Heat Transfer Correlation Method

The thin-layer approximation fails because natural convective boundary layers are not thin. From the interferometric fringes in Fig. 4.2ft (which are essentially isotherms), the thermal boundary layer around a circular cylinder is seen to be nearly 30 percent of the cylinder diameter. For such thick boundary layers, curvature effects are important. Despite this failure, thin-layer solutions provide an important foundation for the development of correlation equations, as explained in the section on heat transfer correlation method. 

Equations are presented in this section for evaluating the heat transfer by natural convection from the external surfaces of bodies of various shapes. The correlation equations are of the form described in the section on the heat transfer correlation method, and the orientation of the surface is given by the surface angle defined in Fig. 4.4. Supporting experimental evidence for each such equation set is outlined after each equation tabulation. The correlations are in terms of Nu, Ra, and Pr, parameters that involve physical properties, a length scale, and a reference temperature difference. Rules for the evaluation of property values are provided in the nomenclature, and the relevant length scale and reference temperature difference are provided in a separate definition sketch for each problem. 

The length scales on which Nu and Ra are based, and values of the constants, are provided in Table 4.3a. The basis for these relations was discussed in the section on heat transfer correlation method. 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

The calculation procedure shown is based on Kern s method,1 with modifications to include the heat transfer correlations presented earlier... 

Items 1-4 determine the degree to which the radiation source and material load are thermally coupled and can be addressed with the heat transfer analysis methods outlined in Chap. 7 of this handbook. Items 5 and 6 may be quantified with an analysis, which takes into account the multimode heat transfer effects discussed elsewhere in this handbook. Because of the nonlinear nature of radiative heat transfer, few correlations exist that can be applied to relevant materials processing situations. 

The major part of the book deals with nonideal reaetors. Chapter 4 on pore diffusion plus reaetion ineludes a new method for analyzing laboratory data and has a more eomplete treatment of the effeets of eomplex kineties, particle shape, and pore structure than most other texts. Catalyst design to minimize pore diffusion effects is emphasized. In Chapter 5 heat transfer correlations for tanks, particles, and packed beds, are reviewed, and the conditions required for reactor stability are discussed. Examples of unstable systems are included. The effects of imperfect mixing in stirred tanks and partial mixing in pipeline reactors are discussed in Chapter 6 with examples from the literature. Recommendations for scaleup or scaledown are presented. 

In the Correlations tab are three menus. Unfortunately, there is no single best choice for the mass transfer correlation to use. We will first use the Chen and Chuang (1993) correlation and try others later. For the Heat transfer coefficient method, the Chilton and Colburn correlation is standard, and for the Interfacial area method, the Zuiderweg (1982) correlation is most commonly used. 

The comparisons given in Table 2 are obtained from simulation runs that use Sundaram and Froment s heat transfer correlation(24), five reaction models(22),and Friend and Adler s method for mixture... 

Transfer Coefficient. The design method described depends for its utiHty on the avadabiHty of mass- and heat-transfer coefficients. Typically, ky-a and /i -a are needed. These must be obtained from the standard correlations for mass and heat transfer, from data reported in the Hterature (23—30),... 

Example Buckingham Pi Method—Heat-Transfer Film Coefficient It is desired to determine a complete set of dimensionless groups with which to correlate experimental data on the film coefficient of heat transfer between the walls of a straight conduit with circular cross section and a fluid flowing in that conduit. The variables and the dimensional constant believed to be involved and their dimensions in the engineering system are given below ... 

The mathematical principles of convective heat transfer are complex and outside the scope of this section. The problems are often so complicated that theoretical handling is difficult, and full use is made of empirical correlation formulas. These formulas often use different variables depending on the research methods. Inaccuracy in defining material characteristics, experimental errors, and geometric deviations produce noticeable deviations between correlation formulas and practice. Near the validity boundaries of the equations, or in certain unfavorable cases, the errors can be excessive. 

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. 

Rohsenow, W. H., A Method of Correlating Heat Transfer Data for Surface Boiling of Liquids, Heat Transfer Div. ASME, Atlantic City, NJ. Meeting Nov. 25, (1951) Paper No. 51-A-llO. 

Using Tinker s approach, BELL(12, i22) has described a semi-analytical method, based on work at the University of Delaware, which allows for the effects of major bypass and leakage streams, and which is suitable for use with calculators. In this procedure, the heat transfer coefficient and the pressure drop are obtained from correlations for flow over ideal tube banks, applying correction factors to allow for the effects of leakage, bypassing and flow... 

Colburn, A.P. Trans. Am. Inst. Chem. Eng. 29 (1933) 174. A method of correlating forced convection heat transfer data and a comparison with fluid friction. 

Rousenow. W.M. Trans. Am. Soc. Mech. Ping. 74 (1952) 969. A method of correlating heat transfer data for surface boiling of liquids. 

Experimental results for fixed packed beds are very sensitive to the structure of the bed which may be strongly influenced by its method of formation. GUPTA and Thodos157 have studied both heat transfer and mass transfer in fixed beds and have shown that the results for both processes may be correlated by similar equations based on. / -factors (see Section 10.8.1). Re-arrangement of the terms in the mass transfer equation, permits the results for the Sherwood number (Sh1) to be expressed as a function of the Reynolds (Re,) and Schmidt numbers (Sc) ... 

Figure 5.47 shows a plot of the ratio of the experimental heat transfer coefficient obtained by Bao et al. (2000) divided by the predicted values of Chen (1966) and Gungor and Winterton (1986) for heat transfer to saturated flow boiling in tubes versus liquid Reynolds number. It can be seen that both methods provide reasonable predictions for Rcls > 500, but that both overpredict the heat transfer coefficient at lower values of Rols- For comparison it was assumed that the boiling term of these correlations is zero. 

Prodanovic V, Fraser D, Salcudean M (2002) On transition from partial to fuUy developed subcooled flow boiling. Int J Heat Mass Transfer 45 4727-4738 Qu W, Mudawar I (2003a) Measurement and prediction of pressure drop in two-phase micro-channel heat sinks. Int J Heat Mass Transfer 46 2737-2753 Qu W, Mudawar I (2003b) Flow boiling heat transfer in two-phase micro-channel heat sink. 1 Experimental investigation and assessment of correlation methods. Int J Heat Mass Transfer 46 2755-2771... 

Sedov LI (1993) Similarity and dimensional methods in mechanics, 10th edn. CRC, Boca Raton Shah MM (1982) Chart correlation for saturated boding heat transfer equation and further study. ASHRAE Trans 88 185-196... 

In the correlations used to predict heat-transfer coefficients, the physical properties are usually evaluated at the mean stream temperature. This is satisfactory when the temperature change is small, but can cause a significant error when the change in temperature is large. In these circumstances, a simple, and safe, procedure is to evaluate the heat-transfer coefficients at the stream inlet and outlet temperatures and use the lowest of the two values. Alternatively, the method suggested by Frank (1978) can be used in which equations 12.1 and 12.3 are combined ... 

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... 

In Bell s method the heat-transfer coefficient and pressure drop are estimated from correlations for flow over ideal tube-banks, and the effects of leakage, bypassing and flow in the window zone are allowed for by applying correction factors. 

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