7. Correlations of j and f factors in offset strip fin heat exchangers

The reliable prediction of the heat transfer and pressure drop in offset strip fin is vital and very hard to achieve. Various correlations have been developed by numerous researchers in decades to succeed and fulfill this requirement. Since most of the offset strip fin studies focus to reveal the effect of the geometrical parameters, the large amount of data produced in the researches belong to parametric investigations. Most of the j and f correlations that could be found in literature bases on geometrical parameters as given in Table 3. The nondimensional parameters used in the correlations are, α=s/h, δ= t/l and γ=t/s where length is l, height is h, transverse spacing s and thickness t as noted before.

A particular comparison with respect to the Kays and London's experimental study [5] is taken to the following to see the differences between the approaches for the same particular problem. In the given comparison, the correlations pertain to Wieting [30], Joshi and Webb [4] and Muzychka et al. [31] are examined for a particular fin structure (uninterrupted fin length is

Figure 14. Comparison of j and f correlations with experimental data of Kays and London [4].

1/8 inch—number of fins per inch is 16.00 and double sandwiched fin structure) from Kays London experiments [3]. In Figure 14, it could be seen that, all three correlations, the most cited correlations in literature for this fin type can predict the j and f values in a good agreement, but they are not sufficient to present the transition between laminar and turbulent.

to reveal the effect of the geometrical parameters, the large amount of data produced in the researches belong to parametric investigations. Most of the j and f correlations that could be found in literature bases on geometrical parameters as given in Table 3. The nondimensional parameters used in the correlations are, α=s/h, δ= t/l and γ=t/s where length is l, height is h,

A particular comparison with respect to the Kays and London's experimental study [5] is taken to the following to see the differences between the approaches for the same particular problem. In the given comparison, the correlations pertain to Wieting [30], Joshi and Webb [4] and Muzychka et al. [31] are examined for a particular fin structure (uninterrupted fin length is

Figure 14. Comparison of j and f correlations with experimental data of Kays and London [4].

transverse spacing s and thickness t as noted before.

50 Heat Exchangers– Advanced Features and Applications

That inadequacy leads the researchers to find out a correlation, which can meet and correspond to all regimes at once. Manglik and Bergles tried to meet this with the correlation given in Table 3, which is claimed as giving a continuous solution for the flow regimes turning from laminar to turbulent. The calculations for the same, Kays and London problem (fin structure (1/8—16.00 D)), is also reported in the study (Figure 15).

Figure 15. Comparison of correlation with experimental data of Kays and London [4].

Most of the correlations that could be met in literature are derived from the experimental studies, but unlike the common approach, some researchers try to extract the correlations from their numerical experience such as Kim et al. [2]. In the study, 39 different models are analyzed numerically by commercial CFD software where different geometric parameters and varying fluids are tried. It is also underlined that the earlier correlations are not sufficient to estimate the Colburn j-factor and friction factor when the blockage ratio (β) increases (β =12–27%). So there is a demand to find the answer of that question. The analysis are carried out by different turbulent models and the most suitable one is decided by comparing the findings with the most preferred correlations in literature [3, 4] and then the remaining calculations are performed to obtain a new correlation to attain the best fitting one not only for different fluids but also for different blockage ratios. The correlations are grouped as regarding to their blockage ratio (β). Since the blockage ratios below 20% are not efficient for offset strip fins and very high pressure drop could be seen beyond 35%, the blockage range investigated in the study is taken as 20–35%, the Colburn j-factor and friction f-factor can be correlated as in Table 3.

As mentioned earlier, the blockage ratio is not the only objective of the study [2], but the Prandtl effect is also observed by the usage of different fluids such as water; the correlations according to Prandtl can also be found as in the lower part of Table 3. These correlations are compared by the Manglik and Bergles for the blockage ratio of 12 and 27% in

Figure 16. Comparison of Kim et al. correlation and Manglik and Bergles correlation for the blockage ratio of β = 12% and β = 27% for friction factor [2].

Figure 17. Comparison of Kim et al. correlation and Manglik and Bergles correlation for the blockage ratio of β = 12% and β = 27% for Colburn factor [2].

Figures 16 and 17. As it could be seen, the M&B correlation starts to overestimate when the blockage ratio is over 20%.
