Heat transfer coefficients empirical correlations

Likewise, the microscopic heat-transfer term takes accepted empirical correlations for pure-component pool boiling and adds corrections for mass-transfer and convection effects on the driving forces present in pool boiling. In addition to dependence on the usual physical properties, the extent of superheat, the saturation pressure change related to the superheat, and a suppression factor relating mixture behavior to equivalent pure-component heat-transfer coefficients are correlating functions. 

Mist-cooling heat transfer characteristics have been reviewed by Nishio and Ohkubo [146], and an attempt has been made to correlate existing experimental data. The mist-cooling convective heat transfer coefficient is correlated in terms of relevant flow parameters such as droplet diameter d, droplet velocity Vd, and the volume flux of the droplets V by the empirical equation... 

Convective Heat Transfer. The simplest correlations for the convective heat transfer coefficient empirically relate he to the solids concentration, expressed in terms of the mixture density for the gas/ solid medium in the bed (pb),... 

The axial profile of the hot-channel cladding surface temperature is next calculated by assuming a surface heat flux and employing empirical correlations for the surface heat transfer coefficient. The correlation Nu = 5 + 0.025(Pe) as developed for long tubes is often recommended. For purposes of fuel assembly design, this correlation appears conservative on the basis of data obtained by Dwyer and Kalish (7) for parallel flow through an equilateral-triangular array of rods. 

Results of diying tests can be correlated empirically in terms of overall heat-transfer coefficient or length of a transfer unit as a function of operating variables. The former is generally apphcable to all types of dryers, while the latter applies only in the case of continuous diyers. The relationship between these quantities is as follows. 

This method for vertical thermosiphon reboilers is based on semi-empirical correlations of experimental data and is stated to predict heat transfer coefficients 30 percent, which is about the same range of accuracy for most boiling coefficient data. The advantage of this method is that it has had significant design experience in the industry to support it. It is also adaptable to other types of reboilers used in the industry. See Figures 10-110 and 10-111. 

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. 

The complex flow pattern on the shell-side, and the great number of variables involved, make it difficult to predict the shell-side coefficient and pressure drop with complete assurance. In methods used for the design of exchangers prior to about 1960 no attempt was made to account for the leakage and bypass streams. Correlations were based on the total stream flow, and empirical methods were used to account for the performance of real exchangers compared with that for cross flow over ideal tube banks. Typical of these bulk-flow methods are those of Kern (1950) and Donohue (1955). Reliable predictions can only be achieved by comprehensive analysis of the contribution to heat transfer and pressure drop made by the individual streams shown in Figure 12.26. Tinker (1951, 1958) published the first detailed stream-analysis method for predicting shell-side heat-transfer coefficients and pressure drop, and the methods subsequently developed... 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

With the above functions and empirical correlations, it becomes possible to calculate the overall convective heat transfer coefficient hc by Eqs. (16, 4, and 22-24). Figure 26 shows a plot presented by Lints and Glicksman which compares predictions by this method with experimental data from several different sources. Reasonably good agreement is obtained over a range of bed densities corresponding to approximately 0.5 to 3% volumetric solid concentration. 

For practical purposes, heat-transfer engineers often use empirical or semi-empirical correlations to predict h values. These formulations are usually based on the dimensionless numbers described before. In this case, the appropriate formulation should be used to prevent significant errors. If dimensionless correlations are applicable under conditions of gas extraction, then heat-transfer coefficients can be determined from these correlations and the influence of parameter variations may be derived also from them. 

Nusselt Number Empirical correlations can be obtained for a particular size of tube diameter and particular flow conditions. To generalize such results and to apply the correlations to different sizes of equipment and different flow conditions, the heat-transfer coefficient, hy is traditionally nondimensionalized by the use of the Nusselt number, Nuy named after Wilhelm Nusselt,... 

Heat transfer coefficients are empirical data and derived correlations. They are in the form of overall coefficients U for frequently occurring operations, or as individual film coefficients and fouling factors. 

The bed-to-surface heat transfer coefficient may vary with the radial position in the bed. Wender and Cooper (1958) correlated the data of coefficients for heat transfer to immersed vertical tubes and proposed the following empirical correlation for 0.01 < Rep < 100... 

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... 

The similarities between the governing equations for heat, mass, and momentum transfer suggest that empirical correlations for the mass-transfer coefficient would be similar to those for the heat-transfer coefficient. This turns out to be the case, and some of the empirical relations for mass-transfer coefficients are presented below. Gilliland 14] presented the equation... 

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 ... 

The parameter C is directly related to the solids concentration of the bed. The results deduced from the heat transfer coefficients show that the value of the parameter C increases with increasing solids concentration of the bed, but it is almost independent of gas velocity, as shown in Fig. 23. The following empirical correlation (Bai, 1991) is proposed for the calculation of the parameter C ... 

Flows across cylinders and spheres, in general, involve flow separation, which is difficult to handle analytically. Therefore, such flows must be studied experimentally or numerically. Indeed, flow across cylinders and spheres has been studied experimentally by numerous investigators, and several empirical correlations have been developed for (he heat transfer coefficient. 

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