Closure to Discussion of “Heat Transfer in Rotating Rectangular Cooling Channels (AR=4) With Dimples” (2003, ASME J. Turbomach., 125, p. 564)

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The authors appreciate Dr. Ligrani’s comment on the paper. The discrepancy of heat transfer enhancement on the dimpled surface reported by different investigators might be due to the use of different measurement technique for the data taken and reduction. In addition to the aforementioned studies, for example, Zhou and Acharya [15] reported that the heat transfer enhancements of the dimpled surface for nonrotation could be about 1.5–2 times the smooth channel values for a dimple depth to print diameter ratio of 0.29 by using the naphthalene sublimation mass-transfer technique. Moon and Lau 22 showed that the dimpled surface heat transfer for nonrotation enhanced about 1.6–1.8 times the smooth-channel values for the dimple depth to print diameter ratios around 0.2–0.23 by using the standard aluminum plate with heaters and thermocouples. These heat transfer enhancement ratios are close to the present study’s values for nonrotation by using the standard copper plate with heaters and thermocouples. But they are lower than the aforementioned values reported by Chyu et al. [12] using the transient liquid crystal technique, Moon et al. [13] using the transient liquid crystal technique, and Burgess et al. [21] using the IR camera technique. It is likely that using different measurement technique and data analysis could produce 10–20% different heat transfer enhancement values for turbulent channel flow through such a complex dimpled surface. The present study used the traditional copper plate with heaters and thermocouples technique. The purpose was to obtain the regionally averaged heat transfer coefficient per copper plate. According to Fig. 3 in the paper, each copper plate is 2.54 cm by 2.54 cm facing to the cooling flow and with 0.3175-cm thickness. The estimated maximum Biot number of the copper plate is around 0.0022 for the highest heat transfer coefficient case at Re=40,000 of the present study. This means that the temperature gradient within the copper plate is small as expected by using this kind of standard measurement technique. On the other hand, in order to produce 20% heat-transfer coefficient’s discrepancy in the copper plate, it requires 7°C of temperature gradient within each copper plate. This unlikely would happen in the present test condition (Tw=67°C,Tb=32°C). In addition, the high-conductivity copper plate with dimples represents the true span-averaged heat transfer coefficient including the potential end-wall effect from the channel smooth-side walls. For example, the potential smooth-side wall effect on the span-averaged heat transfer coefficient could not be included by viewing only the central 5-dimple area using the IR camera technique shown in Fig. 2 by Mahmood et al. [14]. The central 5-dimple area only might potentially produce higher heat transfer enhancement than the truly span-averaged values including the potential smooth end-wall effect. To solve the issue, the authors plan to further investigate this topic. Again, the authors do appreciate Dr. Ligrani’s insightful comment on the important dimple cooling technology for turbine blade cooling designs.