Prandtl number kinematic viscosity ratio

The Prandtl number is the ratio of the kinematic viscosity (i.e., the momentum diffusivity) to the thermal diflusivity. Because the Schmidt number is analogous to the Prandtl number, one would expect that Sc is the ratio of the momentum diffusivity (i.e., the kinematic viscosity), v, tothe mass diffusivity Dab- Indeed, this is true ... 

The Prandtl number is simply the ratio of kinematic viscosity (t /p) to thermal diffu-sivity (a). Physically, the Prandtl number represents the ratio of the hydrodynamic boundary layer to the thermal boundary layer in the heat transfer between fluids and a stationary wall. In simple fluid flow, it represents the ratio of the rate of impulse transport to the rate of heat transport, ft is determined by the material properties for high viscosity polymer melts, the number is of the order of 10 to 10 . 

Prandt/Number. The Prandtl number, Pr, is the ratio of the kinematic viscosity, V, to the thermal diffusivity, a. 

The Prandtl number of a liquid (PrL) is defined as the ratio of the kinematic viscosity to the thermal diffusivity of the liquid ... 

The Schmidt number is the ratio of kinematic viscosity to molecular diffusivity. Considering liquids in general and dissolution media in particular, the values for the kinematic viscosity usually exceed those for diffusion coefficients by a factor of 103 to 104. Thus, Prandtl or Schmidt numbers of about 103 are usually obtained. Subsequently, and in contrast to the classical concept of the boundary layer, Re numbers of magnitude of about Re > 0.01 are sufficient to generate Peclet numbers greater than 1 and to justify the hydrodynamic boundary layer concept for particle-liquid dissolution systems (Re Pr = Pe). It can be shown that [(9), term 10.15, nomenclature adapted]... 

It is seen that we are comparing kinematic viscosity, thermal diffusivity, and diffu-sivity of the medium for both air and water. In air, these numbers are all of the same order of magnitude, meaning that air provides a similar resistance to the transport of momentum, heat, and mass. In fact, there are two dimensionless numbers that will tell us these ratios the Prandtl number (Pr = pCpv/kj = v/a) and the Schmidt number (Sc = v/D). The Prandtl number for air at 20°C is 0.7. The Schmidt number for air is between 0.2 and 2 for helium and hexane, respectively. The magnitude of both of these numbers are on the order of 1, meaning that whether it is momentum transport, heat transport, or mass transport that we are concerned with, the results will be on the same order once the boundary conditions have been made dimensionless. 

PRANDTL NUMBER. A dimensionless number equal to the ratio of llie kinematic viscosity to the tlienuoiiielric conductivity (or thermal diffusivity), For gases, it is rather under one and is nearly independent of pressure and temperature, but for liquids the variation is rapid, Its significance is as a measure of the relative rates of diffusion of momentum and heat m a flow and it is important m the study of compressible flow and heat convection. See also Heat Transfer. 

The Prandtl number via has been found to be the parameter which relates the relative thicknesses of the hydrodynamic and thermal boundary layers. The kinematic viscosity of a fluid conveys information about the rate at which momentum may diffuse through the fluid because of molecular motion. The thermal diffusivity tells us the same thing in regard to the diffusion of heat in the fluid. Thus the ratio of these two quantities should express the relative magnitudes of diffusion of momentum and heat in the fluid. But these diffusion rates are precisely the quantities that determine how thick the boundary layers will be for a given external flow field large diffusivities mean that the viscous or temperature influence is felt farther out in the flow field. The Prandtl number is thus the connecting link between the velocity field and the temperature field. 

The mass diffusivity Dt], the thermal diffusivity a = k/pCp, and the momentum diffusivity or kinematic viscosity v = fi/p, all have dimensions of (length)2/time, and are called the transport coefficients. The ratios of these quantities yield the dimensionless groups of the Prandtl number, Pr, the Schmidt number, Sc, and the Lewis number, Le... 

The Prandtl number is a dimensionless number named after Ludwig Prandtl. It is defined as the ratio of momentum diffusivity (kinematic viscosity) to the thermal diffusivity, as well as the ratio of viscous diffusion rate to thermal diffusion rate ... 

Prandtl number (Pr, Npd n. A dimensionless group important in the analysis of convection heat transfer, defined as (in consistent units) Cpp/k, where Cp is the specific heat of a fluid at constant pressures, p the viscosity, and k is the thermal conductivity. The Prandtl number is also the ratio of the kinematic viscosity to the thermal diffusivity see both entries). 

The Prandtl number is normally used in heat transfer and represents the ratio of the kinematic viscosity and thermal diffusivity ... 

For heat transfer within the fluid the similarity parameter of importance is the Peclet number, which is the ratio of heat convection and heat conduction. We will revisit heat transfer modes later but for the purposes of flow characterization, the Peclet number is defined in Equation (3.26) below, where it is also given as the product of the Reynolds number and the Prandtl number, Pr (kinematic viscosity thermal diffusivity)... 

Thus, similar to other oxide melts, the BaO-CuO flux has a rather high viscosity, hence it has high Schmidt (Sc) and Prandtl (Pr) numbers the former is defined as a ratio of the kinematic viscosity of melt v and its thermal diffusivity l, Pr = vla. Therefore the Y-solute is transferred to the growing Y123 crystal from the Y211 phase placed at the bottom of the crucible mainly by melt convection. In order to calculate the melt convection, several governing equations have to be considered (Namikawa et al. 1996a) ... 

Prandtl number is analogous to Schmitt number but focuses on heat transfer. It is the ratio of kinematic viscosity to thermal diffusivity. Typical Prandtl numbers are about 1 for gases and about 10 for supercritical fluids. The implieation thermal inhomogeneity in gases degrade rapidly, liquids need stirring, and supercritical fluids mix much more rapidly than liquids. 

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