Skip to main content
SpringerLink
Log in

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

  • Published:
Journal of Engineering Thermophysics Aims and scope

Abstract

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 104 ≤ RA ≤ 107 and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.

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

Similar content being viewed by others

References

  1. De Vahl Davis, G., Natural Convection of Air in a Square Cavity: A Benchmark Numerical Solution, Int. J. Num. Meth. Fluids, 1983, vol. 03, pp. 227–248.

    Article  MATH  Google Scholar 

  2. Freitas, C.J., Street, R.L., Findikakis, A.N., and Koseff, J.R., Numerical Simulation of Three-Dimensional Flow in a Cavity, Int. J. Num. Meth. Fluids, 1985, vol. 5, pp. 561–575.

    Article  MATH  Google Scholar 

  3. Paolucci, S. and Chenoweth, D.R., Natural Convection in Shallow EnclosureswithDifferentially Heated End Walls, J. Heat Transfer, 1988, vol. 110, pp. 625–634.

    Article  Google Scholar 

  4. Ostrach, S., Laminar Flows with Body Force, High Speed Aerodynamics and Jet Propulsion, vol. 4, Princeton Univ. Press, 1964, pp. 528–718.

    Google Scholar 

  5. Ostrach, S., Natural Convection in Enclosures, Advances in Heat Transfer, vol. VII, New York: Academic Press, 1972, pp. 161–227.

    Google Scholar 

  6. Lo, D.C., Young, D.L, and Tsai, C.C., High Resolution of 2DNatural Convection in Cavity by DQ Method, J. Comput. Appl. Math., 2004, vol. 203, pp. 219–236.

    Article  MATH  Google Scholar 

  7. Basak, T., Roy, S., and Balakrishnan, A.R., Effects of Thermal Boundary Conditions on Natural Convection Flows within Square Cavity, Int. J. Heat Mass Transfer, 2006, vol. 49, pp. 4525–4535.

    Article  MATH  Google Scholar 

  8. Fusegi, T., Hyun, J.M., and Kuwahara, K., Natural Convection in a Differentially Heated Square Cavity with Internal Heat Generation, Num. Heat Transfer A, 1992, vol. 21, pp. 215–229.

    Article  ADS  Google Scholar 

  9. Lage, J.L. and Benjan, A., The Ra–Pr Domain of Laminar Natural Convection in an Enclosure Heated from the Side, Num. Heat Transfer A, 1991, vol. 19, pp. 21–41.

    Article  ADS  Google Scholar 

  10. Lage, J.L. and Benjan, A., The Resonance of Natural Convection in an Enclosure Heated Periodically from the Side, Int. J. Heat Mass Transfer, 1993, vol. 36, pp. 2027–2038.

    Article  MATH  Google Scholar 

  11. Xia, C. and Murthy, J.Y., Buoyancy-Driven Flow Transitions in Deep Cavities Heated from Below, ASME Trans. J. Heat Transfer, 2002, vol. 124, pp. 650–659.

    Article  Google Scholar 

  12. November, M. and Nansteel, M.W., Natural Convection in Rectangular Enclosures Heated from Below and Cooled Along One Side, Int. J. Heat Mass Transfer, 1987, vol. 30, pp. 2433–2440.

    Article  Google Scholar 

  13. Hall, J.D., Bejan, A., and Chaddock, J.B., Transient Natural Convection in Rectangular Enclosure with One Heated SideWall, Int. J. Fluid Flow, 1988, vol. 9, pp. 396–404.

    Article  Google Scholar 

  14. Hyun, J.M. and Lee, J.W., Numerical Solutions of Transient Natural Convection in a Square Cavity with Different SideWall Temperature, Int. J. Fluid Flow, 1989, vol. 10, pp. 146–151.

    Article  Google Scholar 

  15. Sarris, I.E., Lekakis, I., and Vlachos, N.S., Natural Convection in Rectangular Tanks Heated Locally from Below, Int. J. HeatMass Transfer, 2004, vol. 47, pp. 3549–3563.

    Article  MATH  Google Scholar 

  16. Corcione, M., Effects of the Thermal Boundary Conditions at the Sidewalls upon Natural Convection in Rectangular Enclosures Heated from Below and Cooled from Above, Int. J. Therm. Sci., 2003, vol. 42, pp. 199–208.

    Article  Google Scholar 

  17. Moukalled, F. and Acharya, S., Natural Convection in the Annulus between Concentric Horizontal Circular and Square Cylinders, AIAA J. Thermophys. Heat Transfer, 1996, vol. 10, pp. 524–531.

    Article  Google Scholar 

  18. Singh, R.K., Sahu, K.B., and Mishra, T.D., Analysis of Heat Transfer and Flow Due to Natural Convection in Air around Heated Square Cylinders of Different Sizes inside an Enclosure, Int. J. Eng. Res. Appl., 2013, vol. 3, pp. 766–771.

    Google Scholar 

  19. Wu, W. and Ching, C.Y., The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities with Different Aspect Ratios, J. Heat Transfer, 2009, vol. 131, pp. 1–11.

    Google Scholar 

  20. Bose, P.K., Sen, D., Panua, R., and Das, A.K., Numerical Analysis of Laminar Natural Convection in a Quadrantal Cavity with a Solid Adiabatic Fin Attached to the Hot Vertical Wall, J. Appl. Fluid Mech., 2013, vol. 6, pp. 501–510.

    Google Scholar 

  21. Hussein, A.K. and Hussain, S.H., Mixed Convection through a Lid-Driven Air-Filled Square Cavity with a HotWavyWall, Int. J. Mech. Mat. Eng., 2010, vol. 5, pp. 222–235.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, NIT Agartala, Tripura, PIN 799046, India

    S. Das & P. Bhattacharya

Authors
  1. S. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Bhattacharya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Bhattacharya.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, S., Bhattacharya, P. A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio. J. Engin. Thermophys. 26, 79–90 (2017). https://doi.org/10.1134/S181023281701009X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S181023281701009X

Search

Navigation