Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 19
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Plotkowski, A. Fezi, K. and Krane, M. J. M. 2015. Advances in the Science and Engineering of Casting Solidification.


    De Césaro Oliveski, Rejane 2013. Correlation for the cooling process of vertical storage tanks under natural convection for high Prandtl number. International Journal of Heat and Mass Transfer, Vol. 57, Issue. 1, p. 292.


    Lin, Wenxian and Armfield, S. W. 2013. Scalings for unsteady natural convection boundary layers on an evenly heated plate with time-dependent heating flux. Physical Review E, Vol. 88, Issue. 6,


    Miana, Mario Cortés, Cristóbal Pelegay, José Luis Valdés, José Ramón and Pütz, Thomas 2013. Characteristic scales in natural convection around an isothermal horizontal cylinder for Pr < 1 fluids. International Journal of Thermal Sciences, Vol. 65, p. 39.


    Iatridis, A. J. Dritselis, C. D. Sarris, I. E. and Vlachos, N. S. 2012. Transient Laminar MHD Natural Convection Cooling in a Vertical Cylinder. Numerical Heat Transfer, Part A: Applications, Vol. 62, Issue. 7, p. 531.


    Lin, Wenxian and Armfield, S. W. 2012. Unified Prandtl number scaling for start-up and fully developed natural-convection boundary layers for both Pr≳1and Pr≲1fluids with isothermal heating. Physical Review E, Vol. 86, Issue. 6,


    Saha, Suvash C. and Khan, M.M.K. 2012. An improved boundary layer scaling with ramp heating on a sloping plate. International Journal of Heat and Mass Transfer, Vol. 55, Issue. 9-10, p. 2268.


    Saha, Suvash C. 2011. Scaling of free convection heat transfer in a triangular cavity for Pr>1. Energy and Buildings, Vol. 43, Issue. 10, p. 2908.


    Younis, O. Pallares, J. and Grau, F. X. 2011. Transient natural convection cooling of a high Prandtl number fluid in a cubical cavity. Meccanica, Vol. 46, Issue. 5, p. 989.


    Miana, Mario Cortes, Cristóbal Pelegay, José Luis Valdes, José Ramón and Putz, Thomas 2010. Transient Thermal Network Modeling Applied to Multiscale Systems. Part I: Definition and Validation. IEEE Transactions on Advanced Packaging, Vol. 33, Issue. 4, p. 924.


    Saha, Suvash C. Patterson, John C. and Lei, Chengwang 2010. Natural convection in attic-shaped spaces subject to sudden and ramp heating boundary conditions. Heat and Mass Transfer, Vol. 46, Issue. 6, p. 621.


    Saha, Suvash C. Patterson, John C. and Lei, Chengwang 2010. Natural convection boundary-layer adjacent to an inclined flat plate subject to sudden and ramp heating. International Journal of Thermal Sciences, Vol. 49, Issue. 9, p. 1600.


    Sarris, I. E. Iatridis, A. I. Dritselis, C. D. and Vlachos, N. S. 2010. Magnetic field effect on the cooling of a low-Pr fluid in a vertical cylinder. Physics of Fluids, Vol. 22, Issue. 1, p. 017101.


    Bednarz, Tomasz P. Lin, Wenxian Patterson, John C. Lei, Chengwang and Armfield, Steven W. 2009. Scaling for unsteady thermo-magnetic convection boundary layer of paramagnetic fluids of Pr>1 in micro-gravity conditions. International Journal of Heat and Fluid Flow, Vol. 30, Issue. 6, p. 1157.


    Lin, Wenxian Armfield, S. W. Patterson, J. C. and Lei, Chengwang 2009. Prandtl number scaling of unsteady natural convection boundary layers forPr>1fluids under isothermal heating. Physical Review E, Vol. 79, Issue. 6,


    Patterson, John C. Lei, Chengwang Armfield, Steve W. and Lin, Wenxian 2009. Scaling of unsteady natural convection boundary layers with a non-instantaneous initiation. International Journal of Thermal Sciences, Vol. 48, Issue. 10, p. 1843.


    XU, FENG PATTERSON, JOHN C. and LEI, CHENGWANG 2009. Transient natural convection flows around a thin fin on the sidewall of a differentially heated cavity. Journal of Fluid Mechanics, Vol. 639, p. 261.


    Lin, Wenxian and Armfield, S.W. 2008. Onset of entrainment in transitional round fountains. International Journal of Heat and Mass Transfer, Vol. 51, Issue. 21-22, p. 5226.


    Xu, Feng Patterson, John C. and Lei, Chengwang 2008. An experimental study of the unsteady thermal flow around a thin fin on a sidewall of a differentially heated cavity. International Journal of Heat and Fluid Flow, Vol. 29, Issue. 4, p. 1139.


