Heat-transfer coefficient prediction

A presence of interfacial waves increases the heat transfer coefficient predicted by Nusselt theory by a factor up to 1.1. An underprediction of a heat transfer coefficient by the Nusselt theory is more pronounced for larger condensate flow rates. For laminar condensation having both a wave-free and wavy portion of the condensate film, the correlation based on the work of Kutateladze as reported in [81] (the fourth correlation from the top of Table 17.23) can be used as long as the flow is laminar. 

In this chapter, a review of the literature dealing with the aforementioned topics is presented. Additionally, flow pattern, pressure drop, heat transfer coefficient and critical heat flux predictive methods are presented. The main findings of a recently published study by Ribatski et al. [2] evaluating pressure drop and heat transfer coefficient predictive methods by comparing their results against a broad database from the literature are also discussed. At the end of the chapter, the current leading prediction methods for two-phase flow and boiling in microchannels are presented. The interested reader can also refer to a later referenced website by Thome [55], where numerous videos of two-phase flows in microchannels are available. 

The mechanism of temperature development in both models is shown in Fig. 6.4. The heat transfer coefficient in the Ganzeveld model is slightly smaller than the heat transfer coefficient predicted by the Janeschitz-Kriegl model, and it is also more sensitive to the actual size of the flight gap. No experimental evidence exists to establish which equation is more accurate for describing the actual heat transfer. Typical experimental values for heat transfer coefficients at the barrel wall in extruders are between 400 and 600W/m K. 

Heat transfer experiments and material research studies have been carried out at Kyushu University, IAEA, the University of Tokyo and elsewhere. Comparison of heat transfer coefficients predicted by different correlations is shown in Fig. 1.60. Accuracy above 500°C is important for the calculation of MCST. Calculated MCSTs with different correlations are compared in Table 1.16 [122]. The largest difference is 44°C. Current heat transfer correlations were developed based on experiments using smooth circular tubes. Experiments on fuel bundle geometry are necessary. The effect of grid spacers on the heat transfer correlation should be included in the prediction of MCST. The correlation of downward flow is necessary for the design. Downward flow is adopted in the low temperature region below the pseudo-critical temperature. 

These small positive and negative errors partially cancel each other. The result is that capital cost targets predicted by the methods described in this chapter are usually within 5 percent of the final design, providing heat transfer coefficients vary by less than one order of magnitude. If heat transfer coefficients vary by more than one order of magnitude, then a more sophisticated approach can sometimes be justified. ... 

The heat-transfer coefficient depends on particle size distribution, bed voidage, tube size, etc. Thus a universal correlation to predict heat-transfer coefficients is not available. However, the correlation of Andeen and Ghcksman (22) is adequate for approximate predictions ... 

Fundamental models correctly predict that for Group A particles, the conductive heat transfer is much greater than the convective heat transfer. For Group B and D particles, the gas convective heat transfer predominates as the particle surface area decreases. Figure 11 demonstrates how heat transfer varies with pressure and velocity for the different types of particles (23). As superficial velocity increases, there is a sudden jump in the heat-transfer coefficient as gas velocity exceeds and the bed becomes fluidized. 

The effective thermal conductivity of a Hquid—soHd suspension has been reported to be (46) larger than that of a pure Hquid. The phenomenon was attributed to the microconvection around soHd particles, resulting in an increased convective heat-transfer coefficient. For example, a 30-fold increase in the effective thermal conductivity and a 10-fold increase in the heat-transfer coefficient were predicted for a 30% suspension of 1-mm particles in a 10-mm diameter pipe at an average velocity of 10 m/s (45). 

I0-38Z ) is solved to give the temperature distribution from which the heat-transfer coefficient may be determined. The major difficulties in solving Eq. (5-38Z ) are in accurately defining the thickness of the various flow layers (laminar sublayer and buffer layer) and in obtaining a suitable relationship for prediction of the eddy diffusivities. For assistance in predicting eddy diffusivities, see Reichardt (NACA Tech. Memo 1408, 1957) and Strunk and Chao [Am. ln.st. Chem. Eng. J., 10, 269(1964)]. 

Annuli Approximate heat-transfer coefficients for laminar flow in annuh may be predicted by the equation of Chen, Hawkins, and Sol-berg [Tron.s. Am. Soc. Mech. Eng., 68, 99 (1946)] ... 

In general, the average heat-transfer coefficient on immersed bodies is predicted by... 

Transition Region Turbulent-flow equations for predicting heat transfer coefficients are usually vahd only at Reynolds numbers greater than 10,000. The transition region lies in the range 2000 < < 10,000. 

Particle-to-fluid heat-transfer coefficients in gas fluidized beds are predicted by the relation (Zenz and Othmer, op. cit.)... 

A pseudo-convective heat-transfer operation is one in which the heating gas (generally air) is passed over a bed of solids. Its nse is almost exchisively limited to drying operations (see Sec. 12, tray and shelf dryers). The operation, sometimes termed direct, is more aldu to the coudnctive mechanism. For this operation, Tsao and Wheelock [Chem. Eng., 74(13), 201 (1967)] predict the heat-transfer coefficient when radiative and conductive effects are absent by... 

The coefficient h is also used to predict (in the constant-rate period) the total overall air-to-sohds heat-transfer coefficient by... 

One manner in which size may be computed, for estimating purposes, is by employing a volumetric heat-transfer concept as used for rotary diyers. It it is assumed that contacting efficiency is in the same order as that provided by efficient lifters in a rotaiy dryer and that the velocity difference between gas and solids controls, Eq. (12-52) may be employed to estimate a volumetric heat-transfer coefficient. By assuming a duct diameter of 0.3 m (D) and a gas velocity of 23 m/s, if the solids velocity is taken as 80 percent of this speed, the velocity difference between the two would be 4.6 m/s. If the exit gas has a density of 1 kg/m, the relative mass flow rate of the gas G becomes 4.8 kg/(s m the volumetric heat-transfer coefficient is 2235 J/(m s K). This is not far different from many coefficients found in commercial installations however, it is usually not possible to predict accurately the acdual difference in velocity between gas and soRds. Furthermore, the coefficient is influenced by the sohds-to-gas loading and particle size, which control the total solids surface exposed to the gas. Therefore, the figure given is only an approximation. 

The following equation can be used to predict heat transfer coefficients from coils to tank walls in agitated tanks. 

The preceding equations are reported to predict actual heat transfer coefficients only about 15% lower than experimental values—the difference can be attributed to the rippling of the film and early turbulence and drainage instabilities on the bottom side of the tube. ... 

Sinek and Young present a design procedure for predicting liquid-side falling film heat transfer coefficients within 20% and overall coefficients within 10%. 

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. 

As discussed in Section 9.4.4, the prediction of pressure drop, and indeed heat transfer coefficients, in the shell is very difficult due to the complex nature of the flow pattern in the segmentally baffled unit. Whilst the baffles are intended to direct fluid across the tubes, the actual flow is a combination of cross-flow between the baffles and axial or parallel flow in the baffle windows as shown in Figure 9.79, although even this does not represent the actual flow pattern because of leakage through the clearances necessary for the fabrication and assembly of the unit. This more realistic flow pattern is shown in Figure 9.80 which is based on the work of TINKER 116) who identifies the various streams in the shell as follows ... 

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