Dimensionless numbers Stanton

By dividing the reaction time by the thermal time constant, one obtains a dimensionless number, the modified Stanton criterion ... 

Heat and mass transfer coefficients are usually reported as correlations in terms of dimensionless numbers. The exact definition of these dimensionless numbers implies a specific physical system. These numbers are expressed in terms of the characteristic scales. Correlations for mass transfer are conveniently divided into those for fluid-fluid interfaces and those for fluid-solid interfaces. Many of the correlations have the same general form. That is, the Sherwood or Stanton numbers containing the mass transfer coefficient are often expressed as a power function of the Schmidt number, the Reynolds number, and the Grashof number. The formulation of the correlations can be based on dimensional analysis and/or theoretical reasoning. In most cases, however, pure curve fitting of experimental data is used. The correlations are therefore usually problem dependent and can not be used for other systems than the one for which the curve fitting has been performed without validation. A large list of mass transfer correlations with references is presented by Perry [95]. 

Stanton number A dimensionless number, St, used for forced convection heat transfer and relates the rate of heat transfer to tlie thermal capacity of a fluid ... 

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. 

Maintenance of proper temperature is a major aspect of reactor operation. The illustrations of several reactors in this chapter depict a number of provisions for heat transfer. The magnitude of required heat transfer is determined by heat and material balances as described in Section 17.3. The data needed are thermal conductivities and coefficients of heat transfer. Some of the factors influencing these quantities are associated in the usual groups for heat transfer namely, the Nusselt, Stanton, Prandtl, and Reynolds dimensionless groups. Other characteristics of particular kinds of reactors also are brought into correlations. A selection of practical results from the abundant literature will be assembled here. Some modes of heat transfer to stirred and fixed bed reactors are represented in Figures 17.33 and 17.18, and temperature profiles in... 

Stanton number for gas-to-liquid transport of gaseous reactant A, kg a L/us , dimensionless. 

Stanton number for liquid-to-actively wetted solid transport of dissolved gaseous reactant A, awsa -aws k/us s dimensionless. 

N, IVc, IVnu IVp. K, IVh. IVs. N Proportionality coefficient, dimensionless group Grashof number, L p P Af/)U Nusselt number, hD/k or hL/k Peclet number, DGc/k Prandtl number, c A/k Reynolds number, DG/ l Stanton number, Number of sealing strips Dimensionless Dimensionless... 

Sometimes it is more convenient to express the heat and mass transfer coefficients in terms of the dimensionless Stanton number as... 

The dimensionless parameter in Eq. 6.107 is the Bodenstein number (Eq. 6.106). The remaining parameter in Eq. 6.108 determines the ratio of effective mass transport to convection, which is defined by the modified (effective) Stanton number (Steff) ... 

In summary, chromatographic batch separation depends on the following dimensionless parameters Peclet and Stanton numbers, dimensionless injection time, Henry coefficients and dimensionless Langmuir parameters. 

Stanton number St Nu h Dimensionless heat transfer coefficient (ratio Forced convection... 

Stanton number (mass transfer) Stn Sh hD Dimensionless mass transfer coefficient Convective mass transfer... 

Thus, Eqs. 6.49 and 6.50 indicate that the skin friction coefficient and Stanton number remain equal to their constant-property values. In terms of these dimensionless transfer coefficients, the effects of the linear dependence of viscosity on temperature just cancel those of the perfect gas variation of the density. It should be noted, however, that the density variation itself still affects the boundary layer thickness. 

StH Stanton number for heat transfer dimensionless. t tray spacing m. 

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