Ideal tube bank heat transfer coefficients

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... 

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. 

The heat transfer coefficient for ideal cross flow over a tube bank is given as3 ... 

Select the appropriate heat-transfer coefficient equation. Heat-transfer coefficients for fluids flowing across ideal-tube banks may be calculated using the equation... 

Heat-transfer coefficient for cross flow over an ideal tube bank Fouling coefficient on outside of tube Heat-transfer coefficient in a plate heat exchanger Shell-side heat-transfer coefficient Heat transfer coefficient to vessel wall or coil Heat transfer factor defined by equation 12.14 Heat-transfer factor defined by equation 12.15 Friction factor... 

The heat transfer coefficient for an ideal cross-flow tube bank can be calculated using the heat transfer factors /f, given in Figure 12.33. Figure 12.33 has been adapted from a similar figure given by Mueller (1973). Mueller includes values for more tube... 

Calculate the shell-side heat-transfer coefficient for an ideal tube bank h. ... 

Accurate predictions of the shell-side heat transfer coefficient and pressure drop are difficult because of the complex geometry and resulting flow patterns. A number of correlations are available, none of which is as accurate as those above for the tube side. All are based on crossflow past an ideal tube bank, either staggered (triangular pitch pattern) or inline (square pitch pattern). Corrections are made for flow distortion due to baffles, leakage, and bypassing. From 1950 to 1963, values of h , the shell-side, convective heat transfer coefficient, were most usually predicted by the correlations of Donohue (1949) and Kern (1950), which are suitable for hand calculations. Both of these correlations are of the general Nusselt number form... 

The heat-transfer phenomena for forced convection over exterior surfaces are closely related to the nature of the flow. The heat transfer in flow over tube bundles depends largely on the flow pattern and the degree of turbulence, which in turn are functions of the velocity of the fluid and the size and arrangement of the tubes. The equations available for the calculation of heat transfer coefficients in flow over tube banks are based entirely on experimental data because the flow Is too complex to be treated analytically. Experiments have shown that, in flow over staggered tube banks, the transition from laminar to turbulent flow Is more gradual than in flow through a pipe, whereas for in-line tube bundles the transition phenomena resemble those observed in pipe flow. In either case the transition from laminar to turbulent flow begins at a Reynolds number based on the velocity in the minimum flow area of about 100, and the flow becomes fully turbulent at a Reynolds number of about 3,000. The equation below can be used to predict heat transfer for flow across ideal tube banks. 

The values of "a" for Equation 7.8 are for ideal tube banks with no bypassing or leakage. For well-built tube bundles fabricated to industry-wide accepted standards for clearances (discussed in Chapter 12), the heat transfer coefficients obtained using these values of "a" are normally multiplied by a factor of 0.7 to account for unavoidable bypassing and leakage. However, more precise results can be obtained by using correction factors for the actual conditions as given below. This method assumes that ... 

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