Dimensionless groups — convection versus conduction. What is the name of the dimensionless number that represents the ratio of convective to conductive heat transfer across a fluid layer?

Introduction / Context:
Dimensionless numbers condense complex transport phenomena into concise parameters. In convective heat transfer, one key number measures how effectively convection transports energy relative to conduction across the same characteristic length.

Given Data / Assumptions:

• A fluid layer or boundary layer with characteristic length L.
• Thermal conductivity k and convective coefficient h are defined.

Concept / Approach:
The Nusselt number Nu is defined as Nu = h * L / k. It expresses the enhancement of heat transfer through a fluid layer due to convection relative to pure conduction. When Nu = 1, convection offers no improvement over conduction; larger Nu indicates stronger convective transport.

Step-by-Step Solution:
Define Nu = (convective heat transfer)/(conductive heat transfer) across the same temperature difference and length scale.Using Fourier’s and Newton’s laws: h * (ΔT) versus k * (ΔT / L) → Nu = h * L / k.Therefore, the required ratio corresponds to the Nusselt number.

Verification / Alternative check:
In laminar flow over a flat plate, textbook correlations give Nu as a function of Reynolds and Prandtl numbers, reinforcing that Nu quantifies convective augmentation.

Why Other Options Are Wrong:
Stanton relates heat transfer to fluid capacity (St = h/(ρ * c_p * u)). Biot compares internal to external resistance (Bi = h * L_c / k_solid). Peclet expresses advective to diffusive transport (Pe = Re * Pr). Prandtl is momentum diffusivity to thermal diffusivity (Pr = ν/α).

Common Pitfalls:
Mixing Biot (solid-conduction focus) with Nusselt (fluid-side enhancement).

Final Answer:
Nusselt number