Which dimensionless number compares momentum diffusion to thermal diffusion?

• A. Nusselt number
• B. Froude number
• C. Prandtl number
• D. Schmidt number

Answer: (C)

Momentum diffusion is how viscous effects spread momentum through the fluid, while thermal diffusion is how heat spreads through conduction. The Prandtl number encapsulates the comparison between these two processes by taking the ratio of momentum diffusivity to thermal diffusivity. It is defined as Pr = ν/α, or equivalently μ c_p / k, where ν is kinematic viscosity, α is thermal diffusivity, μ is dynamic viscosity, c_p is specific heat, and k is thermal conductivity. This number tells you whether momentum or heat diffuses faster: a small Pr means heat diffuses more quickly than momentum, while a large Pr means momentum diffuses faster than heat, affecting the relative thickness of velocity and thermal boundary layers. The other options describe different physical comparisons: Nusselt relates convective to conductive heat transfer, Froude involves inertial versus gravitational forces, and Schmidt compares momentum diffusivity to mass diffusivity.