Green coffee beans (rho=552 kg/m3, k = 0.184 W/m·K, c = 2.56 kJ/kg·K) are dried and roasted in a hot-air stream after harvesting. The hot air is typically at 250ºC, and the convection coefficient is 20 W/m2K. Beans are typically flat ellipsoids with average volume of 44 mm3 and average surface area of 66 mm2. For a flavorful and aromatic medium roast, the beans (initially at 22ºC) must be heated to 200ºC. Determine the required roasting time.