Skip to main content
SpringerLink
Log in

Oberbeck-Boussinesq approximations and geometrical confinement effects of free convection in open cavity

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

An experimental study has been conducted on the free convection in an open cavity to investigate the effect of aspect ratio from 3.33 to 0.33 and Rayleigh number from 1.5 × 106 to 9 × 109. Also, the effect of different lateral dimensions (120 mm × 120 mm and 240 mm × 240 mm) of the bottom plate for free convection is studied. The validity of Oberbeck-Boussinesq approximation is also examined using the different approaches, such as fractional deviation in thermo-physical properties of working fluid, density variation, and Busse’s parameter. The effect of aspect ratio and the Rayleigh number on the heat transfer efficiency in free convection is observed experimentally and a power law relation having the exponent of 0.30 expressed the change in the Nusselt number with Rayleigh number. The mechanism of heat transfer in different conditions is explained using the temperature distributions with respect to Rayleigh number.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

Ac :

surface area (m2)

AR:

aspect ratio

Bd :

Bond number

Cp :

specific heat (kJ/kgK)

g:

gravitational acceleration (m/s2)

h:

convective heat transfer coefficient (W/m2K)

H:

height (m)

k:

thermal conductivity (W/mK)

l:

characteristic length (m)

Nu:

Nusselt number

Pr:

Prandtl number

q:

Heat flux (W)

Qb :

Busse’s Parameter

R:

Resistance (ohm)

Ra:

Rayleigh number

T:

Temperature (K)

V:

Voltage (volt)

α:

Thermal diffusivity ()

β:

Thermal expansion coefficient (1/K)

γ:

Temperature derivative of surface tension ()

ρ:

Density (kg/m3)

ν:

Kinematic viscosity (m2/s)

qc :

Root mean square value

b:

Bottom

m:

Mean

w:

Water layer

References

  1. Grossmann S, Lohse D (2000) Scaling in thermal convection: a unifying theory. J Fluid Mech 407:27–56

    Article  MathSciNet  MATH  Google Scholar 

  2. Nikolaenko EB, Funfschilling D, Ahlers G (2005) Heat transport by turbulent Rayleigh-Bénard convection in cylindrical cells with aspect ratio one and less. J Fluid Mech 523:251–260

    Article  MATH  Google Scholar 

  3. Funfschilling D, Brown E, Nikolaenko A, Ahlers G (2005) Heat transport by turbulent Rayleigh-Bénard convection in cylindrical samples with aspect ratio one and larger. J Fluid Mech 536:145–154

    Article  MATH  Google Scholar 

  4. Puits RD, Resagk C, Tilgner A, Busse FH, Thess A (2007) Structure of thermal boundary layers in Rayleigh-Bénard convection. J Fluid Mech 572:231–254

    Article  MATH  Google Scholar 

  5. Theerthan SA, Arakeri JH (2000) Planform structure and heat transfer in turbulent free convection over horizontal surfaces. Phys Fluids 12:884–894

    Article  MATH  Google Scholar 

  6. Subudhi S, Arakeri JH (2012) Flow visualization in turbulent free convection over horizontal smooth and grooved surfaces. Int Commun Heat Mass Trans 39:414–418

    Article  Google Scholar 

  7. Subudhi S, Arakeri JH (2012) Plume dynamics and heat transfer over horizontal grooved surfaces. Exp Heat Trans 25:58–76

    Article  Google Scholar 

  8. Kumar LGK, Kumar SR, Subudhi S (2016) Experimental study of the turbulent free convection over horizontal smooth or grooved surfaces in an open cavity. Heat Mass Transf 52:245–253

    Article  Google Scholar 

  9. Koschmieder EL, Prahl SA (1990) Surface – tension – driven Bénard convection in small containers. J Fluid Mech 215:571–583

    Article  Google Scholar 

  10. Vouros A, Panidis T (2012) Statistical analysis of turbulent thermal free convection over a horizontal heated plate in an open top cavity. Exp Thermal Fluid Sci 36:44–55

    Article  Google Scholar 

  11. Ahlers G, Brown E, Araujo FF, Funfschilling D, Grossmann S, Lohse D (2001) Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh-Bénard convection. J Fluid Mech 569:409–445

    Article  MATH  Google Scholar 

  12. Niemela JJ, Sreenivasan KR (2003) Confined turbulent convection. J Fluid Mech 481:355–384

    Article  MATH  Google Scholar 

  13. Guyon E, Hulin JP, Petit L, Mitescu CD (2015) Physical hydrodynamics, 2nd edn 536 pp. Oxford U. P, New York

    Book  MATH  Google Scholar 

  14. Kline SJ, McClintock FA (1953) Describing uncertainties in single sample experiments. Mech Eng 75:3–8

    Google Scholar 

  15. Busse F (1967) The stability of finite amplitude cellular convection and its relation to an extremum principle. J Fluid Mech 30:625–649

    Article  MATH  Google Scholar 

  16. Bobenschatz E, Pesch W, Ahlers G (2000) Recent developments in Rayleigh-Bénard convection. Ann Rev Fluid Mech 32:709–778

    Article  MATH  Google Scholar 

  17. Wu XZ, Libchaber A (1992) Scaling relations in thermal turbulence: the aspect-ratio dependence. Phys Rev A 45:842–845

    Article  Google Scholar 

  18. Zhou Q, Xia K (2013) Thermal boundary layer structure in turbulent Rayleigh-Bénard convection in a rectangular cell. J Fluid Mech 721:199–224

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical & Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, India

    Rajesh Choudhary, Adarsh Saini & Sudhakar Subudhi

Authors
  1. Rajesh Choudhary
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adarsh Saini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sudhakar Subudhi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sudhakar Subudhi.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Choudhary, R., Saini, A. & Subudhi, S. Oberbeck-Boussinesq approximations and geometrical confinement effects of free convection in open cavity. Heat Mass Transfer 55, 2095–2102 (2019). https://doi.org/10.1007/s00231-019-02563-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-019-02563-8

Search

Navigation