Which dimensionless number is the ratio of the kinematic viscosity to the thermal diffusivity?

Which dimensionless number is the ratio of the kinematic viscosity to the thermal diffusivity?

• A. The ratio of density to viscosity
• B. The ratio of kinematic viscosity to thermal diffusivity
• C. The ratio of thermal diffusivity to viscosity
• D. The ratio of momentum diffusivity to mass diffusivity

Answer: (B)

The concept here is comparing how quickly momentum diffuses versus how quickly heat diffuses in a fluid. The kinematic viscosity ν = μ/ρ governs momentum diffusion, while the thermal diffusivity α = k/(ρ c_p) governs heat diffusion. Taking their ratio gives a dimensionless number: Pr = ν/α. Expanding in terms of material properties, Pr = (μ/ρ) / (k/(ρ c_p)) = μ c_p / k. This Prandtl number tells you whether momentum or heat diffuses faster: small Pr means heat diffuses faster than momentum, while large Pr means momentum diffuses more slowly relative to heat. Typical values: air ≈ 0.7, water ≈ 7, oils much higher.

The concept here is comparing how quickly momentum diffuses versus how quickly heat diffuses in a fluid. The kinematic viscosity ν = μ/ρ governs momentum diffusion, while the thermal diffusivity α = k/(ρ c_p) governs heat diffusion. Taking their ratio gives a dimensionless number: Pr = ν/α. Expanding in terms of material properties, Pr = (μ/ρ) / (k/(ρ c_p)) = μ c_p / k. This Prandtl number tells you whether momentum or heat diffuses faster: small Pr means heat diffuses faster than momentum, while large Pr means momentum diffuses more slowly relative to heat. Typical values: air ≈ 0.7, water ≈ 7, oils much higher.