Heat transfer coefficient, correlations overall

The rate of heat-transfer q through the jacket or cod heat-transfer areaM is estimated from log mean temperature difference AT by = UAAT The overall heat-transfer coefficient U depends on thermal conductivity of metal, fouling factors, and heat-transfer coefficients on service and process sides. The process side heat-transfer coefficient depends on the mixing system design (17) and can be calculated from the correlations for turbines in Figure 35a. 

The final correlation for the overall boiling heat-transfer coefficient in pipes or channels (20) is a direct addition of the macroscopic (mac) and microscopic (mic) contributions to the coefficient ... 

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. 

Once a specific heat exchanger is chosen, the flow per tube is known, so it is possible to use the correlations of Chapter 2 to calculate a more precise overall heat transfer coefficient (U). An example of calculation of U is given in Chapter 5. 

From these correlations it is possible to calculate the film heat transfer coefficient and the pressure loss for laminar flow. This coefficient, combined with that of the metal and the calculated coefficient for the service fluid together with the fouling resistance, is then used to produce the overall coefficient. As with turbulent flow, an... 

Chapter 7 deals with the practical problems. It contains the results of the general hydrodynamical and thermal characteristics corresponding to laminar flows in micro-channels of different geometry. The overall correlations for drag and heat transfer coefficients in micro-channels at single- and two-phase flows, as well as data on physical properties of selected working fluids are presented. The correlation for boiling heat transfer is also considered. 

This section is concerned with the UA xtiT — Text) term in the energy balance for a stirred tank. The usual and simplest case is heat transfer from a jacket. Then A xt refers to the inside surface area of the tank that is jacketed on the outside and in contact with the fluid on the inside. The temperature difference, T - Text, is between the bulk fluid in the tank and the heat transfer medium in the jacket. The overall heat transfer coefficient includes the usual contributions from wall resistance and jacket-side coefficient, but the inside coefficient is normally limiting. A correlation applicable to turbine, paddle, and propeller agitators is... 

While it is possible to calculate the existing overall heat transfer coefficient from the operating data, it is not possible to calculate the individual film transfer coefficients. The individual film transfer coefficients can be combined in any number of ways to add up to an overall value of 285 W-m 2-K 1. However, the film transfer coefficients can be estimated from the correlations in Appendix C. Given that the tube-side correlations are much more reliable than the shell-side correlations, the best way to determine the individual coefficients is to calculate the coefficient for the tube-side and allocate the shell-side coefficient to add up to U = 285 W-m 2-K 1. Thus, to calculate the tube-side film transfer coefficient, KhT must first be determined. 

The correlation should be used with caution outside the range 0.6 < Tr < 0.8 and should not be used below a pressure of 0.3 bar. When dealing with a clean, nondegrading material, the process fouling coefficient should be increased to around 11,000 W m 2 K 1, but should be reduced to 1400 to 1900 W m 2 K 1 for material that has a tendency to polymerize17. If a shell-side coefficient of process fouling coefficient different from 5700 W m 2 K 1 is required, the corrected overall heat transfer coefficient can be calculated from17 ... 

The boiling film coefficient for a kettle reboiler can be estimated from the correlation for pool boiling. Equation 15.96 gives one such method due to Palen15. However, the correlation requires the heat flux to be known, and therefore the heat transfer area to be known. Hence the calculation will need to be iterative. An initial estimate of the overall heat transfer coefficient of 2000 W-m 2-K 1 gives ... 

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. 

U = the overall heat transfer coefficient, J m-2 s K or W m-2 KT 1, obtained experimentally or from an appropriate correlation A, = the area of the heating or cooling coil, m2 ... 

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. 

Correlations for friction factors and heat transfer coefficients are rated in HEDH. Some overall coefficients based on external bare tube surfaces are in Tables 8.11 and 8.12. For single passes in cross flow, temperature correction factors are represented by Figure 8.5(c) for example charts for multipass flow on the tube side are given in HEDH and by Kays and London (1984), for example. Preliminary estimates of air cooler surface requirements ram be made with the aid of Figures 8.9 and 8.10, which are applied in Example 8.9. 

