Correlations of heat transfer coefficients

Heating or cooling of process fluids in a batch-operated vessel is common in the chemical process industries. The process is unsteady state in nature because the heat flow and/or the temperature vary with time at a fixed point. The time required for the heat transfer can be modified, by increasing the agitation of the batch fluid, the rate of circulation of the heat transfer medium in a jacket and/or coil, or the heat transfer area. Bondy and Lippa [45] and Dream [46] have compiled a collection of correlations of heat transfer coefficients in agitated vessels. Batch processes are sometimes disadvantageous because ... 

Other useful correlations of heat transfer coefficients in packed beds have been proposed. Among these is a simple relation of Calderbank and Pogorski (104)... 

McAdams el al. (Ml), 1940 Correlation of heat transfer coefficients in falling-film heaters, N e = 225-15,000. 

R. Pfeffer, S. Rossetti, and S. Lieblein, Analysis and Correlation of Heat Transfer Coefficient and Friction Factor Data for Dilute Gas-Solid Suspensions, NASA TN D-3603, NASA, Cleveland, OH, 1966. 

Suh IS, Deckwer WD. Unified correlation of heat transfer coefficients in three-phase fluidized beds. Chem Eng Sci 44 1455-1458, 1989. 

Four typical correlations of heat transfer coefficient are applied to SPRAT-F in order to investigate the influence of heat transfer correlations on the MCST. The results are summarized in Table 7.38. The correlation proposed by Watts and Chou [33] gives the highest MCST in all the channels at both BOEC and EOEC. 

Some common correlations of heat transfer coefficients are reported in Table 20.4-3. These all refer to heat transfer across a solid-fluid interface because other situations either are rare or are described in different terms. Like the mass transfer correlations in Section 8.3, these are best presented in terms of dimensionless groups. The two most... 

Fig. 6.32 Comparison of heat transfer coefficient data for R-134s and water with predictions based on Lee and Mudawar correlation. Reprinted from Lee and Mudawar (2005b) with permission...

Because of their proximity to the wall, anchor agitators are more effective in maintaining heat transfer coefficients to higher viscosities. Relatively high torques and larger gear reducers are required, however. Studies by Uhl and Voznick ( ) correlated the heat transfer coefficient in a manner similar to that used with turbine agitators ... 

At the conceptual stage for heat exchanger network synthesis, the calculation of heat transfer coefficient and pressure drop should depend as little as possible on the detailed geometry. Simple models will be developed in which heat transfer coefficient and pressure drop are both related to velocity1. It is thus possible to derive a correlation between the heat transfer coefficient, pressure drop and the surface area by using velocity as a bridge between the two1. 

Correlations for heat transfer coefficient between a single sphere and surrounding gas have been proposed by many researchers (Table 5.2), for example, Whitaker,1584 and Ranz and Marshall,15051 among others. The correlation recommended by Whitaker is accurate to within 30% for the range of parameter values listed. All properties except jus should be evaluated at Tm. For freely falling liquid droplets, the Ranz-Marshall correlation 505 is often used. The correlations may be applied to mass transfer processes simply by replacing Nu and Pr with Sh and Sc, respectively, where Sh and Sc are the Sherwood number and Schmidt number, respectively. Modifications to the Ranz-Marshall correlation have been made by researchers to account... 

Table 5.2. Correlations for Heat Transfer Coefficient of a Single Sphere in Gas...

This second method does not lend itself to the development of quantitative correlations which are based solely on true physical properties of the fluids and which, therefore, can be measured in the laboratory. The prediction of heat transfer coefficients for a new suspension, for example, might require pilot-plant-scale turbulent-flow viscosity measurements, which could just as easily be extended to include experimental measurement of the desired heat transfer coefficient directly. These remarks may best be summarized by saying that both types of measurements would have been desirable in some of the research work, in order to compare the results. For a significant number of suspensions (four) this has been done by Miller (M13), who found no difference between laboratory viscosities measured with a rotational viscometer and those obtained from turbulent-flow pressure-drop measurements, assuming, for suspensions, the validity of the conventional friction-factor—Reynolds-number plot.11 It is accordingly concluded here that use of either type of measurement is satisfactory use of a viscometer such as that described by Orr (05) is recommended on the basis that fundamental fluid properties are more readily determined under laminar-flow conditions, and a means is provided whereby heat transfer characteristics of a new suspension may be predicted without pilot-plant-scale studies. 

