A double-pipe heat exchanger consists of a length of 1-in, schedule-40 pipe inside an equal length of 3-in, schedule-40 pipe.

Water flows at a velocity of 1.393 m/s in the annular region between the pipes and enters the heat exchanger at 30°C. Oil flows in the inner pipe at an average velocity of 1 m/s and enters at 100°C. The water and oil flow countercurrently. Following are the properties of the water and oil:

Determine how long the pipe lengths must be in order for the oil to leave the exchanger at 50°C. You may assume that both fluids are clean and that there is no fouling or tube wall resistances.

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Water @30°C r = 998 kg/m³ Oil @100°C r = 690 kg/m³ Cp=4216 J/kg/K k = 0.60 W/m/K m = 700 × 106 kg/m/sm= 511 × 106 kg/m/sm= 945 × 106 kg/m/s = 2421 J/kg/K Oil @50°C r = 727 kg/m³ Cp = 2201 J/kg/K k = 0.1295 W/m/K Cp k= 0.1179 W/m/K