Free convection transition: identify the governing non-dimensional criterion For natural convection over surfaces, transition from laminar to turbulent flow is governed by a critical value of which parameter(s)? Choose the most appropriate option.

Concept/Approach
In free convection, buoyancy and viscous forces dominate. The transition criterion is commonly expressed in terms of the Rayleigh number, Ra = Gr × Pr.

Implication
Thus both Grashof number (buoyancy vs viscous) and Prandtl number (momentum vs thermal diffusivity) are involved. For many vertical surfaces, transition is observed around Ra ≈ 10⁹.

Why others are incorrect

• Reynolds number governs forced convection, not natural convection.
• Grashof alone is incomplete; fluid thermal properties (Pr) also matter.

Final Answer
Prandtl number and Grashof number (i.e., Rayleigh number)