Number Prandtl

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

For sources, units, and remarks, see Table 2-228. v = specific volume, mVkg h = specific enthalpy, kj/kg s = specific entropy, kJ/(kg-K) c = specific beat at constant pressure, kJ/(kg-K) i = viscosity, 10 Pa-s and k = tberni conductivity, VW(m-K). For specific beat ratio, see Table 2-200 for Prandtl number, see Table 2-369. 

PHYSICAL AND CHEMICAL DATA TABLE 2-309 Specific Heat at Constant Pressure, Thermal Conductivity, Viscosity, and Prandtl Number of R32 Gas... 

Thermal conductivity, W/(m-K) Temperature, K Viscosity, 10 Pa-s Temperature, K Prandtl number, dimensio Temperature, K nless... 

The dimensionless group hD/k is called the Nusselt number, Nn , and the group Cp i./k is the Prandtl number, Np. . The group DVp/ i is the familiar Reynolds number, encountered in fluid-friction problems. These three... 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

The classical (and perhaps more famihar) form of dimensionless expressions relates, primarily, the Nusselt number hD/k, the Prandtl number c l//c, and the Reynolds number DG/ I. The L/D and viscosity-ratio modifications (for Reynolds number <10,000) also apply. 

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... 

Circular Tubes Numerous relationships have been proposed for predicting turbulent flow in tubes. For high-Prandtl-number fluids, relationships derived from the equations of motion and energy through the momentum-heat-transfer analogy are more complicated and no more accurate than many of the empirical relationships that have been developed. 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

Since the Schmidt number, Prandtl number, latent heat of vaporization, and humid heat are all essentially independent of pressure, the adiabatic-saturation-temperature and wet-bulb-temperature hues will be substantially equal at pressures different from atmospheric. 

In die dehnition of the Prandtl number, Cp is the heat capacity of the gas at constant pressure. 

A = Surface area ft based on tube ID C = Gas specific heat. Btu/lb°F d = Tube inner diameter, in. k = Gas thermal conductivity, Btu/ft-h°F L = Tube length, ft N = Total number of tubes in boiler Pr = Gas Prandtl number Q = Duty of the boiler. Btu/h... 

Other dimensionless parameters, namely the Reynolds number, Prandtl number, and Nusselt number ean be represented as follows ... 

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