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Heat and Mass Transfer

, Volume 55, Issue 8, pp 2095–2102 | Cite as

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

  • Rajesh Choudhary
  • Adarsh Saini
  • Sudhakar SubudhiEmail author
Original
  • 189 Downloads

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.

Nomenclature

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)

Greek Letters

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

Sub-script

b

Bottom

m

Mean

w

Water layer

Notes

References

  1. 1.
    Grossmann S, Lohse D (2000) Scaling in thermal convection: a unifying theory. J Fluid Mech 407:27–56MathSciNetCrossRefzbMATHGoogle Scholar
  2. 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 523:251–260CrossRefzbMATHGoogle Scholar
  3. 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 536:145–154CrossRefzbMATHGoogle Scholar
  4. 4.
    Puits RD, Resagk C, Tilgner A, Busse FH, Thess A (2007) Structure of thermal boundary layers in Rayleigh-Bénard convection. J Fluid Mech 572:231–254CrossRefzbMATHGoogle Scholar
  5. 5.
    Theerthan SA, Arakeri JH (2000) Planform structure and heat transfer in turbulent free convection over horizontal surfaces. Phys Fluids 12:884–894CrossRefzbMATHGoogle Scholar
  6. 6.
    Subudhi S, Arakeri JH (2012) Flow visualization in turbulent free convection over horizontal smooth and grooved surfaces. Int Commun Heat Mass Trans 39:414–418CrossRefGoogle Scholar
  7. 7.
    Subudhi S, Arakeri JH (2012) Plume dynamics and heat transfer over horizontal grooved surfaces. Exp Heat Trans 25:58–76CrossRefGoogle Scholar
  8. 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 52:245–253CrossRefGoogle Scholar
  9. 9.
    Koschmieder EL, Prahl SA (1990) Surface – tension – driven Bénard convection in small containers. J Fluid Mech 215:571–583CrossRefGoogle Scholar
  10. 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 36:44–55CrossRefGoogle Scholar
  11. 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 569:409–445CrossRefzbMATHGoogle Scholar
  12. 12.
    Niemela JJ, Sreenivasan KR (2003) Confined turbulent convection. J Fluid Mech 481:355–384CrossRefzbMATHGoogle Scholar
  13. 13.
    Guyon E, Hulin JP, Petit L, Mitescu CD (2015) Physical hydrodynamics, 2nd edn 536 pp. Oxford U. P, New YorkCrossRefzbMATHGoogle Scholar
  14. 14.
    Kline SJ, McClintock FA (1953) Describing uncertainties in single sample experiments. Mech Eng 75:3–8Google Scholar
  15. 15.
    Busse F (1967) The stability of finite amplitude cellular convection and its relation to an extremum principle. J Fluid Mech 30:625–649CrossRefzbMATHGoogle Scholar
  16. 16.
    Bobenschatz E, Pesch W, Ahlers G (2000) Recent developments in Rayleigh-Bénard convection. Ann Rev Fluid Mech 32:709–778CrossRefzbMATHGoogle Scholar
  17. 17.
    Wu XZ, Libchaber A (1992) Scaling relations in thermal turbulence: the aspect-ratio dependence. Phys Rev A 45:842–845CrossRefGoogle Scholar
  18. 18.
    Zhou Q, Xia K (2013) Thermal boundary layer structure in turbulent Rayleigh-Bénard convection in a rectangular cell. J Fluid Mech 721:199–224MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical & Industrial EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia

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