The Kern Method

The tube-side heat-transfer coefficient may be calculated in two ways. The first uses the Dittus-Boelter equation for heat-transfer in a turbulent environment. This equation is given below. 

This correlation is widely accepted. All the variables relate to the fluid properties inside the tubes. As a check a second correlation recommended by Kern is used. It employs the heat-transfer factor (jh) which is a function of Reynolds number. This equation is shown below. 

The variables shown are consistent with Equation 10.1. To obtain a conservative design, the lower value obtained from using these two equations will be used in further design calculations. 

The shell-side heat-transfer coefficient in the Kern method is calculated using Equation 10.2. An equivalent diameter is calculated which is representative of the shell-side fluid passage geometry. Equation 10.2 therefore becomes  

In Equation 10.3 all variables relate to the properties of the shell-side fluid. 

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This compares to assumed value of 0.001 + 0.001 = 0.002 The Kern method is usually easier to handle for pressure systems than for vacuum systems. The recirculation ratio is higher and, therefore, requires more trials to narrow-in on a reasonable value for the low pressure systems. The omission of two-phase flow in pressure drop analysis may be a serious problem in the low pressure system, because a ratio on the high side may result, causing a high hj value. In general, however, for systems from atmospheric pressure and above, the method usually gives conservative results when used within Kern s limitations. 

The design calculations highlighted the shortcomings of the Kern method of exchanger design. The Kern method fails to account for shell-side inefficiencies such as bypassing, leakage, crossflow losses, and window losses. This leads to a marked overestimate of the shell-side heat-transfer coefficient and shell-side pressure drop. The Bell method is recommended to correct these deficiencies. 

The Kern method is inaccurate for calculating the shell-side heat-transfer coefficient and shell-side pressure drop (Ref. E2, p. 545). Kern makes no account of the effect of bypss and leakage in the shell-fluid passage. For these reasons the Bell Method (Ref. E9) is employed to serve as a check on the preliminary design. 

The other parameter also needing revision was the shell-side pressure drop. This was reduced from 50 kPa (Kern method) to around 6 kPa. The Kern method is subject to overestimates of the pressure drop for the reasons already discussed. 

H.4 Tube-side Heat-transfer Coefficient (The Kern method) 314 H.5 Shell-side Heat-transfer Coefficient (The Kern method) 315 H.6 Overall Heat-transfer Coefficient 316... 

H.7 Tube-side Pressure Drop (The Kern Method) 317... 

H.4 Tube-side Heat-transfer Coefficient (The Kern Method)... 

This design based upon the Kern method appears to be quite adequate, on the basis of the results obtained. 

This value is obviously much lower than that calculated by the Kern method. This means that the previously calculated value for the overall heat-transfer coefficient must also be revised. 

A simpler method due to Kem (1950, pp. 147-152) nominally considers only the drop across the tube banks, but actually takes account of the added pressure drop through baffle windows by employing a higher than normal friction factor to evaluate pressure drop across the tube banks. Example 8.8 employs this procedure. According to Taborek (HEDH, 1983, 3.3.2), the Kern predictions usually are high, and therefore considered safe, by a factor as high as 2, except in laminar flow where the results are uncertain. In the case worked out by Ganapathy (1982, pp. 292-302), however, the Bell and Kem results are essentially the same. 

If this 33% reduction in the overall heat-transfer coefficient and the 90% reduction in pressure drop had not been discovered, this would have caused a significant underestimate in the design to occur. This example should therefore serve to highlight the need for a more rigorous design approach to shell-side evaluation than that proposed by Kern. The Bell method proved quite adequate in this regard. 

C- and 0- tracer methods m and flow and relaxation methods . (Other unpublished work has been quoted .) The references chosen are merely illustrative of the overlapping chronological sequence. The subject has been reviewed several times literature prior to 1958 is analyzed in entertaining fashion by Kern . Probably the major sources of discrepancy between the results arise from the experimental errors of the various methods. Table 4 lists rate coefficients, which appear to be the best available for the main reactions as they have been envisaged. An attempt has been made to explain the most discrepant study . Reaction (1)... 

The cases of multipass exchangers with liquid contimionsly added to the tank are covered by Kern, as cited earlier. An alternative method for all mnltipass-exchanger gases, including those presented as well as cases with two or more shells in series, is as follows ... 

The first series of soluble oligo(/ ara-phenylene)s OPVs 24 were generated by Kern and Wirth [48] and shortly after by Heitz and Ulrich [49]. They introduced alkyl substituents (methyls) in each repeat unit and synthesized oligomers 24 up to the hexamer. Various synthetic methods, like the copper-catalyzed Ullmann coupling, the copper-catalyzed condensation of lithium aryls, and the twofold addition of organomelallic species to cyclohexane-1,4-dione, have been thereby investigated. 

It is shown in Section 9.9.5 that, with the existence of various bypass and leakage streams in practical heat exchangers, the flow patterns of the shell-side fluid, as shown in Figure 9.79, are complex in the extreme and far removed from the idealised cross-flow situation discussed in Section 9.4.4. One simple way of using the equations for cross-flow presented in Section 9.4.4, however, is to multiply the shell-side coefficient obtained from these equations by the factor 0.6 in order to obtain at least an estimate of the shell-side coefficient in a practical situation. The pioneering work of Kern(28) and DoNOHUE(lll who used correlations based on the total stream flow and empirical methods to allow for the performance of real exchangers compared with that for cross-flow over ideal tube banks, went much further and. 

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