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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Prandtl number ： ウィキペディア英語版 Prandtl number The Prandtl number (Pr) is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. That is, the Prandtl number is given as: :$\backslash mathrm\; =\; \backslash frac\; =\; \backslash frac\}\; =\; \backslash frac$ where: * $\backslash nu$ : momentum diffusivity (kinematic viscosity), $\backslash nu\; =\; \backslash mu/\backslash rho$, (SI units: m2/s) * $\backslash alpha$ : thermal diffusivity, $\backslash alpha\; =\; k/(\backslash rho\; c\_p)$, (SI units: m2/s) * $\backslash mu$ : dynamic viscosity, (SI units: Pa s = N s/m2) * $k$ : thermal conductivity, (SI units: W/m-K) * $c\_p$ : specific heat, (SI units: J/kg-K) * $\backslash rho$ : density, (SI units: kg/m3). Note that whereas the Reynolds number and Grashof number are subscripted with a length scale variable, the Prandtl number contains no such length scale in its definition and is dependent only on the fluid and the fluid state. As such, the Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity. Typical values for are: * around 0.015 for mercury * around 0.16-0.7 for mixtures of noble gases or noble gases with hydrogen * around 0.7-0.8 for air and many other gases * between 4 and 5 for R-12 refrigerant * around 7 for water (At 20 °C) * 13.4 and 7.2 for seawater (At 0°C and 20°C respectively) * between 100 and 40,000 for engine oil * around 1 for Earth's mantle. Small values of the Prandtl number, , means the thermal diffusivity dominates. Whereas with large values, , the momentum diffusivity dominates the behavior. For example, the listed value for liquid mercury indicates that the heat conduction is more significant compared to convection, so thermal diffusivity is dominant. However, for engine oil, convection is very effective in transferring energy from an area in comparison to pure conduction, so momentum diffusivity is dominant. In heat transfer problems, the Prandtl number controls the relative thickness of the momentum and thermal boundary layers. When is small, it means that the heat diffuses quickly compared to the velocity (momentum). This means that for liquid metals the thickness of the thermal boundary layer is much bigger than the velocity boundary layer. The mass transfer analog of the Prandtl number is the Schmidt number. ==See also== *Turbulent Prandtl number *Magnetic Prandtl number 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Prandtl number」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.