Dimensionless numbers – Identify Re·Pr The product of the Reynolds number and the Prandtl number is known as which dimensionless group?

Introduction / Context:
Dimensionless numbers condense complex transport phenomena into ratios that govern similarity and scaling. Recognizing relationships among Reynolds (Re), Prandtl (Pr), Stanton (St), Peclet (Pe), and others is foundational for convective heat transfer analysis.

Given Data / Assumptions:

• Standard definitions: Re = inertia/viscous, Pr = momentum diffusivity/thermal diffusivity.
• Single-phase convection in ducts or external flows.

Concept / Approach:
Peclet number measures the relative importance of advection to thermal diffusion: Pe = Re * Pr. It features prominently in convection–diffusion equations and in assessing axial conduction effects in heat exchangers.

Step-by-Step Solution:
Write Re = ρ * V * L / μ and Pr = μ * c_p / k.Multiply: Re * Pr = (ρ * V * L / μ) * (μ * c_p / k) = ρ * V * L * c_p / k.Recognize Pe = ρ * c_p * V * L / k = Re * Pr.

Verification / Alternative check:
From convection correlations: Nu = f(Re, Pr). Also, Stanton number satisfies St = Nu / (Re * Pr), highlighting Pe in the denominator if rearranged.

Why Other Options Are Wrong:

• Stanton number is Nu/(RePr), not RePr itself.
• Biot number compares internal to external resistance (h * L / k_s), unrelated to RePr.
• Grashof pertains to buoyancy in natural convection.
• Nusselt is a heat transfer coefficient group hL/k, not a product of Re and Pr.

Common Pitfalls:
Interchanging St and Pe; forgetting that Pr links momentum and thermal diffusivities, so Pe collapses convective–diffusive transport into one group.

Final Answer:
Peclet number