Each correction factor is determined using a series of correlations and figures in Ref. E2 (pp. 553-569). The overall heat-transfer coefficient is recalculated from Equation 10.4. 

For plate-fin heat exchangers in single-phase flow, the heat transfer coefficients are related to the developed heat transfer surface, and the area ratio must be taken into account. As related to the projected surface, the overall heat transfer coefficient is very high. Heat transfer and pressure drop can be estimated from correlations (43 44), but these correlations give only an estimate of the performance, because local modification of the fin geometry will affect heat transfer and pressure drop. 

It is noted that most of the models and correlations that are developed are based on bubbling fluidization. However, most of them can be extended to the turbulent regime with reasonable error margins. The overall heat transfer coefficient in the turbulent regime is a result of two counteracting effects, the vigorous gas-solid movement, which enhances the heat transfer and the low particle concentration, which reduces the heat transfer. 

Heat transfer studies on fixed beds have almost invariably been made on tubes of large diameter by measuring radial temperature profiles (1). The correlations so obtained involve large extrapolations of tube diameter and are of questionable validity in the design of many industrial reactors, involving the use of narrow tubes. In such beds it is only possible to measure an axial temperature profile, usually that along the central axis (2), from which an overall heat transfer coefficient (U) can be determined. The overall heat transfer coefficient (U) can be then used in one--dimensional reactor models to obtain a preliminary impression of longitudinal product and temperature distributions. 

In discussing particle shape effects it seems sensible to compare overall heat transfer coefficients for different shapes relative to a common base,i.e. with regard to pressure drop/extem-al surface area for non-porous supports or pressure drop/solid volume for porous supports. Thus, Fig. 4 is constructed from the heat transfer correlations in Table II, together with pressure drop data collected over the packings at NTP in a 24 an diameter tube. 

The overall heat transfer coefficient U in Eqn. (3) is based on the measured temperature difference between the central axis of the bed and the coolant. It is derived by asymptotic matching of thermal fluxes between the one-dimensional (U) and two-dimensional (kr,eff kw,eff) continuum models of heat transfer. Existing correlations are employed to describe the underlying heat transfer processes with the exception of Eqn. (7), which is a new result for the apparent solid phase conductivity (k g), including the effect of the tube wall. Its derivation is based on an analysis of stagnant bed conductivity data (8, 9), accounting for "central-core" and wall thermal resistances. 

Forced convection heat transfer is probably the most common mode in the process industries. Forced flows may be internal or external. This subsection briefly introduces correlations for estimating heat-transfer coefficients for flows in tubes and ducts flows across plates, cylinders, and spheres flows through tube banks and packed beds heat transfer to nonevaporating falling films and rotating surfaces. Section 11 introduces several types of heat exchangers, design procedures, overall heat-transfer coefficients, and mean temperature differences. 

Selecting an approximate overall heat-transfer coefficient is a problem because of insufficient data. Although there are correlations available for calculating the individual heat-transfer coefficients and hence the overall heat-transfer coefficients, at the preliminary stage of the process design, we try to avoid detailed calculations. The best we can do is to select a coefficient that best matches the conditions in the CSTR. Because the jacket liquid is water, and the reactor liquid is a dilute aqueous solution, we find that from Table 7.6, Uj varies from 60 to 110 Btu/h-ft -°F (341 to 625 wW-°F) The average value is 85 Btu/h fP "F (483 W/m -K). From Equation 7.4.9, we find that the standard 8000 gal (30.3 m ) reactor has a jacket area of 466 tf (43.3 m ). From Equation 7.4.7, the heat that can be transferred to the jacket,... 

Heat exchangers are complicated devices, and the results obtained with the simplifled approaches presented above should be used with care. For example, we assumed that the overall heat transfer coefficient V is constant throughout the heat exchanger and tliat the convection heat transfer coefficients can he predicted using the convection correlations. However, it should be kept in mind that the uncertainty in the predicted value of U can exceed 30 percent. Thus, it is natural to tend to overdesign the hear exchangers in order to avoid unpleasant surprises. 

Correlations for friction factors and heat transfer coefficients are cited in HEDH. Some overall coefficients based on external bare tube surfaces are in Tables 8.11 and 8.12. For single passes in cross flow, temperature correction factors are represented by... 

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