Prandtl number of a fluid

Momentum diffuses more strongly relative to thermal diffusion. In common boundary-layer models, the thermal boundary layer may be thinner than the velocity layer. Exact interpretation still depends on geometry and correlation. Evaluate properties at a stated film or bulk temperature appropriate to the correlation. Application: Parameterize fluid boundary-layer and heat-transfer correlations. The numerical example For μ=1.0 mPa·s, cp=4180 J/(kg·K), and k=0.60 W/(m·K), water has Pr≈6.97 anchors the idea in a concrete measurement case. The corresponding units are Pr dimensionless; ν and α in m²/s; μ in Pa·s; cp in J/(kg·K); k in W/(m·K). For μ=1.0 mPa·s, cp=4180 J/(kg·K), and k=0.60 W/(m·K), water has Pr≈6.97. This checks that the reference quantities are compatible.

Pr=ν/α directly compares diffusivities. Substituting ν=μ/ρ and α=k/(ρcp) cancels density to give μcp/k. Both forms must use properties at the same temperature. Evaluate properties at a stated film or bulk temperature appropriate to the correlation. The corresponding units are Pr dimensionless; ν and α in m²/s; μ in Pa·s; cp in J/(kg·K); k in W/(m·K). For μ=1.0 mPa·s, cp=4180 J/(kg·K), and k=0.60 W/(m·K), water has Pr≈6.97. This checks that the reference quantities are compatible. Scope: The property form assumes consistent local properties and α=k/(ρcp), ν=μ/ρ. It compares momentum and thermal boundary-layer diffusion only within a specified flow model. Properties vary with temperature, so choose an appropriate reference or temperature-dependent evaluation. A practical application is Parameterize fluid boundary-layer and heat-transfer correlations.

No. Viscosity, heat capacity and conductivity vary with temperature and pressure. Water can therefore have quite different Pr values across an operating range. Use property tables or validated models at the appropriate state. Evaluate properties at a stated film or bulk temperature appropriate to the correlation. Scope: The property form assumes consistent local properties and α=k/(ρcp), ν=μ/ρ. It compares momentum and thermal boundary-layer diffusion only within a specified flow model. Properties vary with temperature, so choose an appropriate reference or temperature-dependent evaluation. A practical application is Parameterize fluid boundary-layer and heat-transfer correlations.

Write the quantity and unit from the variable list next to every value: Pr dimensionless; ν and α in m²/s; μ in Pa·s; cp in J/(kg·K); k in W/(m·K). Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For μ=1.0 mPa·s, cp=4180 J/(kg·K), and k=0.60 W/(m·K), water has Pr≈6.97. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Evaluate properties at a stated film or bulk temperature appropriate to the correlation.

The background states this starting condition: The property form assumes consistent local properties and α=k/(ρcp), ν=μ/ρ. It compares momentum and thermal boundary-layer diffusion only. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Evaluate properties at a stated film or bulk temperature appropriate to the correlation.