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Referring to Tables 5-7 and 5-8, the Reynolds number for ethanol vapor flow (ReD,eth,v) through the channels is 2,130, the absolute roughness of the channel surface (e) is estimated to be 1.5 μm, and the hydraulic diameter of the channels (Dh) is 0.761 mm. The Churchill friction factor (fchurch) is therefore found to be 0.03. With an ethanol mass flux of 30.9 kg m-2 s-1, an ethanol density of 2.43 kg m-3, and a hydraulic diameter of 0.761 mm, the pressure drop per unit length for ethanol through the single-phase portion of the condenser is 7.86 kPa m-1. The required length of the first section of the condenser is found using the formulas for each area in equation (5.28): A N NN πDL (5.52) s,in s,tube ch t row h cond,sp 2N N t row w t L (5.53) t t cond,sp A From Table 5-9, the number of channels per tube (Nch) is 17, the number of tubes per row (Nt) is 30, and the number of rows (Nrow) is 2. With a tube width of 20.4 mm and a tube thickness of 1.5 mm, the required inner tube surface area is 0.088 m2 and the required outer tube surface area is 0.095 m2. Therefore, the required length of the single-phase section of the condenser is 0.037 m. Note that the fin efficiency of the areas between the microchannels has been neglected here. This can be justified by calculating the fin efficiency (equation (5.33) and equation (5.34)) and treating the area between the microchannels as a rectangular fin with thickness equal to 0.41 mm (minimum distance between microchannels) and fin height equal to the hydraulic radius of 0.38 mm. Taking the thermal conductivity of the fin as 240 W m-1 K-1 and using the single-phase ethanol heat transfer coefficient of 110 W m-2 K-1, the fin efficiency is 99.99%. For the two-phase section of the condenser, the ethanol heat transfer coefficient is higher at 3,650 W m-2 K-1 which gives a fin efficiency of 99.64%. The fin efficiencies are very close to 100% and can therefore be neglected without significantly affecting the results. 96PDF Image | WASTE HEAT RECOVERY FROM A HIGH TEMPERATURE DIESEL ENGINE
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