Green coffee beans, after harvesting, are dried and roasted in a fluidized-bed roaster. This type of roaster has hot air, typically at 250°C, and the air blows through a screen or perforated plate above which the beans float in an agitated suspension (fluidization) in the hot air as they get heated. As the beans heat up, they get dried and roasted to the required condition. They are typically flat ellipsoids that have an average volume of 44 mm³ and an average surface area of 66 mm². For a flavorful and aromatic medium roast, the beans have to be heated to 200°C. If the beans are initially at 22°C at the time they enter the roaster and the convective heat transfer coefficient of the heating air is 20 W/m² • K, determine the required roasting time. Coffee bean thermophysical properties are k = 0.184 W/m•K, c = 2.564 kJ/kg•K, and p = 552 kg/m³.