Liquids Prandtl numbers

Actual tray pressure drop, in. liquid Prandtl number dimensionless Fractional opening in the circumference or a valve or. Pi... 

It is the product of the bubble Reynolds and the liquid Prandtl number divided by the boiling Nusselt number (Nu,), which is equivalent to the Stanton number in single-phase convective heat transfer. 

Figure B-5, Liquid Prandtl numbers. (Reproduced with permission from reference Copyright 1997, American Chemical Society.)...

Prandtl Z-M<7w/g (1875-1953) Ger. phys., founder of modern hydrodynamics and aerodynamics, proved sound barrier, boundary layer on moving surfaces in liquids, Prandtl number named after him Presl Jan Svatopluk (1791-1849) Czech, chem., originator of modern nomenclature in chemistry and botany Priestley Joseph (1733-1804) Brit, chem., phlogistonist, explained some composites of air, history of electricity and light Prigogine Ilya (1917-2003) Rus. bom Belgian phys. chemist, inventor of nonequilibrium thermodynamics, propagator of the theory of chaos ( La nouvelle alliance avec la nature )... 

The analogy has been reasonably successful for simple geometries and for fluids of very low Prandtl number (liquid metals). For high-Prandtl-number fluids the empirical analogy of Colburn [Trans. Am. Tn.st. Chem. Ting., 29, 174 (1933)] has been veiy successful. A J factor for momentum transfer is defined asJ =//2, where/is the friction fac tor for the flow. The J factor for heat transfer is assumed to be equal to the J factor for momentum transfer... 

HETP = height equivalent to a theoretical plate, ft HTU = height of a transfer unit, ft L = liquid mass velocity, Ib/hr-ft m = exponent a 1.0 n = exponent 0.44 Pr = Prandtl number, dimensionless Sc = Schmidt number dimensionless U, = linear velocity of gas based on total column cross-sectional area, ft/sec... 

Nusselt and Reynolds numbers are based on the diameter of the heating element, the conductivity and viscosity of the liquid, and the nominal gas velocities. The heat-transfer coefficient is constant for nominal liquid velocities above 10 cm/sec. The results were obtained for Prandtl numbers from 5 to 1200, but no effect of this variation was observed. 

In the buffer zone the value of d +/dy+ is twice this value. Obtain an expression for the eddy kinematic viscosity E in terms of the kinematic viscosity (pt/p) and y+. On the assumption that the eddy thermal diffusivity Eh and the eddy kinematic viscosity E are equal, calculate the value of the temperature gradient in a liquid flowing over the surface at y =15 (which lies within the buffer layer) for a surface heat flux of 1000 W/m The liquid has a Prandtl number of 7 and a thermal conductivity of 0.62 W/m K. 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

Thus at small Pol the growth rate of the oscillations is negative and the capillary flow is stable. The absolute value of sharply increases with a decrease of the capillary tube diameter. It also depends on the thermal diffusivity of the liquid and the vapor, as well as on the value of the Prandtl number. 

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

The gas-phase wall heat-transfer coefficient can be evaluated by using the gas-phase Reynolds number and Prandtl number in Eq. (33). The thermal conductivities of liquids are usually two orders of magnitude larger than the thermal conductivities of gases therefore, the liquid-phase wall heat-transfer coefficient should be much larger than the gas-phase wall heat-transfer coefficient, and Eq. (34) simplifies to... 

L/pj-A)(S/psA), liquid-solids velocity ratio, dimensionless Number of heat-transfer stages, dimensionless = hdp/kg, Nusselt number, dimensionless Pressure drop, gm-wt/cm2 = Cpu kg, Prandtl number, dimensionless = dpiipj U, Reynolds number, dimensionless S Mass velocity of solids, gm/cirf sec... 

The experimental results obtained for a wide range of systems(96-99) are correlated by equation 6.58, in terms of the Nusselt number (Nu = hd/k) for the particle expressed as a function of the Reynolds number (Re c = ucdp/fx) for the particle, the Prandtl number Pr for the liquid, and the voidage of the bed. This takes the form ... 

The gas film coefficient is dependent on turbulence in the boundary layer over the water body. Table 4.1 provides Schmidt and Prandtl numbers for air and water. In water, Schmidt and Prandtl numbers on the order of 1,000 and 10, respectively, results in the entire concentration boundary layer being inside of the laminar sublayer of the momentum boundary layer. In air, both the Schmidt and Prandtl numbers are on the order of 1. This means that the analogy between momentum, heat, and mass transport is more precise for air than for water, and the techniques apphed to determine momentum transport away from an interface may be more applicable to heat and mass transport in air than they are to the liquid side of the interface. 

One other measurement technique that has been used to measure Kl over a shorter time period, and is thus more responsive to changes in wind velocity, is the controlled flux technique (Haupecker et al., 1995). This technique uses radiated energy that is turned into heat within a few microns under the water surface as a proxy tracer. The rate at which this heat diffuses into the water column is related to the liquid film coefficient for heat, and, through the Prandtl-Schmidt number analogy, for mass as well. One problem is that a theory for heat/mass transfer is required, and Danckwert s surface renewal theory may not apply to the low Prandtl numbers of heat transfer (Atmane et al., 2004). The controlled flux technique is close to being viable for short-period field measurements of the liquid film coefficient. 

The Prandtl number is based on liquid properties on the grounds that the film resistance is probably a liquid film. 

A key feature of catalytic slurry reactors is that the particles are small ( 0.1 mm), so it is relatively easy to promote suspension by the mechanical action of the impeller. Moreover, because of their small size they travel together with the liquid, and therefore a significant mass transfer resistance develops at the liquid/solid interface that cannot be removed completely with the standard impellers. Also, because of the liquids large Prandtl number, the catalyst and the liquid are at the same temperature, so hot spots do not occur in multiphase slurry reactors. 

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. 

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