Prandtl number
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Prandtl number
(′pränt·əl ′nəm·bər)
(fluid mechanics) A dimensionless number used in the study of diffusion in flowing systems, equal to the kinematic viscosity divided by the molecular diffusivity. Symbolized Prm. Also known as Schmidt number 1 (NSc).
(thermodynamics) A dimensionless number used in the study of forced and free convection, equal to the dynamic viscosity times the specific heat at constant pressure divided by the thermal conductivity. Symbolized NPr.
Oxford Dictionary of Units & Measures:
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Prandtl number
[Etymology: L. Prandtl; Germany 1875-1953] rheology. Symbol Pr. Characterizing a particular matter, the dimensionless ratio of the kinematic viscosity to the thermal diffusivity, identically the ratio of the Schmidt number to the Lewis number.
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Prandtl number
The Prandtl number 
is a dimensionless number; the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It is named after the German physicist Ludwig Prandtl.
It is defined as:
where:
: kinematic viscosity, 
, (SI units : m2/s)
: thermal diffusivity, 
, (SI units : m2/s)
: dynamic viscosity, (SI units : Pa s = (N s)/m2)
: thermal conductivity, (SI units : W/(m K) )
: specific heat, (SI units : J/(kg K) )
: 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:
(Low - conductive transfer strong)
- 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 degrees Celsius)
- 13.4 and 7.2 for seawater (At 0 degrees Celsius and 20 degrees Celsius respectively)
- between 100 and 40,000 for engine oil
- around 1×1025 for Earth's mantle.
(High - convective transfer strong)
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.
See also
References
- White, F. M. (2006). Viscous Fluid Flow (3rd. ed.). New York: McGraw-Hill. ISBN 0-07-240231-8.
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McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved.
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Oxford Dictionary of Units & Measures
A Dictionary of Weights, Measures, and Units. Copyright © Donald Fenna 2002, 2004. All rights reserved.
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Mentioned in
heat transfer factor
(rheology)
Rayleigh number 2
(thermodynamics)
Lewis number
(rheology)
Schmidt number
(rheology)
Graetz number
(rheology)
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