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.
Mechanical Engineering
Heat Transfer, Refrigeration and Air Conditioning
Difficulty: Easy
Choose an option
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AReynolds number only
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BGrashof number only
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CReynolds number and Grashof number
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DPrandtl number and Grashof number (i.e., Rayleigh number)
Answer
Correct Answer: Prandtl number and Grashof number (i.e., Rayleigh number)
Explanation
Concept/ApproachIn free convection, buoyancy and viscous forces dominate. The transition criterion is commonly expressed in terms of the Rayleigh number, Ra = Gr × Pr.
ImplicationThus 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 AnswerPrandtl number and Grashof number (i.e., Rayleigh number)