Prandtl number effect on the transition in natural convection along a vertical surface
The present study was motivated by certain 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 we think of the natural convection boundary layer near a vertical wall, for which the textbook teaches us to associate the constant Ra ≈ 109 with the height of transition to the turbulent flow, regardless of the Prandtl number. In order to test this idea, we re-examined the experimental record of observations on transition in vertical natural convection boundary layer flow. Indeed, the empirical data described 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 ≈ 109, while in high-Pr fluids the transition Rayleigh number is higher than 109. It appears that the constant Grashof number Gr ≈ 109 (i.e., not Ra ≈ 109) marks the transition in the wide Pr range 0.001-1000.
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