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Transfer Coefficients in Turbulent Flow

Most practically useful situations involve turbulent flow, and for these it is generally not possible to compute mass-transfer coefficients because we cannot describe the flow conditions mathematically. Instead, we rely principally on experimental data. The data are limited in scope, however, with respect to circumstances and situations as well as to range of fluid properties. Therefore it is important to be able to extend their applicability to situations not covered experimentally and to draw upon knowledge of other transfer processes (of heat, particularly) for help. [Pg.54]

To this end, there are many theories which attempt to interpret or explain the behavior of mass-transfer coefficients, such as the film, penetration, surface-renewal, and other theories. They are all speculations, and are continually being revised. It is helpful to keep in mind that transfer coefficients, for both heat and mass transfer, are expedients used to deal with situations which are not fully understood. They include in one quantity effects which are the result of both molecular and turbulent diffusion. The relative contribution of these effects, and indeed the detailed character of the turbulent diffusion itself, differs from one situation to another. The ultimate interpretation or explanation of the transfer coefficients will come only when the problems of the fluid mechanics are solved, at which time it will be possible to abandon the concept of the transfer coefficient. [Pg.54]

It will be useful first to describe briefly an elementary view of fluid turbulence, as a means of introducing the definitions of terms used in describing transfer [Pg.54]

Kolmogoroff [34] defined the velocity u and length scale of these small eddies in terms of the power input per unit mass of the fluid, P/m  [Pg.55]

The size of the smallest eddies can be estimated in the case of pipe flow in the following manner. [Pg.56]


When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. [Pg.381]

We mentioned earlier that flow in smooth tubes is usually fully turbulent for Re > 10,000. Tltrbulent flow is commonly utilized in practice because of the higher heat transfer coefficients associated with it Most correlations for the friction and heat transfer coefficients in turbulent flow are based on experimental studies because of the difficulty in dealing with turbulent flow theoretically. [Pg.491]

Heat delivery. Convection and conduction from hot gas sweeping by is the leading mode of heat transfer to a drying coating to supply the latent heat of vaporization of solvent. Except when solvent evaporation is so very rapid as to produce an appreciable convective velocity away from the surface, in turbulent gas flow the mechanisms of heat transfer to and solvent transfer away from the evaporating surface are virtually identical combinations of convective action with thermal conduction on the one hand and molecular diffusion on the other. This is reflected in useful correlations, like Colburn s, of the mass transfer coefficient with the more easily measured heat transfer coefficient in turbulent flow. It is also the reason that the now fairly extensive literature on the performance and design of driers focuses on heat transfer coefficients and heat delivery rates. [Pg.248]

Sherwood et al. (19Z5) report that transition from laminar to turbulent occurs in the Reynolds number range from 250 to 500. Although they do not report any correlations for the liquid mass-transfer coefficient in turbulent flow, Treybal (1980) reports the following correlation for a liquid film with constant surface concentration at a somewhat higher range of Reynolds numbers. [Pg.638]

Correlations for Mass Transfer Coefficients in Turbulent Flow... [Pg.211]

The situation is often encountered in which a fluid flows through a conduit having a noncircular cross section, such as an annulus. The heat-transfer coefficients for turbulent flow can be determined by using the same equations that apply to pipes and tubes if the pipe diameter D appearing in these equations is replaced by an equivalent diameter De. Best results are obtained if... [Pg.594]

As seen in the previous section, flow is considered to be laminar when Re < 2300 and turbulent when Re > 104. Transition flow occurs in the range of 2300 < Re < 104. Few correlations or formulas for computing the friction factor and heat transfer coefficient in transition flow are available. In this section, the formula developed by Bhatti and Shah [45] is presented to compute the friction factor. It follows ... [Pg.331]

The fully developed friction factor and heat transfer coefficients for turbulent flow in an asymmetrically heated rectangular duct have been reported by Rao [59]. In this investigation, the experimental region of the Reynolds number was from 104 to 5 x 104. [Pg.374]

Fig. 4-65. Effect of viscosity changes on die overall heat transfer coefficient under turbulent flow conditions in a stirred vessel... Fig. 4-65. Effect of viscosity changes on die overall heat transfer coefficient under turbulent flow conditions in a stirred vessel...
If the concentration of the liquid surface is not constant, there will be mass transfer and a mass-transfer resistance on the gas side also. In separation processes, the gas-phase resistance often controls (the gas-phase mass-transfer coefficient is often significandy smaller than the liquid-phase mass-transfer coefficient). For turbulent flow of the gas in a wetted wall tube, the following correlation was originally reported by Gilliland (see Sherwood et al.. 1975 or Wankat and Knaebel. 2008T... [Pg.639]

The heat-transfer coefficient for turbulent flow is somewhat greater for a pipe than for a smooth tube. This effect is much less than in fluid friction, and it is usually neglected in calculations. Also, for liquid metals that have Prandtl numbers 1, other correlations must be used to predict the heat-transfer coefficient. (See Section 4.5G.) For shapes of tubes other than circular, the equivalent diameter can be used as discussed in Section 4.5E. [Pg.239]

A considerable amount of experimental and theoretical work is available on the heat transfer coefficient for turbulent flow in channels. Through most of fhe correlations were developed based on circular pipe, with appropriate corrective factors, the correlations can be applied to various geometries. The heat transfer coefficients at the entrance region of the channel are higher. For nonmetallic fluids (Pr > 1) the laminar layer is very thin compared to the turbulent region, and the heat transfer coefficient is less sensitive to boundary conditions. For liquid metals (Pr < 0.4), conduction heat transfer is important and the boundary conditions have an impact on the heat transfer coefficient. For fully developed turbulent flow of nonmetallic fluid the heat transfer coefficient is expressed as ... [Pg.752]

For low values of the Reynolds number, such as 10, where sn eamline flow should certainly apply, the Nusselt number has a value of about 2, and a typical value of the average heat transfer coefficient is 10 ". For a Reynolds number of 104, where the gas is certainly in turbulent flow, the value of the Nusselt number is typically 20. Hence there is only a difference of a factor of ten in the heat transfer coefficient between tlrese two extreme cases. [Pg.278]

Hubbard and Lightfoot (HI la) earlier reported a Sc,/3 dependence on the basis of measurements in which the Schmidt number was varied over a very large range. The data did not exclude a lower Reynolds number exponent than 0.88, and reaffirmed the value of the classical Chilton-Colburn equation for practical purposes. Recent measurements on smooth transfer surfaces in turbulent channel flow by Dawson and Trass (D8) also firmly suggest a Sc13 dependence and no explicit dependence of k+ on the friction coefficient, with Sh thus depending on Re0,875. The extensive data of Landau... [Pg.270]

The value of the heat transfer coefficient of the gas is dependent on the rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of the gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are carried out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in the definition of this number when a gas is flowing along a tube is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in turbulent flow. For the flow... [Pg.277]


See other pages where Transfer Coefficients in Turbulent Flow is mentioned: [Pg.94]    [Pg.95]    [Pg.54]    [Pg.94]    [Pg.95]    [Pg.54]    [Pg.177]    [Pg.472]    [Pg.177]    [Pg.504]    [Pg.10]    [Pg.188]    [Pg.1418]    [Pg.497]    [Pg.29]    [Pg.743]    [Pg.177]    [Pg.70]    [Pg.90]    [Pg.152]    [Pg.421]    [Pg.296]    [Pg.315]    [Pg.334]    [Pg.338]    [Pg.813]    [Pg.855]    [Pg.1120]   


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