Lasagna pasta (wide flat noodles 0.3 cm in thickness) is produced industrially by continuously extruding well-mixed dough to form a 10 cm wide ribbon. The ribbon emerges from the extruder with a water content of 0.05 g/cm³ and passes through a tunnel drier at a velocity of 0.5 cm/s. Dry air at 1 atm absolute pressure and 300 K flows in the drier at a high flow rate to reduce the average moisture content of the pasta to 20% of the initial value. After leaving the drier, the lasagna ribbon is cut to length for packaging. The distribution coefficient of water over the pasta at equilibrium is measured and found to be = 4,000 defined as the concentration of water in the pasta divided by the concentration of water vapor in air. The diffusivity of water in the pasta is estimated to be 2.2 ×

10⁻⁵ cm²/s. The average mass transfer coefficient at the past-air interface is 1.2 cm/s.

(a) Sketch the lasagna as it flows into the drier and write the differential material balance equation and initial and boundary conditions needed to determine the required length of the drier assuming that both internal and external mass transfer resistances are important and if only the external resistance is considered.

(b) Calculate the length of the tunnel drier required if external mass transfer is assumed to be controlling.

(c) Calculate the length of the tunnel drier required if internal mass transfer is assumed to be controlling.

(d) Calculate the length of the tunnel drier required if both internal and external resistances are considered.

(e) Calculate the concentration of water in the centerline of the lasagna and at its surface when it emerges from the drier, considering both internal and external mass transfer resistances. the length of the tunnel drier required if internal mass transfer is assumed to be controlling.

(d) Calculate the length of the tunnel drier required if both internal and external resistances are considered.