# 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 .
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Prandtl Number

one of the similarity criteria of thermal processes in liquids and gases; Pr = v/a = μcp/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 /pcp is the thermal diffusivity, and cp 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,

S. L. VISHNEVETSKII

References in periodicals archive ?
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In the case of convective heat transfer, there are several dimensional parameters that are important, namely Nusselt number, Reynolds number Prandtl number, and Rayleigh number.
This situation happens when the frequencies' ratio is equal to six in the case of low Prandtl number or is equal to three in the case of high Prandtl number, which can be more convenient to be reproduced experimentally, since one can look only for small natural integer frequencies' ratio.
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To solve the governing nondimensional unsteady equations (4) subject to initial and boundary conditions (5), we apply Laplace transform technique for the case of unit Prandtl number and Schmidt number, as for arbitrary Prandtl number or Schmidt number, the Laplace transform technique leads to a difficult inverse transformation step (integrand of the Bromwich integral becomes a complicated multivalued function).
The results for velocity and temperature distribution reveal the flow kinematics under the effects of key physical parameters of the problem namely non linear shrinking parameter s, magnetic parameter M, porosity parameter K, mixed convection parameter and Prandtl number Pr .
Thakare, Parekh (2014) have published a paper aimed towards presenting the CFD study of vortex tube carried out to gain an understanding about influence of thermophysical properties such as thermal diffusivity, Prandtl number, specific gas constant and thermal conductivity of different gases and turbulence models on its performance.
The Rayleigh number (Ra) is defined as the product of the Grashof number (Gr), which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number (Pr), which describes the relationship between momentum diffusivity and thermal diffusivity.
According to a study by Brethouwer (2011), the turbulent Prandtl number associated with heat transfer in rotating channels is lower than the typical value of 0.9 for a stationary channel.
In order to investigate the influence of solid particles volume fraction [phi] on the heat transfer characteristics, the Reynolds and Prandtl number of the nanofluids can be expressed as:

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