Prandtl Number

Ludwig Prandtl's boundary-layer paper of 1904 was eight pages long and reorganised fluid mechanics; the group that carries his name asks which boundary layer is thicker, the velocity one or the thermal one. Pr = 1 means they grow together. Gases cluster tightly near 0.7 — air is 0.707 at room temperature — because momentum and heat are carried by the same wandering molecules. Water is about 7 at 20 °C and falls to 1.75 at 100 °C. Engine oil can exceed 10,000, so its thermal layer is a sliver inside a very thick velocity layer. Liquid metals sit at 0.004–0.03, heat sprinting far ahead of momentum, which is why sodium-cooled reactors need their own correlations entirely.

Worked example: water at 20 °C with μ = 1.002 × 10⁻³ Pa·s, cₚ = 4182 J/(kg·K) and k = 0.598 W/(m·K) gives Pr = 7.01. Because Pr is a pure property, the trap is temperature: water's viscosity halves between 20 °C and 55 °C, so a Prandtl number picked off the wrong row of the table poisons every correlation downstream. Evaluate properties at the film temperature, the average of wall and bulk, unless the correlation you are using explicitly says otherwise.