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 .

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 ?
In these equations, Gk represent the generation of turbulence kinetic energy due to the mean velocity gradients, from [mu]t s2 where S is the modulus of the mean rate-of-strain tensor, [sigma]k and [sigma][member of] are the effective prandtl number for turbulent kinetic energy and rate of dissipation, respectively and pt is modeled as [mu]t=[rho]k2/[member of] (Ao+As (k[U.
l]: Permeation Reynolds number at lower wall t: Time (s) R: Permeation Reynolds number at upper wall Pr: Prandtl number Sc: Schmidt number.
The latter is a reflection of the fact that addition of nanoparticles to the base-fluid decreases the nanofluid Prandtl number and increases the thermal diffusivity, which causes the reduction in the temperature gradients and, accordingly, increases the thermal boundary thickness.
For various values of Prandtl number (Pr), suction parameter (S), and radiation parameter (F), the profiles of translational velocity across boundary layer are shown in Figure 5(a).
1]), heat source/sink parameter ([alpha]) and opposite trend can be seen with Prandtl number (Pr).
9 depicts the effects of Prandtl number Pr on [theta] for [omega] = 10,Re = 1and t = 0.
Abdou, Experimental investigation of turbulent heat transfer of high Prandtl number fluid flow under strong magnetic field, Fusion Sci.
r] Prandtl number q Volumetric heat generation [W/m.
2] ppb parts per billion Pr Prandtl number of liquid Jet in stage 2, [[upsilon].