flows in closed cavities with variable fluid properties. InNumerical methods in heat transfer (eds) R W Lewis, K Morgan, O C Zienkiewicz (New York: John Wiley)

    Google Scholar 

  • Lilly D K 1969 Numerical simulation of two-dimensional turbulence.Phys. Fluids Supp. II 12: 240–249

    Google Scholar 

  • Lochet R, Lemonnier D, Doan-Kim-Son 1983 Correlations en convection naturelle turbulente influence de la pression et de la nature du gaz.Int. J. Heat Mass Transfer 26: 1221–1227

    Article  Google Scholar 

  • MacGregor R K, Emery A F 1969 Free convection through vertical layers—Moderate and high Prandtl number fluids.J. Heat Transfer 91: 391–401

    Google Scholar 

  • Mallinson G D, De Vahl Davis G 1977 Three-dimensional natural convection in a box: a numerical study.J. Fluid Mech. 83: 1–31

    Article  Google Scholar 

  • Mordchelles-Regnier G, Kaplan C 1963 Visualization of natural convection on a plane wall and in a vertical gap by differential interferometry: transitional and turbulent regimes. InHeat Transfer and Fluid Mechanics Institute (Stanford: University Press)

    Google Scholar 

  • N’Dame A 1992Etude expérimentale de la convection naturelle en cavité: de l’état stationnaire au chaos. Ph D thesis, Université de Poitiers, France

    Google Scholar 

  • Newhouse S, Ruelle D, Takens P 1978 Occurrence of strange axiom A attractors near quasi periodic flows onT m,m ≥ 3.Commun. Math. Phys. 64: 35–40

    Article  MATH  MathSciNet  Google Scholar 

  • Ostrach S 1972 Natural convection in enclosures. InAdvances in heat transfer (New York: Academic Press) vol. 8

    Google Scholar 

  • Ostrach S 1982 Natural convection heat transfer in cavities and cells. InHeat Transfer 1982 (ed.) U Grigull, E Hahne, K Stephan, J Straub (Washington,DC: Hemisphere) vol. 1

    Google Scholar 

  • Paolucci S 1982 On the filtering of sound from the Navier-Stokes equations. Tech. Rep.SAND82-8257, Sandia National Laboratories Report

  • Paolucci S 1990 Direct numerical simulation of two-dimensional turbulent natural convection in an enclosed cavity.J. Fluid Mech. 215: 229–262

    Article  Google Scholar 

  • Paolucci S, Chenoweth D R 1988 Natural convection in shallow enclosures with differentially heated endwalls.J. Heat Transfer 110: 625–634

    Google Scholar 

  • Paolucci S, Chenoweth D R 1989 Transition to chaos in a differentially heated vertical cavity.J. Fluid Mech. 201: 379–410

    Article  Google Scholar 

  • Patterson J C 1984 On the existence of an oscillatory approach to steady natural convection in cavities.J. Heat Transfer 106: 104–108

    Google Scholar 

  • Patterson J C, Imberger J 1980 Unsteady natural convection in a rectangular cavity.J. Fluid Mech. 100: 65–86

    Article  MATH  Google Scholar 

  • Penot F, N’Dame A, Le Quéré P 1990 Investigation of the route to turbulence in a differentially heated cavity. InHeat Transfer 1990 (ed.) G Hetsroni (Washington,DC: Hemisphere) vol. 2

    Google Scholar 

  • Peyret R, Taylor T D 1983Computational methods for fluid flow (New York: Springer)

    MATH  Google Scholar 

  • Piacsek S A, Williams G P 1970 Conservation properties of convection difference schemes.J. Comput. Phys. 6: 362–392

    Article  Google Scholar 

  • Polezhaev V I 1967 Numerical solution of a system of two-dimensional unsteady Navier-Stokes equations for a compressible gas in a closed region.Fluid Dynamics 2: 70–74

    Article  MATH  Google Scholar 

  • Polezhaev V I 1968 Flow and heat transfer in laminar natural convection in a vertical layer.Teplo i Massoobmen 1: 631–640

    Google Scholar 

  • Quon C 1972 High Rayleigh number convection in an enclosure — A numerical study.Phys. Fluids 15: 12–19

    Article  MATH  Google Scholar 

  • Roux B, Grondin J C, Bontoux P, De Vahl Davis G 1980 Reverse transition from multicellular to monocellular motion in vertical fluid layer.Phys. Chem. Hydrodyn. 3: 292–297

    Google Scholar 

  • Rubel A, Landis F 1970 Laminar natural convection in a rectangular enclosure with moderately large temperature differences. InHeat Transfer 1970 (eds) U Grigull, E Hahne (Washington,DC: Hemisphere) vol. 4

    Google Scholar 

  • Shiralkar G S, Gadgil A, Tien C L 1981 High Rayleigh number convection in shallow enclosures with different end temperatures.Int. J. Heat Mass Transfer 24: 1621–1629

    Article  MATH  Google Scholar 

  • Sparrow E M, Gregg J L 1958 The variable fluid-property problem in free convection.Trans. ASME 80: 879–886

    Google Scholar 

  • Thorpe S A 1968 On standing internal gravity waves of finite amplitude.J. Fluid Mech. 32: 489–528

    Article  MATH  Google Scholar 

  • Tichy J, Gadgil A 1982 High Rayleigh number laminar convection in low aspect ratio enclosures with adiabatic horizontal walls and differentially heated vertical walls.J. Heat Transfer 104: 103–110

    Google Scholar 

  • Vest C M, Arpaci V S 1969 Stability of natural convection in a vertical slot.J. Fluid Mech. 36: 1–15

    Article  MATH  Google Scholar 

  • White F M 1974Viscous fluid flow (New York: McGraw-Hill)

    MATH  Google Scholar 

  • Yang K T 1987 Natural convection in enclosures. InHandbook of single-phase convective heat transfer (eds) S Kakac, R K Shah, W Aung (New York: Wiley-Interscience)

    Google Scholar 

  • Yang K T 1988 Transitions and bifurcations in laminar buoyant flows in confined enclosures.J. Heat Transfer 110: 1191–1204

    Article  Google Scholar 

  • Yewell R, Poulikakos D, Bejan A 1982 Transient natural convection — Experiments in shallow enclosures.J. Heat Transfer 104: 533–538

    Google Scholar 

  • Yin S H, Wung T Y, Chen K 1978 Natural convection in an air layer enclosed within rectangular cavities.Int. J. Heat Mass Transfer 21: 307–315

    Article  Google Scholar 

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Paolucci, S. The differentially heated cavity. Sadhana 19, 619–647 (1994). https://doi.org/10.1007/BF02744398

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