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Energies 2022, 15, 1316 Figure 17. Comparison between 1 mm and 2 mm thick helical fins, TRINI test rig, 146 μm particles. The results represent the mean values between the two tubes in the respective configuration. Clearly, the 2 mm thick fins show higher HTCs in general and a m1o4roef 2s2table net HTC than the 1 mm thick fins, which is not surprising given the lower fin efficiency of thinner fins [18] (pp. 1273–1274). This is the only graph where a first order polynomial was used for the regression analysis. The results of this experiment are inconsistent with the previous results (the gross heat transfer coefficient decreases with increasing degree of fluidization) and show a much greater variability. It is believed that the small distance between the fins caused local disturbances in the sand flow, leading to bad results. The results of this experiment are therefore not taken into account. Finally, Figure 19 shows the comparison between the best performing finned tubes (9/2) and plain tubes. Fiigguurere191.9C.oCmopmarpisaonribseotnwbeentwpleaiennapndlahienliacanlldy hfinenliecdaltulybefsin, pnitecdh 9tumbmes, ,thpiictkcnhes9s m2 mm,,tThRicINknI ess 2 m tesst trirgi,g1,4164μ6mμpmartpicalerst.icles. The results of the last fin configuration with a fin spacing of 6 mm and a fin thickness Finally, Figure 19 shows the comparison between the best performing finned tubes (o9f/12)mamndaprelasinhotuwbnesi.n Figure 18. Energies 2022, 15, x FOR PEER REVIEW Figure 18. Results of helically finned tubes, pitch 6 mm, fin thickness 1 mm, TRINI test rig, 146 μm Figure 18. Results of helically finned tubes, pitch 6 mm, fin thickness 1 mm, TRINI test rig, 146 μm particles. Indices 1 and 2 refer to the different heated tubes. particles. Indices 1 and 2 refer to the different heated tubes. At the most promising degree of fluidization of 4, the finned tubes show a (virtual) At the most promising degree of fluidization of 4, the finned tubes show a HTC about 3.5 times greater than that of the plain tubes. Given that the area multiplier of HTC about 3.5 times greater than that of the plain tubes. Given that the area mul the 9/2 fin configuration is 4.31 (see Table 1), the effective fin efficiency is about 81%. the 9/2 fin configuration is 4.31 (see Table 1), the effective fin efficiency is about 8 4. Discussion As mentioned in the Introduction, several correlations for predicting the heat transfer 4. Discussion between an immersed surface and the surrounding fluidized bed exist, but none of them As mentioned in the Introduction, several correlations for predicting the heat consider finned tubes or an imposed horizontal mass flow. Therefore, only the plain tube results of the individual test rigs may be compared to these correlations, for which three between an immersed surface and the surrounding fluidized bed exist, but none were chosen: consider finned tubes or an imposed horizontal mass flow. Therefore, only the pl results of the individual test rigs may be compared to these correlations, for whi were chosen: • Grewal [4], which is based on the correlations by Andeen and Glicksman Bansal [3], utilizes the boundary layer approach. It considers horizontal tu and takes the pitch between the tubes into account: m t bPDF Image | Heat Transfer between Finned Tubes
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