The mold used in an injection molding process con-sists of

Chapter 8, Problem 8.105

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The mold used in an injection molding process con-sists of a top half and a bottom half. Each half is60 mm?60 mm?20 mm and is constructed of metal(??7800 kg/m3, c?450 J/kg?K). The cold mold(100C) is to be heated to 200C with pressurizedwater (available at 275C and a total flow rate of0.02 kg/s) prior to injecting the thermoplastic material.The injection takes only a fraction of a second, and thehot mold (200C) is subsequently cooled with coldwater (available at 25C and a total flow rate of0.02 kg/s) prior to ejecting the molded part. After partejection, which also takes a fraction of a second, theprocess is repeated. a) In conventional mold design, straight cooling(heating) passages are bored through the mold in alocation where the passages will not interfere withthe molded part. Determine the initial heating rateand the initial cooling rate of the mold when five5-mm-diameter, 60-mm-long passages are boredin each half of the mold (10 passages total). Thevelocity distribution of the water is fully devel-oped at the entrance of each passage in the hot (orcold) mold.(b) New additive manufacturing processes, known as selective freeform fabrication, or SFF, are usedto construct molds that are configured with con-formal cooling passages.Consider the same moldas before, but now a 5-mm- diameter, coiled, con-formal cooling passage is designed within eachhalf of the SFF-manufactured mold. Each of thetwo coiled passages has N?2 turns. The coiledpassage does not interfere with the molded part.The conformal channels have a coil diameterC?50 mm. The total water flow remains thesame as in part (a) (0.01 kg/s per coil). Determinethe initial heating rate and the initial cooling rateof the mold.(c) Compare the surface areas of the conventional andconformal cooling passages. Compare the rate atwhich the mold temperature changes for moldsconfigured with the conventional and conformalheating and cooling passages. Which cooling pas-sage, conventional or conformal, will enable pro-duction of more parts per day? Neglect the pres-ence of the thermoplastic material