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 Pr_m. Also known as Schmidt number 1 (N_Sc).

(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 N_Pr.

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 It might be outdated or ideologically biased.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 = μc_p/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 /pc_p is the thermal diffusivity, and c_p 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

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References in periodicals archive

Figure 9 depicts the influence of Prandtl number Pr.

Effects of slip and convective conditions on MHD flow of nanofluid over a porous nonlinear stretching/shrinking sheet

where [[sigma].sub.[epsilon]] is the Prandtl number of turbulent kinetic energy dissipation rate, [C.sub.[epsilon]1] and [C.sub.[epsilon]2] the constants of turbulent model, respectively.

Numerical Simulation the Air Jet Flow Field of a Dual Slot Inset Blunt Die in the Melt Blowing Nonwoven Process

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.

Mathematical Modeling of Thermal Management at Different Atmospheric Pressure Conditions

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.

Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation

Here Tfr is the freezing point of the base liquid (273.16K).kb is the Boltzmann constant(kb[approximately equal to] 1.38*1023J/K),df is the fluid molecular diameter ,dp is the diameter of nanoparticles (10 nm [less than or equal to] dp [less than or equal to] 150 nm), T is the nanofluid temperature (294[less than or equal to]T(K) [less than or equal to]324), x is the particle volume concentration which is valid for 0.2%[less than or equal to]x[less than or equal to]9%, prf is these prandtl number of the base fluid, [rho]f and uf are the density and the dynamic viscosity of the base fluid respectively and uB is the nanopr article Brownian velocity which is calculated as the ratio between dp and the time TD= dp2/6D BY assuming the absence of agglomeration.

Performance of the heat transfer behavior of Tri Ethylene Glycol (TEG) based cuo and sin nanofluids in a rectangular pipe under the turbulent flow condition

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).

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

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 .

MHD MIXED CONVECTION BOUNDARY LAYER FLOW THROUGH POROUS MEDIUM DUE TO POROUS NON-LINEARLY SHRINKING SURFACE

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.

Overview of numerical methods for simulating Ranque-Hilsch effect within vortex tubes/ Skaitiniu metodu, skirtu nagrineti Ranke-Hilc efekta sukuriniame vamzdyje, analize

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.

Investigation of attic space airflow and temperature distribution using a computational fluid dynamics program

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.

Heat Transfer and Pressure Drop Performance of the Air Bearing Heat Exchanger

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:

Laminar forced convection heat transfer characteristics from a heated cylinder in water based nanofluids