Skip to main content
SpringerLink
Log in

Effect of thermal boundary condition of an inner cube on three-dimensional natural convection in a cubical

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

We numerically investigated three-dimensional (3-D) natural convection in a vertical cubic enclosure with an inner cube for Rayleigh numbers (Ra) in the range of 103 ≤ Ra ≤ 106. For the inner cube at the center, four different thermal boundary conditions (adiabatic, neutral, and hot and cold isothermal conditions) were considered in order to investigate their effect on flow and thermal fields. For Ra = 103 and Ra = 104, single circulation appears regardless of the thermal boundary condition of the inner cube. When Ra = 105 and Ra = 106, the combined effects of the inner cube as a bluff body and the thermal condition imposed on the inner cube on the fluid flow and thermal fields are significant, and intensify the 3-D effect. Generally, for Ra = 105 and Ra = 106, the convective flow is characterized by the formation of two inner vortices embedded in the primary circulation, and by secondary vortices due to flow separation at the edge of the inner body. As Ra increases, the local Nusselt number varies rapidly in the vertical direction, which is supported by the temperature isosurfaces that form an S-shape. The total surface-averaged Nusselt numbers for the different cases have approximately the same profile with respect to the Rayleigh number as the power function.

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. S. Roh and G. Son, Numerical study of natural convection in a liquefied natural gas tank, J. Mech. Sci. Technol., 26 (10) (2012) 3133–3140.

    Article  Google Scholar 

  2. G. A. Sheikhzadeh, M. Nikfar and A. Fattahi, Numerical study of natural convection and entropy generation of Cuwater nanofluid around an obstacle in a cavity, J. Mech. Sci. Technol., 26 (10) (2012) 3347–3356.

    Article  Google Scholar 

  3. G. F. Zheng, M. Y. Ha, H. S. Yoon and Y. G. Park, A numerical study on mixed convection in a lid-driven cavity with a circular cylinder, J. Mech. Sci. Technol., 27 (1) (2013) 273–286.

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. W. J. Hiller, S. Koch and T. A. Kowalewski, Threedimensional structures in laminar natural convection in a cubic enclosure, Exp. Therm. Fluid Sci., 2 (1) (1989) 34–44.

    Article  Google Scholar 

  6. T. Fusegi, J. Hyun, K. Kuwahara and B. Farouk, A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure, Int. J. Heat Mass Tran., 34 (6) (1991) 1543–1557.

    Article  Google Scholar 

  7. J. Pallarès, I. Cuesta, F. Grau and F. Giralt, Natural convection in a cubical cavity heated from below at low Rayleigh numbers, Int. J. Heat Mass Tran., 39 (15) (1996) 3233–3247.

    Article  Google Scholar 

  8. R. Hernández and R. Frederick, Spatial and thermal features of three-dimensional Rayleigh-Bénard convection, Int. J. Heat Mass Tran., 37 (3) (1994) 411–424.

    Article  MATH  Google Scholar 

  9. R. L. Frederick and F. Quiroz, On the transition from conduction to convection regime in a cubical enclosure with a partially heated wall, Int. J Heat Mass Tran., 44 (9) (2001) 1699–1709.

    Article  MATH  Google Scholar 

  10. M. Y. Ha and M. J. Jung, A numerical study on threedimensional conjugate heat transfer of natural convection and conduction in a differentially heated cubic enclosure with a heat-generating cubic conducting body, Int. J. Heat Mass Tran., 43 (23) (2000) 4229–4248.

    Article  MATH  Google Scholar 

  11. J. Kim and P. Moin, Application of a fractional step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59 (2) (1985) 308–323.

    Article  MATH  MathSciNet  Google Scholar 

  12. Y. Zang, R. L. Street and J. R. Koseff, A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates, J. Comput. Phys., 114 (1) (1994) 18–33.

    Article  MATH  MathSciNet  Google Scholar 

  13. J. Mohd-Yusof, Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries, Annual Research Briefs Center for Turbulence Research, NASA Ames and Stanford University (1997) 317.

    Google Scholar 

  14. E. A. Fadlun, R. Verzicco, P. Orlandi and J. Mohd-Yusof, Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J. Comput. Phys., 161 (2000) 35–60.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Kim, D. Kim and H. Choi, An immersed-boundary finite volume method for simulations of flow in complex geometries, J. Comput. Phys., 171 (1) (2001) 132–150.

    Article  MATH  MathSciNet  Google Scholar 

  16. J. Kim and H. Choi, An immersed-boundary finite-volume method for simulation of heat transfer in complex geometries, KSME International Journal, 18 (6) (2004) 1026–1035.

    Google Scholar 

  17. H. S. Yoon, M. Y. Ha, B. S. Kim and D. H. Yu, Effect of the position of a circular cylinder in a square enclosure on natural convection at Rayleigh number of 107, Phys. Fluids, 21 (4) (2009) 1–11.

    Article  Google Scholar 

  18. B. S. Kim, D. S. Lee, M. Y. Ha and H. S. Yoon, A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations, Int. J. Heat Mass Tran., 51 (7-3) (2008) 1888–1906.

    Article  MATH  Google Scholar 

  19. J. M. Lee, M. Y. Ha and H. S. Yoon, Natural convection in a square enclosure with a circular cylinder at different horizontal and diagonal locations, Int. J. Heat Mass Tran., 53 (25-3) (2010) 5905–5919.

    Article  MATH  Google Scholar 

  20. H. S. Yoon, D. H. Yu, M. Y. Ha and Y. G. Park, Threedimensional natural convection in an enclosure with a sphere at different vertical locations, Int. J. Heat Mass Tran., 53 (15-3) (2010) 3143–3155.

    Article  MATH  Google Scholar 

  21. A. Gilmanov, F. Sotiropoulos and E. Balaras, A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids, J. Comput. Phys., 191 (2) (2003) 660–669.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Global Core Research Center for Ships and Offshore Plants, Pusan National University, Jang Jeon 2-Dong, Geum Jeong Gu, Busan, 609-735, Korea

    H. S. Yoon

  2. Department of Naval Architecture and Ocean Engineering, Pusan National University, Jang Jeon 2-Dong, Geum Jeong Gu, Busan, 609-735, Korea

    J. H. Jung & H. S. Lee

  3. Korea Energy Technology Center, ABS Busan Korea, 88-7, Jungang-dong 4-ga, Jung-gu, Busan, 600-014, Korea

    B. Y. Koo

Authors
  1. H. S. Yoon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. H. Jung
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. S. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. Y. Koo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. S. Yoon.

Additional information

Recommended by Associate Editor Ji Hwan Jeong

Hyun Sik Yoon holds a position of Professor in Global Core Research Center for Ships and Offshore Plants at Pusan National University in the Korea. His research interests include flow control, heat and mixing enhancement, flow-structure interaction and biomimetics. He has authored over 100 publications in refereed journals and refereed proceedings of international conferences. He is also the recipient of numerous research grants from the National Science Foundation (NSF), other funding agencies as well as academic awards.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yoon, H.S., Jung, J.H., Lee, H.S. et al. Effect of thermal boundary condition of an inner cube on three-dimensional natural convection in a cubical. J Mech Sci Technol 29, 4527–4543 (2015). https://doi.org/10.1007/s12206-015-0952-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-015-0952-x

Keywords

Search

Navigation