Most unfortunately, an incorrect correlation for heat-transfer coefficients for surface condensers has become widely disseminated in several books devoted to heat transfer. This correlation predicts heat-transfer coefficients, for clean condensers, of about 650, when the water-side velocity is about 6 ft/s. Use of this correlation has led to some extremely serious problems, with which your author is intimately acquainted. 

As noted, most of the heat transfer models and correlations for gas-solid fluidization systems were originally developed for dense-phase fluidized beds (see Chapter 9). In the following, the behavior of heat transfer coefficients between the suspension (or bed) and the particle, between the suspension (or bed) and the gas, and between the suspension (or bed) and the wall or heat transfer surface are discussed. 

Empirical dimensionless group correlations have been used in the scale-up process. In particular, the correlation for the inside film heat transfer coefficient for agitated, jacketed vessels has been employed for the scale-up to a larger vessel. Reaction calorimeters are often used to give some indication of heat transfer coefficients compared to water in the same unit. Correlation for plant heat transfer is of the general form... 

Convection is the transfer of energy by conduction and radiation in moving, fluid media. The motion of the fluid is an essential part of convective heat transfer. A key step in calculating the rate of heat transfer by convection is the calculation of the heat-transfer coefficient. This section focuses on the estimation of heat-transfer coefficients for natural and forced convection. The conservation equations for mass, momentum, and energy, as presented in Sec. 6, can be used to calculate the rate of convective heat transfer. Our approach in this section is to rely on correlations. 

To predict the radial profile of heat transfer coefficient in fast fluidized beds, an empirical correlation has been proposed by Bi et al. (1989) in dimensionless form as follows ... 

Heat-transfer coefficient in condensation Mean condensation heat-transfer coefficient for a single tube Heat-transfer coefficient for condensation on a horizontal tube bundle Mean condensation heat-transfer coefficient for a tube in a row of tubes Heat-transfer coefficient for condensation on a vertical tube Condensation coefficient from Boko-Kruzhilin correlation Condensation heat transfer coefficient for stratified flow in tubes Local condensing film coefficient, partial condenser Convective boiling-heat transfer coefficient... 

Figure 17.37. Some measured and predicted values of heat transfer coefficients in fluidized beds. 1 Btu/hr(sgft)(°F) = 4.88 kcal/(hr)(m )(°C) = 5.678 W/(m )(°C). (a) C o mp arisen of correlations for heat transfer from silica sand with particle size 0.15 mm dia nuiaized in air. Conmtions are identified in Table 17.19 Leva, 1959). (b) Wall heat transfer coefficients as function of the superficial fluid velocity, data of Varygin and Martyushin. Particle sizes in microns (1) ferrosilicon, i 82.5 (2) hematite, d = 173 (3) Carborundum, d = 137 (4) quartz sand, d = 140 (5) quartz sand, d = 198 (6) quartz sand, d = 216 (7) quartz sand, d = 428 (8) quartz sand, d = 51.5 (9) quartz sand, d = 650 (10) quartz sand, d = 1110 (11) glass spheres, d= 1160. Zabrqdskystal, 1976,Fig. 10.17). (c) Effect of air velocity and particle physical properties on heat transfer between a fluidized bed and a submerged coil. Mean particle diameter 0.38 mm (I) BAV catalyst (II) iron-chromium catalyst (III) silica gel (IV) quartz (V) marble Zabrodsky et at, 1976, Fig. 10.20).

Most of the present data points belong to the heat flux dependent regime so that it has been possible to correlate the heat transfer coefficient in this region with m, q and x. Finally, the following expressions were obtained. For T>h = 2 mm and Bo > 4.3 lO, ... 

Most of the correlations were taken from Penney (1983) and from tables 5 and 6 in Fasano et al., (1994) for the HE-3 impeller and the bottom head. The correlation for heat transfer coefficients for helical ribbon impellers was taken from Ishibashi et al. (1979). The correlations given by Penney (1983) (p. 879) use the same sources. 

TABLE 10.2. Summary of Heat Transfer Coefficient Correlations for Agitated Vessels... 

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