**Papers Published**

- Bejan, A. and Lage, J.L.,
*The Prandtl number effect on the transition in natural convection along a vertical surface*, Trans. ASME, J. Heat Transf. (USA), vol. 112 no. 3 (1990), pp. 787 - 90 .

(last updated on 2007/04/08)**Abstract:**

It has been suggested 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 associates the constant Ra≈10^{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 re-examined 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≈10^{9}, while in high-Pr fluids the transition Rayleigh number is higher than 10^{9}. It appears that the constant Grashof number Gr≈10^{9}(i.e., not Ra≈10^{9}) marks the transition in the wide Pr range 0.001-1000**Keywords:**

convection;external flows;laminar to turbulent transitions;