Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 84
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Farrow, Duncan E. 2016. A numerical model of periodically forced circulation near the shore of a lake. Environmental Fluid Mechanics,


    Rivière, David Selva, Bertrand Chraibi, Hamza Delabre, Ulysse and Delville, Jean-Pierre 2016. Convection flows driven by laser heating of a liquid layer. Physical Review E, Vol. 93, Issue. 2,


    Turan, Osman Poole, Robert J. and Chakraborty, Nilanjan 2014. Influences of Boundary Conditions on Laminar Natural Convection of Bingham Fluids in Rectangular Enclosures With Differentially Heated Side Walls. Heat Transfer Engineering, Vol. 35, Issue. 9, p. 822.


    Farrow, Duncan E. 2013. Periodically driven circulation near the shore of a lake. Environmental Fluid Mechanics, Vol. 13, Issue. 3, p. 243.


    Turan, Osman Poole, Robert J. and Chakraborty, Nilanjan 2012. Influences of boundary conditions on laminar natural convection in rectangular enclosures with differentially heated side walls. International Journal of Heat and Fluid Flow, Vol. 33, Issue. 1, p. 131.


    Turan, Osman Poole, Robert J. and Chakraborty, Nilanjan 2011. Aspect ratio effects in laminar natural convection of Bingham fluids in rectangular enclosures with differentially heated side walls. Journal of Non-Newtonian Fluid Mechanics, Vol. 166, Issue. 3-4, p. 208.


    Arpino, F. Massarotti, N. and Mauro, A. 2010. High Rayleigh Number Laminar-Free Convection in Cavities: New Benchmark Solutions. Numerical Heat Transfer, Part B: Fundamentals, Vol. 58, Issue. 2, p. 73.


    Wu, W. and Ching, C.Y. 2010. Laminar natural convection in an air-filled square cavity with partitions on the top wall. International Journal of Heat and Mass Transfer, Vol. 53, Issue. 9-10, p. 1759.


    Wu, W. and Ching, C. Y. 2010. Laminar Natural Convection in a Square Cavity with a Partition on the Heated Vertical Wall. Experimental Heat Transfer, Vol. 23, Issue. 4, p. 298.


    MAO, YADAN LEI, CHENGWANG and PATTERSON, JOHN C. 2009. Unsteady natural convection in a triangular enclosure induced by absorption of radiation – a revisit by improved scaling analysis. Journal of Fluid Mechanics, Vol. 622, p. 75.


    Wu, Wenjiang and Ching, Chan Y. 2009. The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities With Different Aspect Ratios. Journal of Heat Transfer, Vol. 131, Issue. 5, p. 052501.


    Li, You-Rong Zhao, Xin-Xing Wu, Shuang-Ying and Peng, Lan 2008. Asymptotic solution of thermocapillary convection in a thin annular pool of silicon melt. Physics of Fluids, Vol. 20, Issue. 8, p. 082107.


    Wu, W. Ewing, D. and Ching, C.Y. 2008. Investigation of a large top wall temperature on the natural convection plume along a heated vertical wall in a square cavity. International Journal of Heat and Mass Transfer, Vol. 51, Issue. 7-8, p. 1551.


    Bahloul, Ali 2006. Boundary layer and stability analysis of natural convection in a porous cavity. International Journal of Thermal Sciences, Vol. 45, Issue. 7, p. 635.


    Coman, Melissa A. Hughes, Graham O. Kerr, Ross C. and Griffiths, Ross W. 2006. The effect of a barrier on laminar convection in a box with differentially heated endwalls. International Journal of Heat and Mass Transfer, Vol. 49, Issue. 17-18, p. 2903.


    Wu, W. Ewing, D. and Ching, C.Y. 2006. The effect of the top and bottom wall temperatures on the laminar natural convection in an air-filled square cavity. International Journal of Heat and Mass Transfer, Vol. 49, Issue. 11-12, p. 1999.


    Prud'homme, M. and Bougherara, H. 2005. Weakly non-linear stability of stratified natural convection in a vertical cavity with lateral temperature gradient. International Communications in Heat and Mass Transfer, Vol. 32, Issue. 1-2, p. 32.


    Prud’homme, Michel Bougherara, Habiba and Bahloul, Ali 2003. Convection in a vertical cavity submitted to crossed uniform heat fluxes. International Journal of Heat and Mass Transfer, Vol. 46, Issue. 20, p. 3831.


    Leppinen, D.M. 2002. Natural convection in a shallow cylindrical annuli. International Journal of Heat and Mass Transfer, Vol. 45, Issue. 14, p. 2967.


    Naumann, Robert J. 2000. An analytical model for transport from quasi-steady and periodic accelerations on spacecraft. International Journal of Heat and Mass Transfer, Vol. 43, Issue. 16, p. 2917.


    ×

Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

  • D. E. Cormack (a1), L. G. Leal (a1) and J. H. Seinfeld (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112074001364
  • Published online: 01 March 2006
Abstract

Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6·983, 10 ≤ Gr 2 × 104 and 0·05 [les ] A [les ] 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A [lsim ] 0·1 and Gr2A3Pr2 [lsim ] 105. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax