In free (natural) convection heat transfer, the onset of transition from laminar to turbulent boundary layer flow over a heated surface is governed by a critical combination of dimensionless groups. Which parameter(s) determine this transition threshold most directly for natural convection?

Introduction / Context:
Natural (free) convection arises when buoyancy forces due to density differences drive fluid motion without any external pumping. Predicting when its boundary layer changes from laminar to turbulent is important for heat exchanger design, electronics cooling, and thermal insulation analysis. Unlike forced convection, where Reynolds number dominates, natural convection relies on buoyancy–viscosity and thermal-diffusion effects captured by specific dimensionless numbers.

Given Data / Assumptions:

• No externally imposed flow (pure free convection).
• Property variations are modest (Boussinesq approximation is reasonable).
• Heated or cooled surface induces buoyancy-driven boundary layers.

Concept / Approach:
For free convection, the strength of buoyancy relative to viscous forces is measured by the Grashof number, Gr. The relative importance of momentum and thermal diffusion is given by the Prandtl number, Pr. Their product Ra = Gr * Pr is the Rayleigh number. Empirical criteria for transition on vertical plates are typically expressed as a critical Rayleigh number (for example, order of 10^9), meaning that both Gr and Pr jointly control the onset of turbulence.

Step-by-Step Solution:

Verification / Alternative check:
Correlations for Nusselt number in natural convection use Ra ranges with distinct laminar and turbulent regimes, confirming the centrality of Gr and Pr via Ra.

Why Other Options Are Wrong:

• Gr alone: Incomplete, because fluid thermal properties via Pr also matter.
• Re or Gr+Re: Reynolds governs forced convection, not free convection.

Common Pitfalls:
Applying forced-convection transition criteria (e.g., critical Re) to buoyancy-driven flows, which can lead to large heat-transfer prediction errors.

Final Answer:
Grashoff number & Prandtl number.