Prandtl Number

one of the similarity criteria of thermal processes in liquids and gases; Pr = v/a = μc_p/λ, where v = μ /p is the coefficient of kinematic viscosity, μ is the coefficient of dynamic viscosity, p is the density, λ is the thermal conductivity, a - λ /pc_p is the thermal diffusivity, and c_p is the specific heat of the medium at constant pressure. Named after L. Prandtl, the Pr number is a physical characteristic of a medium and depends only on the thermodynamic state. For gases, it hardly varies with change in temperature; for diatomic gases, Pr ≈ 0,72, and for triatomic and polyatomic gases, Pr varies from about 0.75 to 1.0. In nonmetallic liquids, Pr varies more markedly with temperature for liquids of higher viscosity. For example, for water, Pr - 13.5 at 0°C, and Pr = 1.74 at 100°C; for transformer oil, Pr = 866 at 0°C and Pr - 43.9 at 100°C. For liquid metals, Pr ≪ 1 and changes little with temperature. For example, for sodium Pr - 0.0115 at 100°C and Pr = 0.0039 at 700°C.

The Prandtl number is related to the other similarity criteria —the Peclet number Pe and the Reynolds number Re —by the formula Pr = Pe/Re,