Chapter 1, Problem 1.68P

Following the hot vacuum forming of a paper-pulp mixture, the product, an egg carton, is transported on a conveyor for 18 s toward the entrance of a gas-fired oven where it is dried to a desired final water content. Very little water evaporates during the travel time. So, to increase the productivity of the line, it is proposed that a bank of infrared radiation heaters, which provide a uniform radiant flux of $5000{\text{W/m}}^{\text{2}},$ be installed over the conveyor. The carton has an exposed area of $0.0625{\text{m}}^{\text{2}}$ and a mass of 0.220 kg, $75\%$ of which is water after the forming process.

The chief engineer of your plant will approve the purchase of the heaters if they can reduce the water content by $10\%$ of the total mass. Would you recommend the purchase? Assume the heat of vaporization of water is $h_{fg}=2400\text{kJ/kg}.$