Skip to main content
    • Aa
    • Aa

Cooling of a Pr

  • WENXIAN LIN (a1) (a2), S. W. ARMFIELD (a3) and JOHN C. PATTERSON (a1)

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.

Corresponding author
Author to whom correspondence should be addressed:
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? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 22 *
Loading metrics...

Abstract views

Total abstract views: 72 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd September 2017. This data will be updated every 24 hours.