    ×
  • Journal of Fluid Mechanics, Volume 574
  • March 2007, pp. 85-108

Cooling of a Pr<1 fluid in a rectangular container

  • WENXIAN LIN (a1) (a2), S. W. ARMFIELD (a3) and JOHN C. PATTERSON (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112006003703
  • Published online: 10 March 2007
Abstract

The flow behaviour associated with the cooling of an initially quiescent isothermal Newtonian fluid with Prandtl number Pr less than unity in a rectangular container by unsteady natural convection with an imposed lower temperature on vertical sidewalls is investigated by scaling analysis and direct numerical simulation. The flow is dominated by two distinct stages of development. i.e the boundary-layer development stage adjacent to the sidewall and the subsequent cooling-down stage. The first stage can be further divided into a start-up stage, transitional stage, and steady-state stage. The parameters characterizing the flow behaviour are the boundary-layer thickness, the maximum vertical velocity within the boundary layer, the time for the boundary layer to reach the steady state, the Nusselt number across the sidewall at the boundary-layer development stage, the time for the fluid in the container to be fully cooled down, and the average fluid temperature over the whole volume of the container.

Copyright
Corresponding author
Author to whom correspondence should be addressed: wenxian.lin@jcu.edu.au.
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

W. Lin & S. W. Armfield 2001 Natural convection cooling of rectangular and cylindrical containers. Intl J. Heat Fluid Flow 22, 7281.

S. W. Armfield & R. L. Street 1999 The fractional-step method for the Navier–Stokes equations on staggered grids: the accuracy of three variations. J. Comput. Phys. 153, 660665.

A. Javam , J. Imberger & S. W. Armfield 1999 Numerical study of internal wave reflection from sloping boundaries. J. Fluid Mech. 396, 183201.

J. M. Hyun 1994 Unsteady buoyant convection in an enclosure. Adv. Heat Transfer 24, 277320.

J. C. Patterson & S. W. Armfield 1990 Transient features of natural convection in a cavity. J. Fluid Mech. 219, 469497.

W. Lin & S. W. Armfield 2003 The Reynolds and Prandtl number dependence of weak fountains. Computational Mech. 31, 379389.

J. C. Patterson 1984. Unsteady natural convection in a cavity with internal heating and cooling. J. Fluid Mech. 140, 135151.

J. C. Patterson & J. Imberger 1980. Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 6586.

S. W. Armfield & J. C. Patterson 1991 Direct simulation of wave interactions in unsteady natural convection in a cavity. Intl J. Heat Mass Transfer 34, 929940.

S. W. Armfield & J. C. Patterson 1992 Wave properties of natural-convection boundary layers. J. Fluid Mech. 239, 195211.

R. J. Goldstein , E. R. G. Eckert , W. E. Ibele 2003 Heat transfer – a review of 2001 literature. Intl J. Heat Mass Transfer 46 18871992.

J. M. Hyun 1984 Transient process of thermally stratifying an initially homogeneous fluid in an enclosure. Intl J. Heat Mass Transfer 27, 19361938.

J. M. Hyun 1985 Effect of the Prandtl number on heatup of a stratified fluid in a enclosure. Trans. ASME: J. Heat Transfer 107, 982984.

B. P. Leonard 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comp. Meth. Appl. Mech. Engng 19, 5998.

W. Lin & S. W. Armfield 1999 Direct simulation of natural convection cooling in a vertical circular cylinder. Intl J. Heat Mass Transfer 42, 41174130.

W. Lin & S. W. Armfield 2000 Direct simulation of weak axisymmetric fountains in a homogeneous fluid. J. Fluid Mech. 403, 6788.

S. W. Armfield 1991 Finite-difference solutions of the Navier–Stokes equations on staggered and non-staggered grids. Computers Fluids 20, 117.

S. W. Armfield & W. Debler 1993 Purging of density stabilized basins. Intl J. Heat Mass Transfer 36, 519530.

R. J. Goldstein & D. G. Briggs 1964 Transient free convection about vertical plates and circular cylinders. Trans. ASME: J. Heat Transfer 86, 490500.

H. S. Kwak , K. Kuwahara & J. M. Hyun 1998 Convective cool-down of a contained fluid through its maximum density temperature. Intl J. Heat Mass Transfer 41, 323333.

V. F. Nicolette & K. T. Yang 1985 Transient cooling by natural convection in a two-dimensional square enclosure. Intl J. Heat Mass Transfer 28, 17211732.

D. R. Otis & J. Roessler 1987 Development of stratification in a cylindrical enclosure. Intl J. Heat Mass Transfer 30, 16331636.

S. G. Schladow , J. C. Patterson & R. L. Street 1989 Transient flow in a side-heated cavity at high Rayleigh number: a numerical study. J. Fluid Mech. 200, 121148.

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