The mold used in an injection molding process consists of a top half and a bottom half. Each half is 60 mm × 60 mm × 20 mm and is constructed of metal (ρ = 7800 kg/m³, c = 450 J/kg. K). The cold mold (100°C) is to be heated to 200°C with pressurized water (available at 275°C and a total flow rate of 0.02 kg/s) prior to injecting the thermoplastic material. The injection takes only a fraction of a second, and the hot mold (200°C) is subsequently cooled with cold water (available at 25°C and a total flow rate of 0.02 kg/s) prior to ejecting the molded part. After part ejection, which also takes a fraction of a second, the process is repeated.

      (a) In conventional mold design, straight cooling (heating) passages are bored through the mold in a location where the passages will not interfere with the molded part. Determine the initial heating rate and the initial cooling rate of the mold when five 5-mm-diameter, 60-mm-long passages are bored in each half of the mold (10 passages total), The velocity distribution of the water is fully developed at the entrance of each passage in the hot (or cold) mold.

(b) New additive manufacturing processes, known as selective freeform fabrication, or SFF, are used to construct molds that are configured with conformal cooling passages. Consider the same mold as before, but now a 5-mm-diameter, coiled, conformal cooling passage is designed within each half of the SFF-manufactured mold. Each of the two coiled passages has N = 2 turns. The coiled passage does not interfere with the molded part. The conformal channels have a coil diameter C = 50 mm. The total water flow remains the same as in part (a) (0.01 kg/s per coil). Determine the initial heating rate and the initial cooling rate of the mold. 

  (c) Compare the surface areas of the conventional and conformal cooling passages. Compare the rate at which the mold temperature changes for molds configured with the conventional and conformal heating and cooling passages. Which cooling passage, conventional or conformal, will enable production of more parts per day? Neglect the presence of the thermoplastic material.