Prandtl number

Prandtl number

The Prandtl number mathrm{Pr} is a dimensionless number approximating the ratio of momentum diffusivity (kinematic viscosity) and thermal diffusivity. It is named after the German physicist Ludwig Prandtl.

It is defined as::mathrm{Pr} = frac{ u}{alpha} = frac{mbox{viscous diffusion rate{mbox{thermal diffusion rate = frac{c_p mu}{k}

* u : kinematic viscosity, u = mu/ ho, (SI units : m2/s)
* alpha : thermal diffusivity, alpha = k/( ho c_p), (SI units : m2/s)
* mu : viscosity, (SI units : Pa s)
* "k" : thermal conductivity, (SI units : W/(m K) )
* cp : specific heat, (SI units : J/(kg K) )
* ho : density, (SI units : kg/m3 )

Note that whereas the Reynolds number and Grashof number are subscripted with a length scale variable, Prandtl number contains no such length scale in its definition and is dependent only on the fluid and the fluid state. As such, Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity.

Typical values for mathrm{Pr} are:

* around 0.7-0.8 for air and many other gases,
* around 0.16-0.7 for mixtures of noble gases or noble gases with hydrogen
* around 7 for water
* around 10e|24 for Earth's mantle
* between 100 and 40,000 for engine oil,
* between 4 and 5 for R-12 refrigerant
* around 0.015 for mercury

For mercury, heat conduction is very effective compared to convection: thermal diffusivity is dominant.For engine oil, convection is very effective in transferring energy from an area, compared to pure conduction: momentum diffusivity is dominant.

In heat transfer problems, the Prandtl number controls the relative thickness of the momentum and thermal boundary layers. When "Pr" is small, it means that the heat diffuses very 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.

ee also

*Turbulent Prandtl number
*Magnetic Prandtl number


* "Viscous Fluid Flow", F. M. White, McGraw-Hill, 3rd. Ed, 2006
* "Effects of Prandtl number and a new instability mode in a plane thermal plume. R. Lakkaraju, M Alam. Journal of Fluid Mechanics, vol. 592, 221-231 (2007)

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Prandtl number — Prandtlio skaičius statusas T sritis fizika atitikmenys: angl. Prandtl number vok. Prandtl Zahl, f rus. число Прандтля, n pranc. nombre de Prandtl, m …   Fizikos terminų žodynas

  • Prandtl number — Prandtlio skaičius statusas T sritis Standartizacija ir metrologija apibrėžtis Judesio kiekio ir šilumos pernašos skaičiavimams vartojamas nedimensinis dydis, išreiškiamas skysčio arba dujų kinematinės klampos ir molekulių difuzijos koeficiento… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

  • Prandtl number — Prandtlio skaičius statusas T sritis chemija apibrėžtis Medžiagos kinematinės klampos ir difuzijos koeficiento santykis. atitikmenys: angl. Prandtl number rus. критерий Прандтля; число Прандтля …   Chemijos terminų aiškinamasis žodynas

  • prandtl number — ˈpräntəl noun Usage: usually capitalized P Etymology: after Ludwig Prandtl died 1953 German physicist; translation of German Prandtlsche zahl : the ratio of the product of the coefficient of viscosity and the specific heat at constant pressure to …   Useful english dictionary

  • Prandtl number — /prahn tl/, Physics, Thermodynam. the ratio of the fluid viscosity to the thermal conductivity of a substance, a low number indicating high convection. [1930 35; named after Ludwig Prandtl (1875 1953), German physicist] * * * …   Universalium

  • Prandtl number — Смотри число Прандтля (Pr) …   Энциклопедический словарь по металлургии

  • Turbulent Prandtl number — The turbulent Prandtl number (Pr t) is a non dimensional term defined as the ratio between the momentum eddy diffusivity and the heat transfer eddy diffusivity. It is useful for solving the heat transfer problem of turbulent boundary layer flows …   Wikipedia

  • Magnetic Prandtl number — The Magnetic Prandtl number is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity. It is defined as: where: Rem is the magnetic Reynolds number Re… …   Wikipedia

  • Prandtl-Zahl — Prandtlio skaičius statusas T sritis fizika atitikmenys: angl. Prandtl number vok. Prandtl Zahl, f rus. число Прандтля, n pranc. nombre de Prandtl, m …   Fizikos terminų žodynas

  • Prandtl-Meyer function — describes the angle through which a flow can turn isentropically for the given initial and final Mach number. It is the maximum angle through which a sonic (M = 1) flow can be turned around a convex corner. For an ideal gas, it is expressed as… …   Wikipedia