The Prandtl number effect on the transition in natural convection along a vertical surface

Journal Article · Wed Aug 01 00:00:00 EDT 1990 · Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States)

DOI:https://doi.org/10.1115/1.2910457· OSTI ID:5288148

Bejan, A; Lage, J L ^[1]

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1. Duke Univ., Durham, NC (USA)

As is often the case, the decision to embark on a new project was triggered by a set of coincidental and mutually reinforcing observations: (i) There is a definite lack of information (theoretical, numerical, experimental) on natural convection in low-Pr fluids (Lykoudis, 1989). This observation was stressed recently also by Wolff et al. (1988). (ii) Georgiadis (1989) drew attention to the line of work represented by Chao et al. (1982) and Bertin and Ozoe (1986), who showed numerically that the onset of Benard convection appears to be influence by the Prandtl number in the Pr < 1 range. (iii) The authors were struck by Bertin and Ozoe's (1986) discovery that they were unable to obtain numerically a steady flow below a certain Prandtl number (Pr = 0.001), even though the Rayleigh number based on height seemed sufficiently low (Ra = 2,800). The present study was motivated by these observations and the apparent suggestion that in low-Pr fluids the laminar flow expires at unexpectedly low Rayleigh numbers. This idea is particularly interesting if they think of the natural convection boundary layer near a vertical wall, for which the textbook teaches to associate the constant Ra {approx} 10{sup 9} with the height of transition to the turbulent flow, regardless of the Prandtl number (e.g., Incropera and DeWitt, 1985, p. 427). In order to test this idea, the authors reexamined the experimental record of observations on transition in vertical natural convection boundary layer flow. Indeed, the empirical data described next show that the Prandtl number has a strong influence on the transition Rayleigh number. In low-Pr fluids the transition occurs at Rayleigh numbers much lower than the often-mentioned Ra {approx} 10{sup 9}, while in high-Pr fluids the transition Rayleigh number is higher than 10{sup 9}. It appears that the constant Grashof number Gr {approx} 10{sup 9} (i.e., not Ra {approx} 10{sup 9}) marks the transition in the wide Pr range 0.001-1000.

• OSTI ID: 5288148
• Journal Information: Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States), Vol. 112:3; ISSN 0022-1481
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
SURFACES
NATURAL CONVECTION
EXPERIMENTAL DATA
HEAT TRANSFER
LAMINAR FLOW
PRANDTL NUMBER
CONVECTION
DATA
ENERGY TRANSFER
FLUID FLOW
INFORMATION
MASS TRANSFER
NUMERICAL DATA
420400* - Engineering- Heat Transfer &amp; Fluid Flow