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Transient natural convection of low‐Prandtl‐number fluids in a differentially heated cavity
Author(s) -
Mohamad A. A.,
Viskanta R.
Publication year - 1991
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650130105
Subject(s) - grashof number , prandtl number , natural convection , mechanics , turbulent prandtl number , physics , film temperature , oscillation (cell signaling) , combined forced and natural convection , nusselt number , thermodynamics , reynolds number , convection , classical mechanics , chemistry , biochemistry , turbulence
The transient convective motion in a two‐dimensional square cavity driven by a temperature gradient is analysed. The cavity is filled with a low‐Prandtl‐number fluid and the vertical walls are maintained at constant but different temperatures, while the horizontal boundaries are adiabatic. A control volume approach with a staggered grid is employed to formulate the finite difference equations. Numerically accurate solutions are obtained for Prandtl numbers of 0·001, 0·005 and 0·01 and for Grashof numbers up to 1 × 10 7 . It was found that the flow field exhibits periodic oscillation at the critical Grashof numbers, which are dependent on the Prandtl number. As the Prandtl number is decreased, the critical Grashof number and the frequency of oscillation decrease. Prior to the oscillatory flow, steady state solutions with an oscillatory transient period were predicted. In addition to the main circulation, four weak circulations were predicted at the corners of the cavity.